From 9b34cd1db5bdbdfa73269d319e3e91f1e43d534d Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 17:55:42 -0500 Subject: [PATCH 01/23] Changed a comment in rowerdynamics.m (just for testing the branching in github) --- model/makerowerdynamics.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/model/makerowerdynamics.m b/model/makerowerdynamics.m index 48bd8bc..aaafa30 100644 --- a/model/makerowerdynamics.m +++ b/model/makerowerdynamics.m @@ -53,7 +53,7 @@ fprintf(fid2,'%% par.Kcrm %% cable stiffness parameter \n'); fprintf(fid2,'%%\n'); fprintf(fid2,'%% Output:\n'); - fprintf(fid2,'%% f...................(6x1) 5 joint torques (Nm) and cable force (N)\n'); + fprintf(fid2,'%% f...................(6x1) 5 joint torques and cable force\n'); fprintf(fid2,'%% df_dq...............(6x5) Jacobian matrix df/dq\n'); fprintf(fid2,'%% df_dqd..............(6x5) Jacobian matrix df/dqdot\n'); fprintf(fid2,'%% df_dqdd.............(6x5) Jacobian matrix df/dqdotdot\n'); From 1940775c142acfe692f51e051cd050e015e31c89 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 18:29:38 -0500 Subject: [PATCH 02/23] rowerdynamics.m deleted from repository This file must be built from source --- model/dynfun.m | 22 ++++++++++++++-------- model/makerowerdynamics.m | 16 +++++++++------- model/rowerdynamics.al | 31 +++++++++++++++++++------------ 3 files changed, 42 insertions(+), 27 deletions(-) diff --git a/model/dynfun.m b/model/dynfun.m index 3e641e6..ba97f63 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -1,8 +1,8 @@ - function [f, dfdx, dfdxdot, dfdu,L , dLdq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix - % the 13 dynamics equations of the system, in the form + function [f, dfdx, dfdxdot, dfdu, L, dLdq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix + % The 13 dynamics equations of the system, in the form % f(x, dx/dt, u) = 0 - % where x contains the 13 state variables and u are the 5 torques - % p contains the 5 model parameters + % where x contains the 13 state variables and u are the 5 joint torques + % This function also outputs the wrist-sprocket distance L and related Jacobian global model @@ -11,7 +11,10 @@ m = model.parameters.m ; K = model.parameters.K; % shock cord stiffness L0 = model.parameters.L0; % the wrist-sprocket distance when shock cord has zero force + + % we think that Kcrm=0 and Bcrm=large will work well Kcrm = model.parameters.Kcrm; % chain rachet mechanism stiffness + Bcrm = model.parameters.Bcrm; % chain rachet mechanism damping f = zeros(13,1); @@ -50,10 +53,11 @@ dfdxdot(8:12, 8:12) = dz_dqdd(1:5,1:5); dfdu(8:12, :) = -speye(5); - % flywheel dynamics, flywheel sees cable force, minus the shock cord - % force + % extract the wrist-sprocket distance and its velocity from z L = z(6); + Ldot = z(7); dLdq = dz_dq(6,:); + dLdotdq = dz_dq(7,:); % dynamics of the flywheel % m*a - Fdamping - Fcrm = 0 @@ -68,12 +72,14 @@ %use epsilon for non-linear spring to remove the non-linearity in the %derivatives epsilon = 0.000001; - Fsc= Kcrm * (L - x(1) ); + Fsc= Kcrm * (L - x(1)) + Bcrm * (Ldot - x(7)); Fcrm = (Fsc + sqrt(Fsc^2+epsilon^2))/2 ; dFcrmdFsc = (1+Fsc/sqrt(Fsc^2+epsilon^2))/2; f(13) = x(13) - Fcrm - K*(L - L0); dfdx(13,13) = 1; dfdx(13,1) = Kcrm*dFcrmdFsc; - dfdx(13,2:6) = -(dFcrmdFsc*Kcrm + K)*dLdq; + dfdx(13,7) = Bcrm*dFcrmdFsc; + dfdx(13,2:6) = -(dFcrmdFsc*Kcrm + K)*dLdq - dFcrmdFsc*Bcrm*dLdotdq; + dfdx(13,8:12) = -dFcrmdFsc*Bcrm*dLdq; % because dLdot/dqdot = dL/dq end \ No newline at end of file diff --git a/model/makerowerdynamics.m b/model/makerowerdynamics.m index aaafa30..223cc8d 100644 --- a/model/makerowerdynamics.m +++ b/model/makerowerdynamics.m @@ -33,13 +33,13 @@ % write function header fprintf(fid2,'%% This file was generated by makerowerdynamics.m on %s\n', datetime); - fprintf(fid2,'function [f, df_dq, df_dqd, df_dqdd, df_dxfw, stick] = rowerdynamics(q,qd,qdd,xfw,par);\n'); + fprintf(fid2,'function [f, df_dq, df_dqd, df_dqdd, df_dFc, L, dL_dq, dLdot_dq, stick] = rowerdynamics(q,qd,qdd,Fc,par);\n'); fprintf(fid2,'%%\n'); fprintf(fid2,'%% Input:\n'); fprintf(fid2,'%% q...................(5x1) generalized coordinates (rad)\n'); fprintf(fid2,'%% qd..................(5x1) generalized velocities (rad/s)\n'); fprintf(fid2,'%% qdd.................(5x1) generalized accelerations (rad/s^2)\n'); - fprintf(fid2,'%% xfw.................(scalar) flywheel position (m)\n'); + fprintf(fid2,'%% Fc..................(scalar) cable force (N)\n'); fprintf(fid2,'%% par.................(structure) model parameters:\n'); fprintf(fid2,'%% par.TrunkMass, par.TrunkInertia, par.TrunkCM, par.TrunkLen\n'); fprintf(fid2,'%% par.ThighMass, par.ThighInertia, par.ThighCM, par.ThighLen\n'); @@ -49,15 +49,17 @@ fprintf(fid2,'%% par.Xankle, par.Yankle\n'); fprintf(fid2,'%% par.Xsprocket, par.Ysprocket %% point where the cable comes out of the machine\n'); fprintf(fid2,'%% par.a, par.b %% seat path is Y = a*X + b\n'); - fprintf(fid2,'%% par.K, par.C %% seat stiffness and damping\n'); - fprintf(fid2,'%% par.Kcrm %% cable stiffness parameter \n'); + fprintf(fid2,'%% par__Kseat, par__Cseat %% seat stiffness and damping\n'); fprintf(fid2,'%%\n'); fprintf(fid2,'%% Output:\n'); - fprintf(fid2,'%% f...................(6x1) 5 joint torques and cable force\n'); + fprintf(fid2,'%% f...................(6x1) 5 joint torques\n'); fprintf(fid2,'%% df_dq...............(6x5) Jacobian matrix df/dq\n'); fprintf(fid2,'%% df_dqd..............(6x5) Jacobian matrix df/dqdot\n'); fprintf(fid2,'%% df_dqdd.............(6x5) Jacobian matrix df/dqdotdot\n'); - fprintf(fid2,'%% df_dxfw.............(6x1) Jacobian matrix df/dxfw\n'); + fprintf(fid2,'%% df_dFc..............(6x1) Jacobian matrix df/dFc\n'); + fprintf(fid2,'%% L...................(scalar) wrist-sprocket distance (m)\n'); + fprintf(fid2,'%% dL_dq...............(1x6) Jacobian matrix dL/dq\n'); + fprintf(fid2,'%% dLdot_dq............(1x6) Jacobian matrix dLdot/dq\n'); fprintf(fid2,'%% stick...............(7x2) x,y of ankle,knee,hip,shoulder,elbow,wrist,sprocket\n'); fprintf(fid2,'%%\n'); @@ -97,7 +99,7 @@ fprintf(fid2,' df_dq = sparse(df_dq);\n'); fprintf(fid2,' df_dqd = sparse(df_dqd);\n'); fprintf(fid2,' df_dqdd = sparse(df_dqdd);\n'); - fprintf(fid2,' df_dxfw = sparse(df_dxfw);\n'); + fprintf(fid2,' df_dFc = sparse(df_dFc);\n'); fprintf(fid2,'\nend \n'); fclose(fid2); diff --git a/model/rowerdynamics.al b/model/rowerdynamics.al index 057c5ad..df02640 100644 --- a/model/rowerdynamics.al +++ b/model/rowerdynamics.al @@ -2,8 +2,13 @@ % % Autolev code to compute inverse dynamics of the rower model, including the cable model % +% The matlab function makerowerdynamics.m will transform this into a Matlab function that +% looks like this: +% +% function [f, df_dq, df_dqd, df_dqdd, df_dFc, stick] = rowerdynamics(q,qd,qdd,Fc,par) +% % Author: Ton van den Bogert -% Last revised: 12/21/2016 +% Last revised: 2/15/2018 PAUSE 0 AUTOZ ON @@ -36,10 +41,10 @@ Constants par__ForearmMass, par__ForearmInertia, par__ForearmCM, par__ForearmLen Constants par__Xankle, par__Yankle Constants par__Xsprocket, par__Ysprocket % point where the cable comes out of the machine Constants par__a, par__b % seat path is Y = a*X + b -Constants par__K, par__C % seat stiffness and damping -Constants par__Kcrm % cable stiffness parameter +Constants par__Kseat, par__Cseat % seat stiffness and damping +Constants par__Kcrm, par__K % cable stiffness and return spring stiffness Constants par__g % gravity -Constants xfw % flywheel position +Constants Fc % cable force (input from Matlab dynamics function) %---------------------------------- % Define bodies and points @@ -133,17 +138,17 @@ A2pts(Ground, Forearm, Elbow, ForearmO); gravity(-par__g*Ground2>) PP> = (par__a*Ground1> - Ground2>) / sqrt(1+par__a*par__a) % a unit vector that is perpendicular to the line d = dot(P_GroundO_Hip> - par__b*Ground2>,PP>) % perpendicular distance from Hip to the line -force_Hip> += -par__K*d*PP> - par__C*dt(d)*PP> % spring and damper force perpendicular to the line and +force_Hip> += -par__Kseat*d*PP> - par__Cseat*dt(d)*PP> % spring and damper force perpendicular to the line and %------------------------------------------------------- % compute wrist position and cable force %------------------------------------------------------- P_Elbow_Wrist> = par__ForearmLen*Forearm1> V2pts(Ground, Forearm, Elbow, Wrist); % velocity is needed for equations of motion -cable> = P_GroundO_Wrist> - Vector(Ground,par__Xsprocket,par__Ysprocket,0) % vector from sprocket to wrist -Lc = mag(cable>) - xfw; % distance between wrist and flywheel position -Fc = par__K * (Lc + abs(Lc))/2 % cable force is always positive -force_Wrist> += -Fc * unitvec(cable>) % force vector acting on the wrist +cable> = Vector(Ground,par__Xsprocket,par__Ysprocket,0) - P_GroundO_Wrist> % vector from wrist to sprocket +L = mag(cable>); % distance between wrist and sprocket +Ldot = dt(L); +force_Wrist> += Fc * unitvec(cable>) % force vector acting on the wrist %---------------------------------------------------------- % x and y coordinates of the joints and sprocket, stored in a 6x2 matrix @@ -159,7 +164,7 @@ stick = [ par__Xankle, par__Yankle ; & %---------------------------------------------------------------- % generate the outputs %---------------------------------------------------------------- -f = [-fr()-frstar() ; Fc] % the five torques (Nm) and the cable force (N) +f = -fr()-frstar() % the five torques % vectors needed to define Jacobian matrices q = [q1, q2, q3, q4, q5] @@ -170,9 +175,11 @@ qdd = [q1'', q2'', q3'', q4'', q5''] df_dq = ZEE(D(f,q)) df_dqd = ZEE(D(f,qd)) df_dqdd = ZEE(D(f,qdd)) -df_dxfw = ZEE(D(f,xfw)) +df_dFc = ZEE(D(f,Fc)) +dL_dq = ZEE(D(L,q)) +dLdot_dq = ZEE(D(Ldot,q)) -Encode f, df_dq, df_dqd, df_dqdd, df_dxfw, stick +Encode f, df_dq, df_dqd, df_dqdd, df_dFc, L, dL_dq, dLdot_dq, stick Code Algebraic() tmp.m EXIT From 08a096c7dbccd33fee66e015c529b089c528ebf4 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 18:54:58 -0500 Subject: [PATCH 03/23] ignoring .asv files and tmp.m --- .gitignore | 3 +++ model/dynfun.m | 69 +++++++++++++++++++++----------------------------- model/mytest.m | 33 +++++++----------------- 3 files changed, 41 insertions(+), 64 deletions(-) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..406607c --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +model/rowerdynamics.m +*.asv +model/tmp.m \ No newline at end of file diff --git a/model/dynfun.m b/model/dynfun.m index ba97f63..1a7d9af 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -6,25 +6,25 @@ global model - % copy parameter values into variables with meaningful + % copy parameter values into variables with shorter names c = model.parameters.C; m = model.parameters.m ; K = model.parameters.K; % shock cord stiffness L0 = model.parameters.L0; % the wrist-sprocket distance when shock cord has zero force - % we think that Kcrm=0 and Bcrm=large will work well + % Kcrm is probably no longer needed (remove it when confirmed) Kcrm = model.parameters.Kcrm; % chain rachet mechanism stiffness Bcrm = model.parameters.Bcrm; % chain rachet mechanism damping - f = zeros(13,1); - + % initialize the matrices + f = zeros(13,1); dfdx = spalloc(13,13,75); dfdxdot = spalloc(13,13,32); dfdu = spalloc(13,5,5); % x = [x_fw, q1 ...q5, v_fw, qd1...qd5, F] - % velocities are derivative of positions (2:01:00 recording 4) - f(1:6) = xdot(1:6) - x(7:12); %velocities + % velocities are derivative of positions + f(1:6) = xdot(1:6) - x(7:12); dfdx(1:6, 7:12) = -speye(6); dfdxdot(1:6, 1:6) = speye(6); @@ -33,32 +33,15 @@ qd = x(8:12); qdd = xdot(8:12); % rowerdynamics function generated by Autolev computes 5 torques - % using inverse dynamics and also 1 cable force using the - % cable ratchet mechanism model (z is a 6x1 output) - % 13 equations to model the dynamics. The - % first 6 (multibody dynamics and cable force) - [z, dz_dq, dz_dqd, dz_dqdd, dz_dFc] = rowerdynamics(q,qd,qdd,x(13),model.parameters);% inverse dynamics so gives us the z(torques) - % z has 6 elements, the first 5s are the torques, the 6th one is the - % wrist to sprocket distance, which depends on the q which is x(2:6) and - - %that we need to produce this motion with that force being applied to the - %wrist and then we compare those torques (motion trajectory) to the torques that we have in - %our trajectory (torque trajectory) and they have to be equal. - - - f(8:12) = z(1:5) - u; % f is in Nm - dfdx(8:12, 2:6) = dz_dq(1:5,1:5); - dfdx(8:12, 8:12) = dz_dqd(1:5,1:5); - dfdx(8:12, 13) = dz_dFc(1:5); - dfdxdot(8:12, 8:12) = dz_dqdd(1:5,1:5); + % using inverse dynamics and also the wrist-sprocket length L + [z, dz_dq, dz_dqd, dz_dqdd, dz_dFc, L, dL_dq, dLdot_dq] = rowerdynamics(q,qd,qdd,x(13),model.parameters);% inverse dynamics so gives us the z(torques) + f(8:12) = z - u; + dfdx(8:12, 2:6) = dz_dq; + dfdx(8:12, 8:12) = dz_dqd; + dfdx(8:12, 13) = dz_dFc; + dfdxdot(8:12, 8:12) = dz_dqdd; dfdu(8:12, :) = -speye(5); - % extract the wrist-sprocket distance and its velocity from z - L = z(6); - Ldot = z(7); - dLdq = dz_dq(6,:); - dLdotdq = dz_dq(7,:); - % dynamics of the flywheel % m*a - Fdamping - Fcrm = 0 % or m*a - Fdamping - (Ftotal - Fshockcord) = 0 @@ -66,20 +49,26 @@ dfdx(7,7) = 2*c*abs(x(7)); dfdx(7,13) = -1; dfdxdot(7,7) = m; - dfdx(7, 2:6) = K*dLdq; + dfdx(7, 2:6) = K*dL_dq; - %cable force must be equal to cable ratchet force + shock cord force - %use epsilon for non-linear spring to remove the non-linearity in the - %derivatives + % ratchet mechanism force is a function of the wrist-sprocket distance + % L and flywheel position x(1) + + % start with a linear function + F = Kcrm * (L - x(1)) + Bcrm * (Ldot - x(7)); + + % a nonlinear transformation to change negative forces to zero epsilon = 0.000001; - Fsc= Kcrm * (L - x(1)) + Bcrm * (Ldot - x(7)); - Fcrm = (Fsc + sqrt(Fsc^2+epsilon^2))/2 ; + Fcrm = (Fsc + sqrt(Fsc^2 + epsilon^2) )/2; dFcrmdFsc = (1+Fsc/sqrt(Fsc^2+epsilon^2))/2; + + % this says that the force on the wrist is the sum of flywheel force + % and shock cord f(13) = x(13) - Fcrm - K*(L - L0); dfdx(13,13) = 1; - dfdx(13,1) = Kcrm*dFcrmdFsc; - dfdx(13,7) = Bcrm*dFcrmdFsc; - dfdx(13,2:6) = -(dFcrmdFsc*Kcrm + K)*dLdq - dFcrmdFsc*Bcrm*dLdotdq; - dfdx(13,8:12) = -dFcrmdFsc*Bcrm*dLdq; % because dLdot/dqdot = dL/dq + dfdx(13,1) = Kcrm * dFcrmdFsc; + dfdx(13,7) = Bcrm * dFcrmdFsc; + dfdx(13,2:6) = -(dFcrmdFsc * Kcrm + K) * dLdq - dFcrmdFsc * Bcrm * dLdotdq; + dfdx(13,8:12) = -dFcrmdFsc * Bcrm * dLdq; % because dLdot/dqdot = dL/dq end \ No newline at end of file diff --git a/model/mytest.m b/model/mytest.m index cd63d5d..c74b7e1 100644 --- a/model/mytest.m +++ b/model/mytest.m @@ -14,7 +14,7 @@ fixed_yp0 = []; T = 0:0.01:2.0; % simulation time [y0,yp0] = decic(@dyn,T(1),y0,fixed_y0,yp0,fixed_yp0); % find consistent initial conditions - [tt,yy,L] = ode15i(@dyn, T, y0,yp0); % simulate using ode15i + [tt,yy] = ode15i(@dyn, T, y0,yp0); % simulate using ode15i % make the AVI file disp('making AVI file...') @@ -54,13 +54,7 @@ %======================================================================= function f = dyn(t,y, ydot) -% dynfun(t,y,ydot) -% dynamics of the rower model, in implicit form f(y,ydot,t) = 0 -% where y is (q,qdot) - global model - f = zeros(10,1); % f will be a 10x1 matrix - - % extract q, qdot, qdotdot from y and ydot + % extract q, qdot from y q = y(2:6); qd = y(8:12); @@ -71,8 +65,6 @@ % simulation 3, use a leaning back setpoint, to make the human pull % simulation 4, use tstart = 0.5, model should fall down and come back up qsetpoint = [152.5304 ; 18.1593; 114.5404 ; -23.0064; 102.3893] * pi/180; - - tstart = 0.4; if t < tstart kp = 0; @@ -82,21 +74,14 @@ kd = 50; end tau = -kp*(q-qsetpoint) - kd*qd; - [f,~,~,~,L] = dynfun(y,ydot,tau); -% % equations 1-5 of the implicit dynamics: derivative of q must be equal to qdot -% f(1:5) = ydot(1:5) - y(6:10); -% -% % equations 6-10: inverse dynamic torque must be equal to the applied torque -% xfw = 100; % move the flywheel far to the right, so no cable force will be generated -% ff = rowerdynamics(q,qd,qdd,xfw,model.parameters); % do the inverse dynamic calculation -% f(6:10) = tau - ff(1:5); % first 5 elements of ff are the inverse dynamic torques + + % evaluate the implicit dynamics function + f = dynfun(y,ydot,tau); -% if toc > 1.0 -% fprintf('simulating... t = %8.3f\n',t); -% tic -% end + if toc > 1.0 + fprintf('simulating... t = %8.3f\n',t); + tic + end - - end %======================================================================= \ No newline at end of file From 8805dab73a74b3f199c58f398a88b99f57b7c758 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 18:55:26 -0500 Subject: [PATCH 04/23] ignoring rowerdynamics.m --- .gitignore | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/.gitignore b/.gitignore index 406607c..e08a77e 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ model/rowerdynamics.m *.asv -model/tmp.m \ No newline at end of file +model/tmp.m +model/rowerdynamics.m \ No newline at end of file From e059b428cce4202789a28d2053c1c2a7387bc2f2 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 19:01:50 -0500 Subject: [PATCH 05/23] Update mytest.m --- model/mytest.m | 57 +++++++++++++++++++++++++------------------------- 1 file changed, 28 insertions(+), 29 deletions(-) diff --git a/model/mytest.m b/model/mytest.m index c74b7e1..f4c9069 100644 --- a/model/mytest.m +++ b/model/mytest.m @@ -1,11 +1,11 @@ - function mytest -% runs a forward dynamic simulation of the rower model to test the dynamics code - global model +function mytest + % runs a forward dynamic simulation of the rower model to test the dynamics code + global model [~,~,~, model.parameters] = datainterp2; - % choose a suitable initial condition: realistic joint angles, and choose flywheel position y(1) - % to be equal to the L that comes from these joint angles - % and make all velocities zero + % choose a suitable initial condition: realistic joint angles, and choose flywheel position y(1) + % to be equal to the L that comes from these joint angles + % and make all velocities zero y0 = [ 0.1 ;[86.6804 ; 121.4658 ; 60.3518 ; 61.3895 ; 12.4060] * pi/180; 0 ; 0; 0; 0; 0;0; 0]; % initial condition () yp0 = zeros(13,1); % initial guess for state derivatives at t=0 %fixed_y0 = [0 1 1 1 1 1 1 0 0 0 0 0 0]; @@ -24,7 +24,7 @@ figure(1); animate(q,model.parameters); - % make plots + % make plots figure(2) plot(tt, q*180/pi, 'LineWidth',2); legend('q1','q2','q3','q4','q5','f'); @@ -48,40 +48,39 @@ xlabel('time (s)','fontweight','bold','fontsize',10); ylabel('fwvelo (m)','fontweight','bold','fontsize',10); title('fwvelo','fontweight','bold','fontsize',10) - end %======================================================================= function f = dyn(t,y, ydot) % extract q, qdot from y - q = y(2:6); - qd = y(8:12); + q = y(2:6); + qd = y(8:12); - % generate joint torques with a PD controller + % generate joint torques with a PD controller % controller is turned on at tstart - % simulation 1: tstart = 10, model should just fall down - % simulation 2, use initial angles as the setpoint, and tstart = 0 - % simulation 3, use a leaning back setpoint, to make the human pull - % simulation 4, use tstart = 0.5, model should fall down and come back up - qsetpoint = [152.5304 ; 18.1593; 114.5404 ; -23.0064; 102.3893] * pi/180; - tstart = 0.4; - if t < tstart - kp = 0; - kd = 0; - else - kp = 600; - kd = 50; - end - tau = -kp*(q-qsetpoint) - kd*qd; + % simulation 1: tstart = 10, model should just fall down + % simulation 2, use initial angles as the setpoint, and tstart = 0 + % simulation 3, use a leaning back setpoint, to make the human pull + % simulation 4, use tstart = 0.5, model should fall down and come back up + qsetpoint = [152.5304 ; 18.1593; 114.5404 ; -23.0064; 102.3893] * pi/180; + tstart = 0.4; + if t < tstart + kp = 0; + kd = 0; + else + kp = 600; + kd = 50; + end + tau = -kp*(q-qsetpoint) - kd*qd; % evaluate the implicit dynamics function - f = dynfun(y,ydot,tau); + f = dynfun(y,ydot,tau); - if toc > 1.0 + if toc > 1.0 fprintf('simulating... t = %8.3f\n',t); tic - end + end end -%======================================================================= \ No newline at end of file +%======================================================================= From ae45331fde3252a77848d89f9ca3b387b632fd66 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 19:21:33 -0500 Subject: [PATCH 06/23] Model with CRM damping is working in forward simulation --- model/animate.m | 2 +- model/dynfun.m | 16 ++++++++++------ model/makerowerdynamics.m | 18 +++++++++--------- model/mytest.m | 11 +++++++---- model/tmp.avi | Bin 0 -> 2376408 bytes tools/bodyangles.m | 5 +++-- tools/datainterp2.m | 8 +------- 7 files changed, 31 insertions(+), 29 deletions(-) create mode 100644 model/tmp.avi diff --git a/model/animate.m b/model/animate.m index ac8350e..86f39fa 100644 --- a/model/animate.m +++ b/model/animate.m @@ -19,7 +19,7 @@ function animate(q, par) for i = 1:nframes % use the rowerdynamics function to get the stick figure % coordinates at frame i - [~,~,~,~,~,s] = rowerdynamics(q(i,:)',qd,qdd,xfw,par); + [~,~,~,~,~,~,~,~,s] = rowerdynamics(q(i,:)',qd,qdd,xfw,par); clf plot(s(:,1),s(:,2),'o-'); hold on diff --git a/model/dynfun.m b/model/dynfun.m index 1a7d9af..7317c9c 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -32,9 +32,13 @@ q = x(2:6); % the five coordinates of the human model qd = x(8:12); qdd = xdot(8:12); + % rowerdynamics function generated by Autolev computes 5 torques % using inverse dynamics and also the wrist-sprocket length L [z, dz_dq, dz_dqd, dz_dqdd, dz_dFc, L, dL_dq, dLdot_dq] = rowerdynamics(q,qd,qdd,x(13),model.parameters);% inverse dynamics so gives us the z(torques) + Ldot = dL_dq * qd; + + % multibody dynamics f(8:12) = z - u; dfdx(8:12, 2:6) = dz_dq; dfdx(8:12, 8:12) = dz_dqd; @@ -59,16 +63,16 @@ % a nonlinear transformation to change negative forces to zero epsilon = 0.000001; - Fcrm = (Fsc + sqrt(Fsc^2 + epsilon^2) )/2; - dFcrmdFsc = (1+Fsc/sqrt(Fsc^2+epsilon^2))/2; + Fcrm = (F + sqrt(F^2 + epsilon^2) )/2; + dFcrm_dF = (1 + F/sqrt(F^2 + epsilon^2))/2; % this says that the force on the wrist is the sum of flywheel force % and shock cord f(13) = x(13) - Fcrm - K*(L - L0); dfdx(13,13) = 1; - dfdx(13,1) = Kcrm * dFcrmdFsc; - dfdx(13,7) = Bcrm * dFcrmdFsc; - dfdx(13,2:6) = -(dFcrmdFsc * Kcrm + K) * dLdq - dFcrmdFsc * Bcrm * dLdotdq; - dfdx(13,8:12) = -dFcrmdFsc * Bcrm * dLdq; % because dLdot/dqdot = dL/dq + dfdx(13,1) = Kcrm * dFcrm_dF; + dfdx(13,7) = Bcrm * dFcrm_dF; + dfdx(13,2:6) = -(dFcrm_dF * Kcrm + K) * dL_dq - dFcrm_dF * Bcrm * dLdot_dq; + dfdx(13,8:12) = -dFcrm_dF * Bcrm * dL_dq; % because dLdot/dqdot = dL/dq end \ No newline at end of file diff --git a/model/makerowerdynamics.m b/model/makerowerdynamics.m index 223cc8d..0b28382 100644 --- a/model/makerowerdynamics.m +++ b/model/makerowerdynamics.m @@ -52,14 +52,14 @@ fprintf(fid2,'%% par__Kseat, par__Cseat %% seat stiffness and damping\n'); fprintf(fid2,'%%\n'); fprintf(fid2,'%% Output:\n'); - fprintf(fid2,'%% f...................(6x1) 5 joint torques\n'); - fprintf(fid2,'%% df_dq...............(6x5) Jacobian matrix df/dq\n'); - fprintf(fid2,'%% df_dqd..............(6x5) Jacobian matrix df/dqdot\n'); - fprintf(fid2,'%% df_dqdd.............(6x5) Jacobian matrix df/dqdotdot\n'); - fprintf(fid2,'%% df_dFc..............(6x1) Jacobian matrix df/dFc\n'); + fprintf(fid2,'%% f...................(5x1) 5 joint torques\n'); + fprintf(fid2,'%% df_dq...............(5x5) Jacobian matrix df/dq\n'); + fprintf(fid2,'%% df_dqd..............(5x5) Jacobian matrix df/dqdot\n'); + fprintf(fid2,'%% df_dqdd.............(5x5) Jacobian matrix df/dqdotdot\n'); + fprintf(fid2,'%% df_dFc..............(5x1) Jacobian matrix df/dFc\n'); fprintf(fid2,'%% L...................(scalar) wrist-sprocket distance (m)\n'); - fprintf(fid2,'%% dL_dq...............(1x6) Jacobian matrix dL/dq\n'); - fprintf(fid2,'%% dLdot_dq............(1x6) Jacobian matrix dLdot/dq\n'); + fprintf(fid2,'%% dL_dq...............(1x5) Jacobian matrix dL/dq\n'); + fprintf(fid2,'%% dLdot_dq............(1x5) Jacobian matrix dLdot/dq\n'); fprintf(fid2,'%% stick...............(7x2) x,y of ankle,knee,hip,shoulder,elbow,wrist,sprocket\n'); fprintf(fid2,'%%\n'); @@ -70,8 +70,8 @@ fprintf(fid2,' q%1dpp = qdd(%1d);\n', i,i); end - % make sure that f comes out as a 6x1 column vector - fprintf(fid2,' f = zeros(6,1); \n'); + % make sure that f comes out as a 5x1 column vector + fprintf(fid2,' f = zeros(5,1); \n'); % copy the necessary parts of C code from fid1 to fid2 copying = 0; diff --git a/model/mytest.m b/model/mytest.m index f4c9069..308f4e5 100644 --- a/model/mytest.m +++ b/model/mytest.m @@ -1,6 +1,9 @@ function mytest % runs a forward dynamic simulation of the rower model to test the dynamics code global model + tic + + addpath('../tools'); [~,~,~, model.parameters] = datainterp2; % choose a suitable initial condition: realistic joint angles, and choose flywheel position y(1) @@ -34,20 +37,20 @@ figure(3) plot(tt, f, 'LineWidth',2); xlabel('time (s)','fontweight','bold','fontsize',10); - ylabel('force (N)','fontweight','bold','fontsize',10); + ylabel('wrist force (N)','fontweight','bold','fontsize',10); title('Force','fontweight','bold','fontsize',10) figure(4) plot(tt, yy(:,1), 'LineWidth',2); xlabel('time (s)','fontweight','bold','fontsize',10); ylabel('fwpos (m)','fontweight','bold','fontsize',10); - title('fwpos','fontweight','bold','fontsize',10) + title('flywheel position','fontweight','bold','fontsize',10) figure(5) plot(tt, yy(:,7), 'LineWidth',2); xlabel('time (s)','fontweight','bold','fontsize',10); - ylabel('fwvelo 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zzPVHTom<7I{q~HyErL-qo-nG&0Hb=&o;S6BqaLHKKFX-E*BKSnGU^_t`BVEj?DbrF zo`l2ap;Oi8T-{I>Ok+th65WXG~`69k964?`9ABn7tuaiXHjjxwPUWBik zM9#<8Pa@0X>nM?@iTn&-hlzX> zUyq5*j<3r^?!nh*BKP6zG?5MQ^_s}$__|HxOZfUtPzU-ya3jIaMhZo&HiB5%U`0U~e2`vM|A#rp#yFT?u;BCp2#1tRC- zeFKq~;r#=V~sV2k%3O zdM|gM2^S%9wL|E{ST3u@ji&iYw&)E$T4_dMC8wSe?;VEc%MY%AiQ59 zas%Es5m^QApNM=I@1uzP5bvjmJO}Tqi0p>Zlc?;eL68Spb4-#1r?+c0Sh4+Uj@&1v>m+(H4$gFrjNn|&?uO#vZyuT#!9=y*a@-w2}#QOy~yzeBoN8tS@ zkvZ``l*o>FKT6~>ye}oP65gK@`4Zlz5_wFC(T@^&C*HRb`4Qf~5?LDWV~Knk?`MhJ zgZH&W-i-IRM81vpxkR3h_q#+sjQ71nuEqObBCFtiFp;m|{Vyq_jAH{Mqh*%|MziClsA*+f>t`)wj$#QSa{ z58?eckxlVFoX9zNKTc$Eye}uR58j^>`5oS;6L}5ZuM;^D@7syYiudnC-iP<`L@vSm zc_Pc>eLazb@&2C3eR!WwWJA2)C-ObK?SaRiY&@#6_1Z^Dl&hh Date: Thu, 15 Feb 2018 19:22:37 -0500 Subject: [PATCH 07/23] Ignoring rowerdynamics.m (again) --- .gitignore | 1 + 1 file changed, 1 insertion(+) diff --git a/.gitignore b/.gitignore index e08a77e..4e2c163 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,5 @@ model/rowerdynamics.m *.asv model/tmp.m +model/rowerdynamics.m model/rowerdynamics.m \ No newline at end of file From 7f47d94775fc77b15417384df52f3fa81fab73e9 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 19:25:06 -0500 Subject: [PATCH 08/23] Extra legend removed in mytest.m --- model/.gitignore | 1 + model/mytest.m | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) create mode 100644 model/.gitignore diff --git a/model/.gitignore b/model/.gitignore new file mode 100644 index 0000000..220653b --- /dev/null +++ b/model/.gitignore @@ -0,0 +1 @@ +/rowerdynamics.m diff --git a/model/mytest.m b/model/mytest.m index 308f4e5..440b7ef 100644 --- a/model/mytest.m +++ b/model/mytest.m @@ -30,7 +30,7 @@ % make plots figure(2) plot(tt, q*180/pi, 'LineWidth',2); - legend('q1','q2','q3','q4','q5','f'); + legend('q1','q2','q3','q4','q5'); xlabel('time (s)','fontweight','bold','fontsize',10); ylabel('angle (deg)','fontweight','bold','fontsize',10); title('Joint Angles','fontweight','bold','fontsize',10) From 60dfc09aef3fb3032d12aa4943beb26cda70a8f6 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Thu, 15 Feb 2018 19:26:52 -0500 Subject: [PATCH 09/23] Adding rowerdynamics again (not everyone has Autolev) --- model/rowerdynamics.m | 976 +++++++++++++++++++++++------------------- 1 file changed, 540 insertions(+), 436 deletions(-) diff --git a/model/rowerdynamics.m b/model/rowerdynamics.m index 5b3480c..12da1ce 100644 --- a/model/rowerdynamics.m +++ b/model/rowerdynamics.m @@ -1,5 +1,5 @@ -% This file was generated by makerowerdynamics.m on 31-May-2017 12:14:36 -function [f, df_dq, df_dqd, df_dqdd, df_dFc, stick] = rowerdynamics(q,qd,qdd,Fc,par); +% This file was generated by makerowerdynamics.m on 15-Feb-2018 19:25:34 +function [f, df_dq, df_dqd, df_dqdd, df_dFc, L, dL_dq, dLdot_dq, stick] = rowerdynamics(q,qd,qdd,Fc,par); % % Input: % q...................(5x1) generalized coordinates (rad) @@ -18,11 +18,14 @@ % par__Kseat, par__Cseat % seat stiffness and damping % % Output: -% f...................(6x1) 5 joint torques (Nm) and the wrist-sprocket distance (m) -% df_dq...............(6x5) Jacobian matrix df/dq -% df_dqd..............(6x5) Jacobian matrix df/dqdot -% df_dqdd.............(6x5) Jacobian matrix df/dqdotdot -% df_dFc.............(6x1) Jacobian matrix df/dFc +% f...................(5x1) 5 joint torques +% df_dq...............(5x5) Jacobian matrix df/dq +% df_dqd..............(5x5) Jacobian matrix df/dqdot +% df_dqdd.............(5x5) Jacobian matrix df/dqdotdot +% df_dFc..............(5x1) Jacobian matrix df/dFc +% L...................(scalar) wrist-sprocket distance (m) +% dL_dq...............(1x5) Jacobian matrix dL/dq +% dLdot_dq............(1x5) Jacobian matrix dLdot/dq % stick...............(7x2) x,y of ankle,knee,hip,shoulder,elbow,wrist,sprocket % q1 = q(1); @@ -40,14 +43,14 @@ q5 = q(5); q5p = qd(5); q5pp = qdd(5); - f = zeros(6,1); + f = zeros(5,1); % Unit conversions Pi = 3.141592653589793; DEGtoRAD = Pi/180.0; RADtoDEG = 180.0/Pi; % Reserve space and initialize matrices - z = zeros(570,1); + z = zeros(678,1); % Evaluate constants z(1) = cos(q1); @@ -175,363 +178,363 @@ z(132) = z(7)*z(128) + z(8)*z(130); z(133) = z(7)*z(129) + z(8)*z(131); L = (par.ForearmLen^2+par.ShankLen^2+par.ThighLen^2+par.TrunkLen^2+par.UpparmLen^2+z(111)^2+z(112)^2+2*par.ForearmLen*par.ShankLen*z(113)+2*par.ForearmLen*par.ThighLen*z(117)+2*par.ForearmLen*par.UpparmLen*z(72)+2*par.ShankLen*par.ThighLen*z(7)+2*par.ShankLen*par.UpparmLen*z(128)+2*par.ThighLen*par.UpparmLen*z(132)+2*par.TrunkLen*z(111)*z(45)+2*par.TrunkLen*z(112)*z(47)-2*par.ForearmLen*par.TrunkLen*z(121)-2*par.ForearmLen*z(111)*z(74)-2*par.ForearmLen*z(112)*z(76)-2*par.ShankLen*par.TrunkLen*z(124)-2*par.ShankLen*z(111)*z(1)-2*par.ShankLen*z(112)*z(2)-2*par.ThighLen*par.TrunkLen*z(23)-2*par.ThighLen*z(111)*z(9)-2*par.ThighLen*z(112)*z(11)-2*par.TrunkLen*par.UpparmLen*z(43)-2*par.UpparmLen*z(111)*z(49)-2*par.UpparmLen*z(112)*z(51))^0.5; - z(136) = par.ForearmLen^2 + par.ShankLen^2 + par.ThighLen^2 + par.TrunkLen^2 + par.UpparmLen^2 + z(111)^2 + z(112)^2; - z(137) = par.ForearmLen*par.ShankLen; - z(138) = par.ForearmLen*par.ThighLen; - z(139) = par.ForearmLen*par.UpparmLen; - z(140) = par.ShankLen*par.ThighLen; - z(141) = par.ShankLen*par.UpparmLen; - z(142) = par.ThighLen*par.UpparmLen; - z(143) = par.TrunkLen*z(111); - z(144) = par.TrunkLen*z(112); - z(145) = par.ForearmLen*par.TrunkLen; - z(146) = par.ForearmLen*z(111); - z(147) = par.ForearmLen*z(112); - z(148) = par.ShankLen*par.TrunkLen; - z(149) = par.ShankLen*z(111); - z(150) = par.ShankLen*z(112); - z(151) = par.ThighLen*par.TrunkLen; - z(152) = par.ThighLen*z(111); - z(153) = par.ThighLen*z(112); - z(154) = par.TrunkLen*par.UpparmLen; - z(155) = par.UpparmLen*z(111); - z(156) = par.UpparmLen*z(112); - z(157) = z(136) + 2*z(137)*z(113) + 2*z(138)*z(117) + 2*z(139)*z(72) + 2*z(140)*z(7) + 2*z(141)*z(128) + 2*z(142)*z(132) + 2*z(143)*z(45) + 2*z(144)*z(47) - 2*z(145)*z(121) - 2*z(146)*z(74) - 2*z(147)*z(76) - 2*z(148)*z(124) - 2*z(149)*z(1) - 2*z(150)*z(2) - 2*z(151)*z(23) - 2*z(152)*z(9) - 2*z(153)*z(11) - 2*z(154)*z(43) - 2*z(155)*z(49) - 2*z(156)*z(51); - z(158) = z(157)^0.5; - z(159) = par.ForearmLen/z(158); - z(160) = z(111)/z(158); - z(161) = z(112)/z(158); - z(162) = par.ShankLen/z(158); - z(163) = par.ThighLen/z(158); - z(164) = par.TrunkLen/z(158); - z(165) = par.UpparmLen/z(158); - z(166) = Fc*z(159); - z(167) = Fc*z(160); - z(168) = Fc*z(161); - z(169) = Fc*z(162); - z(170) = Fc*z(163); - z(171) = Fc*z(164); - z(172) = Fc*z(165); - z(173) = par.ShankCM*z(96); - z(174) = z(73)*z(108)*z(172) + z(74)*z(78)*z(167) + z(75)*z(108)*z(167) + z(76)*z(78)*z(168) + z(77)*z(108)*z(168) + z(78)*z(121)*z(171) + z(108)*z(123)*z(171) + z(9)*z(20)*z(106) + z(11)*z(12)*z(106) - z(173)*z(1) - z(78)*z(166) - z(72)*z(78)*z(172) - z(78)*z(113)*z(169) - z(78)*z(117)*z(170) - z(108)*z(115)*z(169) - z(108)*z(119)*z(170) - z(95)*(z(76)*z(78)+z(77)*z(87)) - z(97)*(z(9)*z(14)+z(11)*z(12)) - z(98)*(z(25)*z(47)+z(32)*z(48)) - z(99)*(z(51)*z(53)+z(52)*z(59)) - z(9)*z(12)*z(105) - z(10)*z(20)*z(105); - z(175) = par.ThighCM*z(97); - z(176) = z(73)*z(109)*z(172) + z(74)*z(79)*z(167) + z(75)*z(109)*z(167) + z(76)*z(79)*z(168) + z(77)*z(109)*z(168) + z(79)*z(121)*z(171) + z(109)*z(123)*z(171) + par.ThighLen*(z(9)*z(106)-z(10)*z(105)) - z(175)*z(9) - z(79)*z(166) - z(72)*z(79)*z(172) - z(79)*z(113)*z(169) - z(79)*z(117)*z(170) - z(109)*z(115)*z(169) - z(109)*z(119)*z(170) - z(95)*(z(76)*z(79)+z(77)*z(88)) - z(98)*(z(26)*z(47)+z(31)*z(48)) - z(99)*(z(51)*z(54)+z(52)*z(60)); - z(177) = z(98)*z(30)*z(48) + z(73)*z(110)*z(172) + z(74)*z(80)*z(167) + z(75)*z(110)*z(167) + z(76)*z(80)*z(168) + z(77)*z(110)*z(168) + z(80)*z(121)*z(171) + z(110)*z(123)*z(171) + z(99)*(z(51)*z(55)-z(52)*z(61)) - z(80)*z(166) - z(72)*z(80)*z(172) - z(80)*z(113)*z(169) - z(80)*z(117)*z(170) - z(110)*z(115)*z(169) - z(110)*z(119)*z(170) - z(95)*(z(76)*z(80)+z(77)*z(89)); - z(178) = par.UpparmCM*z(99); - z(179) = z(73)*z(107)*z(172) + z(74)*z(81)*z(167) + z(75)*z(107)*z(167) + z(76)*z(81)*z(168) + z(77)*z(107)*z(168) + z(81)*z(121)*z(171) + z(107)*z(123)*z(171) - z(178)*z(52) - z(81)*z(166) - z(72)*z(81)*z(172) - z(81)*z(113)*z(169) - z(81)*z(117)*z(170) - z(107)*z(115)*z(169) - z(107)*z(119)*z(170) - z(95)*(z(76)*z(81)+z(77)*z(86)); - z(180) = par.ForearmCM*z(95); - z(181) = -z(180)*z(77) - par.ForearmLen*(z(115)*z(169)+z(119)*z(170)-z(73)*z(172)-z(75)*z(167)-z(77)*z(168)-z(123)*z(171)); - z(182) = z(2)*z(8) - z(1)*z(7); - z(183) = z(10)*z(23) + z(24)*z(182); - z(184) = z(23)*z(182) - z(10)*z(24); - z(185) = -z(9)*z(23) - z(10)*z(24); - z(186) = -z(9)*z(24) - z(11)*z(23); - z(187) = z(45)*z(48) + z(46)*z(183); - z(188) = z(46)^2 + z(48)^2; - z(190) = -z(1)*z(8)*q1p - z(1)*z(8)*q2p - z(2)*z(7)*q1p - z(2)*z(7)*q2p; - z(191) = z(2)*z(8)*q1p + z(2)*z(8)*q2p - z(1)*z(7)*q1p - z(1)*z(7)*q2p; - z(192) = z(10)*z(23)*q3p + z(23)*z(190) + z(24)*z(191) - z(9)*z(24)*q3p; - z(193) = z(1)*z(7)*q1p + z(1)*z(7)*q2p - z(2)*z(8)*q1p - z(2)*z(8)*q2p; - z(194) = z(23)*z(190) - z(9)*z(24)*q3p - z(11)*z(23)*q3p - z(24)*z(193); - z(195) = z(23)*z(191) - z(9)*z(23)*q3p - z(10)*z(24)*q3p - z(24)*z(190); - z(196) = z(1)*z(8)*q1p + z(1)*z(8)*q2p + z(2)*z(7)*q1p + z(2)*z(7)*q2p; - z(197) = z(23)*z(182)*q3p + z(23)*z(191) + z(24)*z(196) - z(10)*z(24)*q3p; - z(198) = z(45)*q1p*z(194) + z(45)*q2p*z(194) + z(46)*q1p*z(197) + z(46)*q2p*z(197) + z(48)*q1p*z(192) + z(48)*q2p*z(192) + z(183)*q1p*z(195) + z(183)*q2p*z(195) + 2*z(46)*q3p*z(195) + 2*z(48)*q3p*z(194); - z(199) = par.TrunkInertia*z(187); - z(200) = par.TrunkInertia*z(188); - z(201) = par.TrunkInertia*z(198); - z(202) = par.ForearmInertia + par.ShankInertia + par.ThighInertia + par.UpparmInertia + par.ShankMass*par.ShankCM^2; - z(203) = z(202) + z(187)*z(199) + par.ForearmMass*(z(78)^2+z(87)^2) + par.ThighMass*(z(12)^2+z(14)^2) + par.TrunkMass*(z(25)^2+z(32)^2) + par.UpparmMass*(z(53)^2+z(59)^2); - z(204) = par.ForearmInertia + par.ThighInertia + par.UpparmInertia; - z(205) = par.ThighCM*par.ThighMass; - z(206) = z(204) + z(205)*z(14) + z(187)*z(199) + par.ForearmMass*(z(78)*z(79)+z(87)*z(88)) + par.TrunkMass*(z(25)*z(26)+z(31)*z(32)) + par.UpparmMass*(z(53)*z(54)+z(59)*z(60)); - z(207) = z(204) + z(187)*z(200) + par.ForearmMass*(z(78)*z(80)+z(87)*z(89)) - par.TrunkMass*z(30)*z(32) - par.UpparmMass*(z(53)*z(55)-z(59)*z(61)); - z(208) = par.ForearmInertia + par.UpparmInertia; - z(209) = par.UpparmCM*par.UpparmMass; - z(210) = z(208) + z(209)*z(59) + par.ForearmMass*(z(78)*z(81)+z(86)*z(87)); - z(211) = par.ForearmCM*par.ForearmMass; - z(212) = par.ForearmInertia + z(211)*z(87); - z(213) = z(187)*z(201) + par.ForearmMass*(z(78)*z(94)+z(87)*z(91)) + par.ThighMass*(z(12)*z(19)+z(14)*z(16)) + par.TrunkMass*(z(25)*z(38)+z(32)*z(34)) + par.UpparmMass*(z(53)*z(66)+z(59)*z(63)); - z(214) = par.ForearmInertia + par.ThighInertia + par.UpparmInertia + par.ThighMass*par.ThighCM^2; - z(215) = z(214) + z(187)*z(199) + par.ForearmMass*(z(79)^2+z(88)^2) + par.TrunkMass*(z(26)^2+z(31)^2) + par.UpparmMass*(z(54)^2+z(60)^2); - z(216) = z(204) + z(187)*z(200) + par.ForearmMass*(z(79)*z(80)+z(88)*z(89)) - par.TrunkMass*z(30)*z(31) - par.UpparmMass*(z(54)*z(55)-z(60)*z(61)); - z(217) = z(208) + z(209)*z(60) + par.ForearmMass*(z(79)*z(81)+z(86)*z(88)); - z(218) = par.ForearmInertia + z(211)*z(88); - z(219) = z(205)*z(16) + z(187)*z(201) + par.ForearmMass*(z(79)*z(94)+z(88)*z(91)) + par.TrunkMass*(z(26)*z(38)+z(31)*z(34)) + par.UpparmMass*(z(54)*z(66)+z(60)*z(63)); - z(220) = z(204) + z(188)*z(199) + par.ForearmMass*(z(78)*z(80)+z(87)*z(89)) - par.TrunkMass*z(30)*z(32) - par.UpparmMass*(z(53)*z(55)-z(59)*z(61)); - z(221) = z(204) + z(188)*z(199) + par.ForearmMass*(z(79)*z(80)+z(88)*z(89)) - par.TrunkMass*z(30)*z(31) - par.UpparmMass*(z(54)*z(55)-z(60)*z(61)); - z(222) = z(204) + z(188)*z(200) + par.TrunkMass*z(30)^2 + par.ForearmMass*(z(80)^2+z(89)^2) + par.UpparmMass*(z(55)^2+z(61)^2); - z(223) = z(208) + z(209)*z(61) + par.ForearmMass*(z(80)*z(81)+z(86)*z(89)); - z(224) = par.ForearmInertia + z(211)*z(89); - z(225) = z(188)*z(201) + par.ForearmMass*(z(80)*z(94)+z(89)*z(91)) - par.TrunkMass*z(30)*z(34) - par.UpparmMass*(z(55)*z(66)-z(61)*z(63)); - z(226) = par.ForearmInertia + par.UpparmInertia + par.UpparmMass*par.UpparmCM^2; - z(227) = z(226) + par.ForearmMass*(z(81)^2+z(86)^2); - z(228) = par.ForearmInertia + z(211)*z(86); - z(229) = z(209)*z(63) + par.ForearmMass*(z(81)*z(94)+z(86)*z(91)); - z(230) = par.ForearmInertia + par.ForearmMass*par.ForearmCM^2; - z(231) = z(211)*z(91); - z(232) = z(11)*z(24) + z(23)*z(182); - z(233) = z(45)*z(46) + z(46)*z(232) + z(48)*z(183) + z(183)*z(184); - z(234) = z(11)*z(23)*q3p + z(23)*z(196) + z(24)*z(193) - z(24)*z(182)*q3p; - z(235) = z(23)*z(196) - z(10)*z(23)*q3p - z(24)*z(182)*q3p - z(24)*z(191); - z(236) = z(45)*q1p*z(195) + z(45)*q2p*z(195) + z(46)*q1p*z(192) + z(46)*q1p*z(234) + z(46)*q2p*z(192) + z(46)*q2p*z(234) + z(48)*q1p*z(197) + z(48)*q2p*z(197) + z(183)*q1p*z(194) + z(183)*q1p*z(235) + z(183)*q2p*z(194) + z(183)*q2p*z(235) + z(184)*q1p*z(197) + z(184)*q2p*z(197) + z(232)*q1p*z(195) + z(232)*q2p*z(195) + 2*z(46)*q3p*z(194) + 2*z(46)*q3p*z(235) + 2*z(48)*q3p*z(195) + 2*z(184)*q3p*z(195); - z(237) = z(233)*z(201) + par.TrunkInertia*z(187)*z(236); - z(238) = z(233)*(z(199)+par.TrunkInertia*z(187)); - z(239) = par.TrunkInertia*z(46)*(z(48)+z(184)); - z(240) = z(200)*z(233) + 2*z(187)*z(239); - z(241) = z(43)*z(183) + z(44)*z(184); - z(242) = z(43)*z(184) - z(44)*z(183); - z(243) = z(72)*z(241) + z(73)*z(242); - z(244) = z(1)*(z(76)+z(243)); - z(245) = z(9)*z(76) + z(9)*z(243) + z(10)*z(74) + z(11)*z(74); - z(246) = z(1)*(z(51)+z(241)); - z(247) = z(2)*(z(51)+z(241)); - z(248) = z(7)*z(246) - z(8)*z(247); - z(249) = z(1)*(z(47)+z(183)); - z(250) = 2*z(137)*z(244) + 2*z(138)*z(245) + 2*z(141)*z(246) + 2*z(142)*z(248) + 2*z(143)*z(183) + 2*z(144)*z(45) + 2*z(149)*z(2) - 2*z(146)*z(243) - 2*z(147)*z(74) - 2*z(148)*z(249) - 2*z(150)*z(1) - 2*z(152)*z(10) - 2*z(153)*z(9) - 2*z(155)*z(241) - 2*z(156)*z(49); - z(251) = par.UpparmLen*z(250)/(z(157)^0.5*z(158)^2); - z(252) = z(111)*z(250)/(z(157)^0.5*z(158)^2); - z(253) = z(72)*z(242) - z(73)*z(241); - z(254) = z(112)*z(250)/(z(157)^0.5*z(158)^2); - z(255) = par.TrunkLen*z(250)/(z(157)^0.5*z(158)^2); - z(256) = (par.ThighLen*z(10)+z(100)*z(1)-par.ShankLen*z(2)-z(101)*z(182))/z(102)^0.5; - z(257) = par.ThighLen*(z(10)-par.a*z(182))/z(102)^0.5; - z(258) = (par.Kseat*z(103)+par.Cseat*(z(256)*q1p+z(257)*q2p))/z(102)^0.5; - z(259) = par.ForearmLen*z(250)/(z(157)^0.5*z(158)^2); - z(260) = par.ShankLen*z(250)/(z(157)^0.5*z(158)^2); - z(261) = par.ThighLen*z(250)/(z(157)^0.5*z(158)^2); - z(262) = z(1)*(z(77)+z(253)); - z(263) = z(9)*z(77) + z(9)*z(253) + z(10)*z(75) + z(11)*z(75); - z(264) = par.a*(par.Kseat*z(103)+par.Cseat*(z(256)*q1p+z(257)*q2p))/z(102)^0.5; - z(265) = z(173)*z(2) + z(74)*z(78)*z(168) + z(75)*z(108)*z(168) + z(78)*z(167)*z(243) + z(108)*z(167)*z(253) + 0.5*Fc*z(78)*z(259) + 0.5*Fc*z(72)*z(78)*z(251) + 0.5*Fc*z(78)*z(113)*z(260) + 0.5*Fc*z(78)*z(117)*z(261) + 0.5*Fc*z(108)*z(115)*z(260) + 0.5*Fc*z(108)*z(119)*z(261) + z(9)*z(12)*z(106) + z(9)*z(12)*z(264) + z(10)*z(20)*z(106) + z(10)*z(20)*z(264) - z(78)*z(169)*z(244) - z(78)*z(170)*z(245) - z(108)*z(169)*z(262) - z(108)*z(170)*z(263) - 0.5*Fc*z(73)*z(108)*z(251) - 0.5*Fc*z(74)*z(78)*z(252) - 0.5*Fc*z(75)*z(108)*z(252) - 0.5*Fc*z(76)*z(78)*z(254) - 0.5*Fc*z(77)*z(108)*z(254) - 0.5*Fc*z(78)*z(121)*z(255) - 0.5*Fc*z(108)*z(123)*z(255) - z(95)*(z(74)*z(78)+z(75)*z(87)) - z(97)*(z(9)*z(12)+z(10)*z(14)) - z(98)*(z(25)*z(45)+z(32)*z(46)) - z(99)*(z(49)*z(53)+z(50)*z(59)) - z(9)*z(20)*z(258) - z(10)*z(12)*z(105) - z(11)*z(12)*z(258) - z(20)*z(182)*z(105); - z(266) = par.ShankLen*(z(7)*z(23)-z(8)*z(24)); - z(267) = par.ShankLen*(z(7)*z(24)+z(8)*z(23)); - z(268) = z(43)*z(266) - z(44)*z(267); - z(269) = -z(43)*z(267) - z(44)*z(266); - z(270) = z(72)*z(268) + z(73)*z(269); - z(271) = (z(7)*z(24)+z(8)*z(23))*z(6); - z(272) = (z(7)*z(23)-z(8)*z(24))*z(6); - z(273) = z(43)*z(271) + z(44)*z(272); - z(274) = z(43)*z(272) - z(44)*z(271); - z(275) = z(72)*z(273) + z(73)*z(274); - z(276) = z(72)*z(269) - z(73)*z(268); - z(277) = z(72)*z(274) - z(73)*z(273); - z(278) = z(233)*z(201) + par.TrunkInertia*z(187)*z(236) + par.ForearmMass*(z(78)*z(275)+z(87)*z(277)+z(270)*z(94)+z(276)*z(91)) + par.UpparmMass*(z(53)*z(273)+z(59)*z(274)+z(268)*z(66)+z(269)*z(63)) + par.TrunkMass*(z(25)*z(271)+z(32)*z(272)+z(266)*z(38)-z(267)*z(34)) - par.ThighMass*(par.ShankLen*z(8)*z(16)-par.ShankLen*z(7)*z(19)-z(7)*z(14)*z(6)-z(8)*z(12)*z(6)); - z(279) = par.ShankLen*par.ThighMass; - z(280) = z(199)*z(233) + par.TrunkInertia*z(187)*z(233) + 2*par.ForearmMass*(z(78)*z(270)+z(87)*z(276)) + 2*par.UpparmMass*(z(53)*z(268)+z(59)*z(269)) + 2*par.TrunkMass*(z(25)*z(266)-z(32)*z(267)) + 2*z(279)*(z(7)*z(12)-z(8)*z(14)); - z(281) = par.ShankLen*z(205); - z(282) = z(199)*z(233) + par.TrunkInertia*z(187)*z(233) + par.ForearmMass*(z(79)*z(270)+z(88)*z(276)) + par.UpparmMass*(z(54)*z(268)+z(60)*z(269)) + par.TrunkMass*(z(26)*z(266)-z(31)*z(267)) - z(281)*z(8); - z(283) = z(200)*z(233) + 2*z(187)*z(239) + par.TrunkMass*z(30)*z(267) + par.ForearmMass*(z(80)*z(270)+z(89)*z(276)) - par.UpparmMass*(z(55)*z(268)-z(61)*z(269)); - z(284) = z(209)*z(269) + par.ForearmMass*(z(81)*z(270)+z(86)*z(276)); - z(285) = z(1)*z(243) + z(2)*z(74); - z(286) = z(1)*z(241) + z(2)*z(49); - z(287) = z(1)*z(49) - z(2)*z(241); - z(288) = z(7)*z(130) + z(7)*z(286) + z(8)*z(287) - z(8)*z(128); - z(289) = z(1)*z(183) + z(2)*z(45); - z(290) = 2*z(137)*z(285) + 2*z(138)*z(245) + 2*z(141)*z(286) + 2*z(142)*z(288) + 2*z(143)*z(183) + 2*z(144)*z(45) - 2*z(140)*z(8) - 2*z(146)*z(243) - 2*z(147)*z(74) - 2*z(148)*z(289) - 2*z(152)*z(10) - 2*z(153)*z(9) - 2*z(155)*z(241) - 2*z(156)*z(49); - z(291) = par.UpparmLen*z(290)/(z(157)^0.5*z(158)^2); - z(292) = z(111)*z(290)/(z(157)^0.5*z(158)^2); - z(293) = z(112)*z(290)/(z(157)^0.5*z(158)^2); - z(294) = par.TrunkLen*z(290)/(z(157)^0.5*z(158)^2); - z(295) = (par.ThighLen*z(10)-z(101)*z(182))/z(102)^0.5; - z(296) = (par.Kseat*z(104)+par.Cseat*(z(257)*q2p+z(295)*q1p))/z(102)^0.5; - z(297) = par.ForearmLen*z(290)/(z(157)^0.5*z(158)^2); - z(298) = par.ShankLen*z(290)/(z(157)^0.5*z(158)^2); - z(299) = par.ThighLen*z(290)/(z(157)^0.5*z(158)^2); - z(300) = z(1)*z(253) + z(2)*z(75); - z(301) = par.a*(par.Kseat*z(104)+par.Cseat*(z(257)*q2p+z(295)*q1p))/z(102)^0.5; - z(302) = z(73)*z(172)*z(276) + z(74)*z(78)*z(168) + z(74)*z(167)*z(270) + z(75)*z(108)*z(168) + z(75)*z(167)*z(276) + z(76)*z(168)*z(270) + z(77)*z(168)*z(276) + z(78)*z(167)*z(243) + z(108)*z(167)*z(253) + z(121)*z(171)*z(270) + z(123)*z(171)*z(276) + 0.5*Fc*z(78)*z(297) + 0.5*Fc*z(72)*z(78)*z(291) + 0.5*Fc*z(78)*z(113)*z(298) + 0.5*Fc*z(78)*z(117)*z(299) + 0.5*Fc*z(108)*z(115)*z(298) + 0.5*Fc*z(108)*z(119)*z(299) + z(9)*z(12)*z(106) + z(9)*z(12)*z(301) + z(10)*z(20)*z(106) + z(10)*z(20)*z(301) + par.ShankLen*z(7)*z(11)*z(106) + par.ShankLen*z(8)*z(10)*z(105) - z(166)*z(270) - z(72)*z(172)*z(270) - z(78)*z(169)*z(285) - z(78)*z(170)*z(245) - z(108)*z(169)*z(300) - z(108)*z(170)*z(263) - z(113)*z(169)*z(270) - z(115)*z(169)*z(276) - z(117)*z(170)*z(270) - z(119)*z(170)*z(276) - 0.5*Fc*z(73)*z(108)*z(291) - 0.5*Fc*z(74)*z(78)*z(292) - 0.5*Fc*z(75)*z(108)*z(292) - 0.5*Fc*z(76)*z(78)*z(293) - 0.5*Fc*z(77)*z(108)*z(293) - 0.5*Fc*z(78)*z(121)*z(294) - 0.5*Fc*z(108)*z(123)*z(294) - z(95)*(z(74)*z(78)+z(75)*z(87)+z(76)*z(270)+z(77)*z(276)) - z(99)*(z(49)*z(53)+z(50)*z(59)+z(51)*z(268)+z(52)*z(269)) - z(98)*(z(25)*z(45)+z(32)*z(46)+z(47)*z(266)-z(48)*z(267)) - z(97)*(z(9)*z(12)+z(10)*z(14)+par.ShankLen*z(7)*z(11)-par.ShankLen*z(8)*z(9)) - z(9)*z(20)*z(296) - z(10)*z(12)*z(105) - z(11)*z(12)*z(296) - z(20)*z(182)*z(105) - par.ShankLen*z(7)*z(9)*z(105) - par.ShankLen*z(8)*z(9)*z(106); - z(303) = z(45)*z(186) + z(46)*z(48) + z(46)*z(184) + z(183)*z(185); - z(304) = z(11)*z(24)*q3p - z(9)*z(23)*q3p - z(23)*z(193) - z(24)*z(190); - z(305) = z(9)*z(24)*q3p - z(10)*z(23)*q3p - z(23)*z(190) - z(24)*z(191); - z(306) = z(45)*q1p*z(304) + z(45)*q2p*z(304) + z(46)*q1p*z(194) + z(46)*q1p*z(235) + z(46)*q2p*z(194) + z(46)*q2p*z(235) + z(48)*q1p*z(195) + z(48)*q2p*z(195) + z(183)*q1p*z(305) + z(183)*q2p*z(305) + z(184)*q1p*z(195) + z(184)*q2p*z(195) + z(185)*q1p*z(197) + z(185)*q2p*z(197) + z(186)*q1p*z(192) + z(186)*q2p*z(192) + 2*z(46)*q3p*z(305) + 2*z(48)*q3p*z(304) + 2*z(185)*q3p*z(195) + 2*z(186)*q3p*z(194); - z(307) = -z(12)*z(23) - z(20)*z(24); - z(308) = z(28)*z(43) + z(44)*z(307); - z(309) = z(43)*z(307) - z(28)*z(44); - z(310) = z(72)*z(308) + z(73)*z(309); - z(311) = -z(23)*z(22) - z(24)*z(16); - z(312) = z(43)*z(34) + z(44)*z(311); - z(313) = z(43)*z(311) - z(44)*z(34); - z(314) = z(72)*z(312) + z(73)*z(313); - z(315) = z(72)*z(309) - z(73)*z(308); - z(316) = z(72)*z(313) - z(73)*z(312); - z(317) = z(303)*z(201) + par.TrunkInertia*z(187)*z(306) + par.ForearmMass*(z(78)*z(314)+z(87)*z(316)+z(310)*z(94)+z(315)*z(91)) + par.TrunkMass*(z(25)*z(34)+z(28)*z(38)+z(32)*z(311)+z(307)*z(34)) + par.UpparmMass*(z(53)*z(312)+z(59)*z(313)+z(308)*z(66)+z(309)*z(63)); - z(318) = z(199)*z(303) + par.TrunkInertia*z(187)*z(303) + 2*par.ForearmMass*(z(78)*z(310)+z(87)*z(315)) + 2*par.TrunkMass*(z(25)*z(28)+z(32)*z(307)) + 2*par.UpparmMass*(z(53)*z(308)+z(59)*z(309)); - z(319) = par.ThighLen*(z(23)*z(43)-z(24)*z(44)); - z(320) = par.ThighLen*(z(23)*z(44)+z(24)*z(43)); - z(321) = z(72)*z(319) - z(73)*z(320); - z(322) = -z(72)*z(320) - z(73)*z(319); - z(323) = z(199)*z(303) + par.TrunkInertia*z(187)*z(303) + par.ForearmMass*(z(78)*z(321)+z(79)*z(310)+z(87)*z(322)+z(88)*z(315)) + par.TrunkMass*(z(26)*z(28)+z(31)*z(307)+par.ThighLen*z(23)*z(25)-par.ThighLen*z(24)*z(32)) - par.UpparmMass*(z(59)*z(320)-z(53)*z(319)-z(54)*z(308)-z(60)*z(309)); - z(324) = 2*z(46)*z(185) + 2*z(48)*z(186); - z(325) = z(200)*z(303) + par.TrunkInertia*z(187)*z(324) + par.ForearmMass*(z(80)*z(310)+z(89)*z(315)) - par.TrunkMass*z(30)*z(307) - par.UpparmMass*(z(55)*z(308)-z(61)*z(309)); - z(326) = z(209)*z(309) + par.ForearmMass*(z(81)*z(310)+z(86)*z(315)); - z(327) = z(43)*z(46) + z(44)*z(185); - z(328) = z(43)*z(185) - z(44)*z(46); - z(329) = z(72)*z(327) + z(73)*z(328); - z(330) = z(43)*z(48) + z(44)*z(186); - z(331) = z(43)*z(186) - z(44)*z(48); + z(136) = z(2)*z(8) - z(1)*z(7); + z(137) = z(10)*z(23) + z(24)*z(136); + z(138) = z(23)*z(136) - z(10)*z(24); + z(139) = -z(9)*z(23) - z(10)*z(24); + z(140) = z(43)*z(46) + z(44)*z(139); + z(141) = z(43)*z(137) + z(44)*z(138); + z(142) = z(43)*z(138) - z(44)*z(137); + z(143) = z(43)*z(139) - z(44)*z(46); + z(144) = -z(43)*z(45) - z(44)*z(46); + z(145) = z(50)*z(72) + z(73)*z(144); + z(146) = z(72)*z(140) + z(73)*z(143); + z(147) = z(72)*z(141) + z(73)*z(142); + z(148) = -z(9)*z(24) - z(11)*z(23); + z(149) = z(43)*z(48) + z(44)*z(148); + z(150) = z(43)*z(148) - z(44)*z(48); + z(151) = -z(43)*z(47) - z(44)*z(48); + z(152) = z(52)*z(72) + z(73)*z(151); + z(153) = z(72)*z(149) + z(73)*z(150); + z(154) = z(1)*(z(76)+z(147)); + z(155) = z(1)*z(145) + z(2)*z(152); + z(156) = z(1)*z(146) + z(2)*z(153); + z(157) = z(1)*z(147) + z(2)*z(74); + z(158) = z(9)*z(76) + z(9)*z(147) + z(10)*z(74) + z(11)*z(74); + z(159) = z(9)*z(145) + z(11)*z(152); + z(160) = z(9)*z(146) + z(11)*z(153); + z(161) = z(1)*(z(51)+z(141)); + z(162) = z(1)*z(140) + z(2)*z(149); + z(163) = z(1)*z(141) + z(2)*z(49); + z(164) = z(2)*(z(51)+z(141)); + z(165) = z(1)*z(49) - z(2)*z(141); + z(166) = z(1)*z(149) - z(2)*z(140); + z(167) = z(7)*z(130) + z(7)*z(163) + z(8)*z(165) - z(8)*z(128); + z(168) = z(7)*z(161) - z(8)*z(164); + z(169) = z(7)*z(162) + z(8)*z(166); + z(170) = z(1)*(z(47)+z(137)); + z(171) = z(1)*z(137) + z(2)*z(45); + z(172) = par.ForearmLen*par.ShankLen; + z(173) = par.ForearmLen*par.ThighLen; + z(174) = par.ShankLen*par.UpparmLen; + z(175) = par.ShankLen*z(111); + z(176) = par.ThighLen*par.UpparmLen; + z(177) = par.TrunkLen*z(111); + z(178) = par.TrunkLen*z(112); + z(179) = par.ForearmLen*z(111); + z(180) = par.ForearmLen*z(112); + z(181) = par.ShankLen*par.TrunkLen; + z(182) = par.ShankLen*z(112); + z(183) = par.ThighLen*z(111); + z(184) = par.ThighLen*z(112); + z(185) = par.UpparmLen*z(111); + z(186) = par.UpparmLen*z(112); + z(187) = par.ForearmLen^2 + par.ShankLen^2 + par.ThighLen^2 + par.TrunkLen^2 + par.UpparmLen^2 + z(111)^2 + z(112)^2; + z(188) = par.ForearmLen*par.UpparmLen; + z(189) = par.ShankLen*par.ThighLen; + z(190) = par.ForearmLen*par.TrunkLen; + z(191) = par.ThighLen*par.TrunkLen; + z(192) = par.TrunkLen*par.UpparmLen; + z(193) = (z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^0.5; + z(194) = (z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^0.5; + z(195) = (z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^0.5; + z(196) = (z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^0.5; + z(197) = par.ForearmLen*(par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^0.5; + z(198) = z(187) + 2*z(172)*z(113) + 2*z(173)*z(117) + 2*z(174)*z(128) + 2*z(176)*z(132) + 2*z(177)*z(45) + 2*z(178)*z(47) + 2*z(188)*z(72) + 2*z(189)*z(7) - 2*z(175)*z(1) - 2*z(179)*z(74) - 2*z(180)*z(76) - 2*z(181)*z(124) - 2*z(182)*z(2) - 2*z(183)*z(9) - 2*z(184)*z(11) - 2*z(185)*z(49) - 2*z(186)*z(51) - 2*z(190)*z(121) - 2*z(191)*z(23) - 2*z(192)*z(43); + z(199) = z(198)^0.5; + z(200) = par.ForearmLen/z(199); + z(201) = z(111)/z(199); + z(202) = z(112)/z(199); + z(203) = par.ShankLen/z(199); + z(204) = par.ThighLen/z(199); + z(205) = par.TrunkLen/z(199); + z(206) = par.UpparmLen/z(199); + z(207) = Fc*z(200); + z(208) = Fc*z(201); + z(209) = Fc*z(202); + z(210) = Fc*z(203); + z(211) = Fc*z(204); + z(212) = Fc*z(205); + z(213) = Fc*z(206); + z(214) = par.ShankCM*z(96); + z(215) = z(73)*z(108)*z(213) + z(74)*z(78)*z(208) + z(75)*z(108)*z(208) + z(76)*z(78)*z(209) + z(77)*z(108)*z(209) + z(78)*z(121)*z(212) + z(108)*z(123)*z(212) + z(9)*z(20)*z(106) + z(11)*z(12)*z(106) - z(214)*z(1) - z(78)*z(207) - z(72)*z(78)*z(213) - z(78)*z(113)*z(210) - z(78)*z(117)*z(211) - z(108)*z(115)*z(210) - z(108)*z(119)*z(211) - z(95)*(z(76)*z(78)+z(77)*z(87)) - z(97)*(z(9)*z(14)+z(11)*z(12)) - z(98)*(z(25)*z(47)+z(32)*z(48)) - z(99)*(z(51)*z(53)+z(52)*z(59)) - z(9)*z(12)*z(105) - z(10)*z(20)*z(105); + z(216) = par.ThighCM*z(97); + z(217) = z(73)*z(109)*z(213) + z(74)*z(79)*z(208) + z(75)*z(109)*z(208) + z(76)*z(79)*z(209) + z(77)*z(109)*z(209) + z(79)*z(121)*z(212) + z(109)*z(123)*z(212) + par.ThighLen*(z(9)*z(106)-z(10)*z(105)) - z(216)*z(9) - z(79)*z(207) - z(72)*z(79)*z(213) - z(79)*z(113)*z(210) - z(79)*z(117)*z(211) - z(109)*z(115)*z(210) - z(109)*z(119)*z(211) - z(95)*(z(76)*z(79)+z(77)*z(88)) - z(98)*(z(26)*z(47)+z(31)*z(48)) - z(99)*(z(51)*z(54)+z(52)*z(60)); + z(218) = z(98)*z(30)*z(48) + z(73)*z(110)*z(213) + z(74)*z(80)*z(208) + z(75)*z(110)*z(208) + z(76)*z(80)*z(209) + z(77)*z(110)*z(209) + z(80)*z(121)*z(212) + z(110)*z(123)*z(212) + z(99)*(z(51)*z(55)-z(52)*z(61)) - z(80)*z(207) - z(72)*z(80)*z(213) - z(80)*z(113)*z(210) - z(80)*z(117)*z(211) - z(110)*z(115)*z(210) - z(110)*z(119)*z(211) - z(95)*(z(76)*z(80)+z(77)*z(89)); + z(219) = par.UpparmCM*z(99); + z(220) = z(73)*z(107)*z(213) + z(74)*z(81)*z(208) + z(75)*z(107)*z(208) + z(76)*z(81)*z(209) + z(77)*z(107)*z(209) + z(81)*z(121)*z(212) + z(107)*z(123)*z(212) - z(219)*z(52) - z(81)*z(207) - z(72)*z(81)*z(213) - z(81)*z(113)*z(210) - z(81)*z(117)*z(211) - z(107)*z(115)*z(210) - z(107)*z(119)*z(211) - z(95)*(z(76)*z(81)+z(77)*z(86)); + z(221) = par.ForearmCM*z(95); + z(222) = -z(221)*z(77) - par.ForearmLen*(z(115)*z(210)+z(119)*z(211)-z(73)*z(213)-z(75)*z(208)-z(77)*z(209)-z(123)*z(212)); + z(223) = z(45)*z(48) + z(46)*z(137); + z(224) = z(46)^2 + z(48)^2; + z(226) = -z(1)*z(8)*q1p - z(1)*z(8)*q2p - z(2)*z(7)*q1p - z(2)*z(7)*q2p; + z(227) = z(2)*z(8)*q1p + z(2)*z(8)*q2p - z(1)*z(7)*q1p - z(1)*z(7)*q2p; + z(228) = z(10)*z(23)*q3p + z(23)*z(226) + z(24)*z(227) - z(9)*z(24)*q3p; + z(229) = z(1)*z(7)*q1p + z(1)*z(7)*q2p - z(2)*z(8)*q1p - z(2)*z(8)*q2p; + z(230) = z(23)*z(226) - z(9)*z(24)*q3p - z(11)*z(23)*q3p - z(24)*z(229); + z(231) = z(23)*z(227) - z(9)*z(23)*q3p - z(10)*z(24)*q3p - z(24)*z(226); + z(232) = z(1)*z(8)*q1p + z(1)*z(8)*q2p + z(2)*z(7)*q1p + z(2)*z(7)*q2p; + z(233) = z(23)*z(136)*q3p + z(23)*z(227) + z(24)*z(232) - z(10)*z(24)*q3p; + z(234) = z(45)*q1p*z(230) + z(45)*q2p*z(230) + z(46)*q1p*z(233) + z(46)*q2p*z(233) + z(48)*q1p*z(228) + z(48)*q2p*z(228) + z(137)*q1p*z(231) + z(137)*q2p*z(231) + 2*z(46)*q3p*z(231) + 2*z(48)*q3p*z(230); + z(235) = par.TrunkInertia*z(223); + z(236) = par.TrunkInertia*z(224); + z(237) = par.TrunkInertia*z(234); + z(238) = par.ForearmInertia + par.ShankInertia + par.ThighInertia + par.UpparmInertia + par.ShankMass*par.ShankCM^2; + z(239) = z(238) + z(223)*z(235) + par.ForearmMass*(z(78)^2+z(87)^2) + par.ThighMass*(z(12)^2+z(14)^2) + par.TrunkMass*(z(25)^2+z(32)^2) + par.UpparmMass*(z(53)^2+z(59)^2); + z(240) = par.ForearmInertia + par.ThighInertia + par.UpparmInertia; + z(241) = par.ThighCM*par.ThighMass; + z(242) = z(240) + z(241)*z(14) + z(223)*z(235) + par.ForearmMass*(z(78)*z(79)+z(87)*z(88)) + par.TrunkMass*(z(25)*z(26)+z(31)*z(32)) + par.UpparmMass*(z(53)*z(54)+z(59)*z(60)); + z(243) = z(240) + z(223)*z(236) + par.ForearmMass*(z(78)*z(80)+z(87)*z(89)) - par.TrunkMass*z(30)*z(32) - par.UpparmMass*(z(53)*z(55)-z(59)*z(61)); + z(244) = par.ForearmInertia + par.UpparmInertia; + z(245) = par.UpparmCM*par.UpparmMass; + z(246) = z(244) + z(245)*z(59) + par.ForearmMass*(z(78)*z(81)+z(86)*z(87)); + z(247) = par.ForearmCM*par.ForearmMass; + z(248) = par.ForearmInertia + z(247)*z(87); + z(249) = z(223)*z(237) + par.ForearmMass*(z(78)*z(94)+z(87)*z(91)) + par.ThighMass*(z(12)*z(19)+z(14)*z(16)) + par.TrunkMass*(z(25)*z(38)+z(32)*z(34)) + par.UpparmMass*(z(53)*z(66)+z(59)*z(63)); + z(250) = par.ForearmInertia + par.ThighInertia + par.UpparmInertia + par.ThighMass*par.ThighCM^2; + z(251) = z(250) + z(223)*z(235) + par.ForearmMass*(z(79)^2+z(88)^2) + par.TrunkMass*(z(26)^2+z(31)^2) + par.UpparmMass*(z(54)^2+z(60)^2); + z(252) = z(240) + z(223)*z(236) + par.ForearmMass*(z(79)*z(80)+z(88)*z(89)) - par.TrunkMass*z(30)*z(31) - par.UpparmMass*(z(54)*z(55)-z(60)*z(61)); + z(253) = z(244) + z(245)*z(60) + par.ForearmMass*(z(79)*z(81)+z(86)*z(88)); + z(254) = par.ForearmInertia + z(247)*z(88); + z(255) = z(241)*z(16) + z(223)*z(237) + par.ForearmMass*(z(79)*z(94)+z(88)*z(91)) + par.TrunkMass*(z(26)*z(38)+z(31)*z(34)) + par.UpparmMass*(z(54)*z(66)+z(60)*z(63)); + z(256) = z(240) + z(224)*z(235) + par.ForearmMass*(z(78)*z(80)+z(87)*z(89)) - par.TrunkMass*z(30)*z(32) - par.UpparmMass*(z(53)*z(55)-z(59)*z(61)); + z(257) = z(240) + z(224)*z(235) + par.ForearmMass*(z(79)*z(80)+z(88)*z(89)) - par.TrunkMass*z(30)*z(31) - par.UpparmMass*(z(54)*z(55)-z(60)*z(61)); + z(258) = z(240) + z(224)*z(236) + par.TrunkMass*z(30)^2 + par.ForearmMass*(z(80)^2+z(89)^2) + par.UpparmMass*(z(55)^2+z(61)^2); + z(259) = z(244) + z(245)*z(61) + par.ForearmMass*(z(80)*z(81)+z(86)*z(89)); + z(260) = par.ForearmInertia + z(247)*z(89); + z(261) = z(224)*z(237) + par.ForearmMass*(z(80)*z(94)+z(89)*z(91)) - par.TrunkMass*z(30)*z(34) - par.UpparmMass*(z(55)*z(66)-z(61)*z(63)); + z(262) = par.ForearmInertia + par.UpparmInertia + par.UpparmMass*par.UpparmCM^2; + z(263) = z(262) + par.ForearmMass*(z(81)^2+z(86)^2); + z(264) = par.ForearmInertia + z(247)*z(86); + z(265) = z(245)*z(63) + par.ForearmMass*(z(81)*z(94)+z(86)*z(91)); + z(266) = par.ForearmInertia + par.ForearmMass*par.ForearmCM^2; + z(267) = z(247)*z(91); + z(268) = z(11)*z(24) + z(23)*z(136); + z(269) = z(45)*z(46) + z(46)*z(268) + z(48)*z(137) + z(137)*z(138); + z(270) = z(11)*z(23)*q3p + z(23)*z(232) + z(24)*z(229) - z(24)*z(136)*q3p; + z(271) = z(23)*z(232) - z(10)*z(23)*q3p - z(24)*z(136)*q3p - z(24)*z(227); + z(272) = z(45)*q1p*z(231) + z(45)*q2p*z(231) + z(46)*q1p*z(228) + z(46)*q1p*z(270) + z(46)*q2p*z(228) + z(46)*q2p*z(270) + z(48)*q1p*z(233) + z(48)*q2p*z(233) + z(137)*q1p*z(230) + z(137)*q1p*z(271) + z(137)*q2p*z(230) + z(137)*q2p*z(271) + z(138)*q1p*z(233) + z(138)*q2p*z(233) + z(268)*q1p*z(231) + z(268)*q2p*z(231) + 2*z(46)*q3p*z(230) + 2*z(46)*q3p*z(271) + 2*z(48)*q3p*z(231) + 2*z(138)*q3p*z(231); + z(273) = z(269)*z(237) + par.TrunkInertia*z(223)*z(272); + z(274) = z(269)*(z(235)+par.TrunkInertia*z(223)); + z(275) = par.TrunkInertia*z(46)*(z(48)+z(138)); + z(276) = z(236)*z(269) + 2*z(223)*z(275); + z(277) = 2*z(172)*z(154) + 2*z(173)*z(158) + 2*z(174)*z(161) + 2*z(175)*z(2) + 2*z(176)*z(168) + 2*z(177)*z(137) + 2*z(178)*z(45) - 2*z(179)*z(147) - 2*z(180)*z(74) - 2*z(181)*z(170) - 2*z(182)*z(1) - 2*z(183)*z(10) - 2*z(184)*z(9) - 2*z(185)*z(141) - 2*z(186)*z(49); + z(278) = par.UpparmLen*z(277)/(z(198)^0.5*z(199)^2); + z(279) = z(111)*z(277)/(z(198)^0.5*z(199)^2); + z(280) = z(72)*z(142) - z(73)*z(141); + z(281) = z(112)*z(277)/(z(198)^0.5*z(199)^2); + z(282) = par.TrunkLen*z(277)/(z(198)^0.5*z(199)^2); + z(283) = (par.ThighLen*z(10)+z(100)*z(1)-par.ShankLen*z(2)-z(101)*z(136))/z(102)^0.5; + z(284) = par.ThighLen*(z(10)-par.a*z(136))/z(102)^0.5; + z(285) = (par.Kseat*z(103)+par.Cseat*(z(283)*q1p+z(284)*q2p))/z(102)^0.5; + z(286) = par.ForearmLen*z(277)/(z(198)^0.5*z(199)^2); + z(287) = par.ShankLen*z(277)/(z(198)^0.5*z(199)^2); + z(288) = par.ThighLen*z(277)/(z(198)^0.5*z(199)^2); + z(289) = z(1)*(z(77)+z(280)); + z(290) = z(9)*z(77) + z(9)*z(280) + z(10)*z(75) + z(11)*z(75); + z(291) = par.a*(par.Kseat*z(103)+par.Cseat*(z(283)*q1p+z(284)*q2p))/z(102)^0.5; + z(292) = z(214)*z(2) + z(74)*z(78)*z(209) + z(75)*z(108)*z(209) + z(78)*z(147)*z(208) + z(108)*z(208)*z(280) + 0.5*Fc*z(78)*z(286) + 0.5*Fc*z(72)*z(78)*z(278) + 0.5*Fc*z(78)*z(113)*z(287) + 0.5*Fc*z(78)*z(117)*z(288) + 0.5*Fc*z(108)*z(115)*z(287) + 0.5*Fc*z(108)*z(119)*z(288) + z(9)*z(12)*z(106) + z(9)*z(12)*z(291) + z(10)*z(20)*z(106) + z(10)*z(20)*z(291) - z(78)*z(154)*z(210) - z(78)*z(158)*z(211) - z(108)*z(210)*z(289) - z(108)*z(211)*z(290) - 0.5*Fc*z(73)*z(108)*z(278) - 0.5*Fc*z(74)*z(78)*z(279) - 0.5*Fc*z(75)*z(108)*z(279) - 0.5*Fc*z(76)*z(78)*z(281) - 0.5*Fc*z(77)*z(108)*z(281) - 0.5*Fc*z(78)*z(121)*z(282) - 0.5*Fc*z(108)*z(123)*z(282) - z(95)*(z(74)*z(78)+z(75)*z(87)) - z(97)*(z(9)*z(12)+z(10)*z(14)) - z(98)*(z(25)*z(45)+z(32)*z(46)) - z(99)*(z(49)*z(53)+z(50)*z(59)) - z(9)*z(20)*z(285) - z(10)*z(12)*z(105) - z(11)*z(12)*z(285) - z(20)*z(136)*z(105); + z(293) = par.ShankLen*(z(7)*z(23)-z(8)*z(24)); + z(294) = par.ShankLen*(z(7)*z(24)+z(8)*z(23)); + z(295) = z(43)*z(293) - z(44)*z(294); + z(296) = -z(43)*z(294) - z(44)*z(293); + z(297) = z(72)*z(295) + z(73)*z(296); + z(298) = (z(7)*z(24)+z(8)*z(23))*z(6); + z(299) = (z(7)*z(23)-z(8)*z(24))*z(6); + z(300) = z(43)*z(298) + z(44)*z(299); + z(301) = z(43)*z(299) - z(44)*z(298); + z(302) = z(72)*z(300) + z(73)*z(301); + z(303) = z(72)*z(296) - z(73)*z(295); + z(304) = z(72)*z(301) - z(73)*z(300); + z(305) = z(269)*z(237) + par.TrunkInertia*z(223)*z(272) + par.ForearmMass*(z(78)*z(302)+z(87)*z(304)+z(297)*z(94)+z(303)*z(91)) + par.UpparmMass*(z(53)*z(300)+z(59)*z(301)+z(295)*z(66)+z(296)*z(63)) + par.TrunkMass*(z(25)*z(298)+z(32)*z(299)+z(293)*z(38)-z(294)*z(34)) - par.ThighMass*(par.ShankLen*z(8)*z(16)-par.ShankLen*z(7)*z(19)-z(7)*z(14)*z(6)-z(8)*z(12)*z(6)); + z(306) = par.ShankLen*par.ThighMass; + z(307) = z(235)*z(269) + par.TrunkInertia*z(223)*z(269) + 2*par.ForearmMass*(z(78)*z(297)+z(87)*z(303)) + 2*par.UpparmMass*(z(53)*z(295)+z(59)*z(296)) + 2*par.TrunkMass*(z(25)*z(293)-z(32)*z(294)) + 2*z(306)*(z(7)*z(12)-z(8)*z(14)); + z(308) = par.ShankLen*z(241); + z(309) = z(235)*z(269) + par.TrunkInertia*z(223)*z(269) + par.ForearmMass*(z(79)*z(297)+z(88)*z(303)) + par.UpparmMass*(z(54)*z(295)+z(60)*z(296)) + par.TrunkMass*(z(26)*z(293)-z(31)*z(294)) - z(308)*z(8); + z(310) = z(236)*z(269) + 2*z(223)*z(275) + par.TrunkMass*z(30)*z(294) + par.ForearmMass*(z(80)*z(297)+z(89)*z(303)) - par.UpparmMass*(z(55)*z(295)-z(61)*z(296)); + z(311) = z(245)*z(296) + par.ForearmMass*(z(81)*z(297)+z(86)*z(303)); + z(312) = 2*z(172)*z(157) + 2*z(173)*z(158) + 2*z(174)*z(163) + 2*z(176)*z(167) + 2*z(177)*z(137) + 2*z(178)*z(45) - 2*z(179)*z(147) - 2*z(180)*z(74) - 2*z(181)*z(171) - 2*z(183)*z(10) - 2*z(184)*z(9) - 2*z(185)*z(141) - 2*z(186)*z(49) - 2*z(189)*z(8); + z(313) = par.UpparmLen*z(312)/(z(198)^0.5*z(199)^2); + z(314) = z(111)*z(312)/(z(198)^0.5*z(199)^2); + z(315) = z(112)*z(312)/(z(198)^0.5*z(199)^2); + z(316) = par.TrunkLen*z(312)/(z(198)^0.5*z(199)^2); + z(317) = (par.ThighLen*z(10)-z(101)*z(136))/z(102)^0.5; + z(318) = (par.Kseat*z(104)+par.Cseat*(z(284)*q2p+z(317)*q1p))/z(102)^0.5; + z(319) = par.ForearmLen*z(312)/(z(198)^0.5*z(199)^2); + z(320) = par.ShankLen*z(312)/(z(198)^0.5*z(199)^2); + z(321) = par.ThighLen*z(312)/(z(198)^0.5*z(199)^2); + z(322) = z(1)*z(280) + z(2)*z(75); + z(323) = par.a*(par.Kseat*z(104)+par.Cseat*(z(284)*q2p+z(317)*q1p))/z(102)^0.5; + z(324) = z(73)*z(213)*z(303) + z(74)*z(78)*z(209) + z(74)*z(208)*z(297) + z(75)*z(108)*z(209) + z(75)*z(208)*z(303) + z(76)*z(209)*z(297) + z(77)*z(209)*z(303) + z(78)*z(147)*z(208) + z(108)*z(208)*z(280) + z(121)*z(212)*z(297) + z(123)*z(212)*z(303) + 0.5*Fc*z(78)*z(319) + 0.5*Fc*z(72)*z(78)*z(313) + 0.5*Fc*z(78)*z(113)*z(320) + 0.5*Fc*z(78)*z(117)*z(321) + 0.5*Fc*z(108)*z(115)*z(320) + 0.5*Fc*z(108)*z(119)*z(321) + z(9)*z(12)*z(106) + z(9)*z(12)*z(323) + z(10)*z(20)*z(106) + z(10)*z(20)*z(323) + par.ShankLen*z(7)*z(11)*z(106) + par.ShankLen*z(8)*z(10)*z(105) - z(207)*z(297) - z(72)*z(213)*z(297) - z(78)*z(157)*z(210) - z(78)*z(158)*z(211) - z(108)*z(210)*z(322) - z(108)*z(211)*z(290) - z(113)*z(210)*z(297) - z(115)*z(210)*z(303) - z(117)*z(211)*z(297) - z(119)*z(211)*z(303) - 0.5*Fc*z(73)*z(108)*z(313) - 0.5*Fc*z(74)*z(78)*z(314) - 0.5*Fc*z(75)*z(108)*z(314) - 0.5*Fc*z(76)*z(78)*z(315) - 0.5*Fc*z(77)*z(108)*z(315) - 0.5*Fc*z(78)*z(121)*z(316) - 0.5*Fc*z(108)*z(123)*z(316) - z(95)*(z(74)*z(78)+z(75)*z(87)+z(76)*z(297)+z(77)*z(303)) - z(99)*(z(49)*z(53)+z(50)*z(59)+z(51)*z(295)+z(52)*z(296)) - z(98)*(z(25)*z(45)+z(32)*z(46)+z(47)*z(293)-z(48)*z(294)) - z(97)*(z(9)*z(12)+z(10)*z(14)+par.ShankLen*z(7)*z(11)-par.ShankLen*z(8)*z(9)) - z(9)*z(20)*z(318) - z(10)*z(12)*z(105) - z(11)*z(12)*z(318) - z(20)*z(136)*z(105) - par.ShankLen*z(7)*z(9)*z(105) - par.ShankLen*z(8)*z(9)*z(106); + z(325) = z(45)*z(148) + z(46)*z(48) + z(46)*z(138) + z(137)*z(139); + z(326) = z(11)*z(24)*q3p - z(9)*z(23)*q3p - z(23)*z(229) - z(24)*z(226); + z(327) = z(9)*z(24)*q3p - z(10)*z(23)*q3p - z(23)*z(226) - z(24)*z(227); + z(328) = z(45)*q1p*z(326) + z(45)*q2p*z(326) + z(46)*q1p*z(230) + z(46)*q1p*z(271) + z(46)*q2p*z(230) + z(46)*q2p*z(271) + z(48)*q1p*z(231) + z(48)*q2p*z(231) + z(137)*q1p*z(327) + z(137)*q2p*z(327) + z(138)*q1p*z(231) + z(138)*q2p*z(231) + z(139)*q1p*z(233) + z(139)*q2p*z(233) + z(148)*q1p*z(228) + z(148)*q2p*z(228) + 2*z(46)*q3p*z(327) + 2*z(48)*q3p*z(326) + 2*z(139)*q3p*z(231) + 2*z(148)*q3p*z(230); + z(329) = -z(12)*z(23) - z(20)*z(24); + z(330) = z(28)*z(43) + z(44)*z(329); + z(331) = z(43)*z(329) - z(28)*z(44); z(332) = z(72)*z(330) + z(73)*z(331); - z(333) = z(1)*z(329) + z(2)*z(332); - z(334) = z(9)*z(329) + z(11)*z(332); - z(335) = z(1)*z(327) + z(2)*z(330); - z(336) = z(1)*z(330) - z(2)*z(327); - z(337) = z(7)*z(335) + z(8)*z(336); - z(338) = 2*z(137)*z(333) + 2*z(138)*z(334) + 2*z(141)*z(335) + 2*z(142)*z(337) + 2*z(143)*z(46) + 2*z(144)*z(48) + 2*z(151)*z(24) - 2*z(146)*z(329) - 2*z(147)*z(332) - 2*z(148)*z(125) - 2*z(155)*z(327) - 2*z(156)*z(330); - z(339) = par.UpparmLen*z(338)/(z(157)^0.5*z(158)^2); - z(340) = z(111)*z(338)/(z(157)^0.5*z(158)^2); - z(341) = z(72)*z(328) - z(73)*z(327); - z(342) = z(112)*z(338)/(z(157)^0.5*z(158)^2); - z(343) = z(72)*z(331) - z(73)*z(330); - z(344) = par.TrunkLen*z(338)/(z(157)^0.5*z(158)^2); - z(345) = par.ForearmLen*z(338)/(z(157)^0.5*z(158)^2); - z(346) = par.ShankLen*z(338)/(z(157)^0.5*z(158)^2); - z(347) = par.ThighLen*z(338)/(z(157)^0.5*z(158)^2); - z(348) = z(1)*z(341) + z(2)*z(343); - z(349) = z(9)*z(341) + z(11)*z(343); - z(350) = z(73)*z(172)*z(315) + z(74)*z(167)*z(310) + z(75)*z(167)*z(315) + z(76)*z(168)*z(310) + z(77)*z(168)*z(315) + z(78)*z(167)*z(329) + z(78)*z(168)*z(332) + z(108)*z(167)*z(341) + z(108)*z(168)*z(343) + z(121)*z(171)*z(310) + z(123)*z(171)*z(315) + 0.5*Fc*z(78)*z(345) + 0.5*Fc*z(72)*z(78)*z(339) + 0.5*Fc*z(78)*z(113)*z(346) + 0.5*Fc*z(78)*z(117)*z(347) + 0.5*Fc*z(108)*z(115)*z(346) + 0.5*Fc*z(108)*z(119)*z(347) - z(166)*z(310) - z(72)*z(172)*z(310) - z(78)*z(169)*z(333) - z(78)*z(170)*z(334) - z(108)*z(169)*z(348) - z(108)*z(170)*z(349) - z(113)*z(169)*z(310) - z(115)*z(169)*z(315) - z(117)*z(170)*z(310) - z(119)*z(170)*z(315) - 0.5*Fc*z(73)*z(108)*z(339) - 0.5*Fc*z(74)*z(78)*z(340) - 0.5*Fc*z(75)*z(108)*z(340) - 0.5*Fc*z(76)*z(78)*z(342) - 0.5*Fc*z(77)*z(108)*z(342) - 0.5*Fc*z(78)*z(121)*z(344) - 0.5*Fc*z(108)*z(123)*z(344) - z(95)*(z(76)*z(310)+z(77)*z(315)+z(78)*z(332)+z(87)*z(343)) - z(98)*(z(25)*z(48)+z(28)*z(47)+z(32)*z(186)+z(48)*z(307)) - z(99)*(z(51)*z(308)+z(52)*z(309)+z(53)*z(330)+z(59)*z(331)); - z(351) = -z(25)*z(43) - z(41)*z(44); - z(352) = z(56)*z(72) + z(73)*z(351); - z(353) = -z(43)*z(42) - z(44)*z(34); - z(354) = z(72)*z(63) + z(73)*z(353); - z(355) = z(72)*z(351) - z(56)*z(73); - z(356) = z(72)*z(353) - z(73)*z(63); - z(357) = par.ForearmMass*(z(78)*z(354)+z(87)*z(356)+z(352)*z(94)+z(355)*z(91)) + par.UpparmMass*(z(53)*z(63)+z(56)*z(66)+z(59)*z(353)+z(351)*z(63)); - z(358) = 2*par.ForearmMass*(z(78)*z(352)+z(87)*z(355)) + 2*par.UpparmMass*(z(53)*z(56)+z(59)*z(351)); - z(359) = -z(26)*z(43) - z(40)*z(44); - z(360) = z(57)*z(72) + z(73)*z(359); - z(361) = z(72)*z(359) - z(57)*z(73); - z(362) = par.ForearmMass*(z(78)*z(360)+z(79)*z(352)+z(87)*z(361)+z(88)*z(355)) + par.UpparmMass*(z(53)*z(57)+z(54)*z(56)+z(59)*z(359)+z(60)*z(351)); - z(363) = z(39)*(z(43)*z(72)-z(44)*z(73)); - z(364) = z(39)*(z(43)*z(73)+z(44)*z(72)); - z(365) = -par.ForearmMass*(z(78)*z(363)-z(80)*z(352)-z(87)*z(364)-z(89)*z(355)) - par.UpparmMass*(z(55)*z(56)+z(39)*z(43)*z(53)-z(61)*z(351)-z(39)*z(44)*z(59)); - z(366) = z(209)*z(351) + par.ForearmMass*(z(81)*z(352)+z(86)*z(355)); - z(367) = -z(43)*z(45) - z(44)*z(46); - z(368) = z(50)*z(72) + z(73)*z(367); - z(369) = -z(43)*z(47) - z(44)*z(48); - z(370) = z(52)*z(72) + z(73)*z(369); - z(371) = z(1)*z(368) + z(2)*z(370); - z(372) = z(9)*z(368) + z(11)*z(370); - z(373) = 2*z(137)*z(371) + 2*z(138)*z(372) + 2*z(141)*z(129) + 2*z(142)*z(133) + 2*z(154)*z(44) - 2*z(145)*z(123) - 2*z(146)*z(368) - 2*z(147)*z(370) - 2*z(155)*z(50) - 2*z(156)*z(52); - z(374) = par.UpparmLen*z(373)/(z(157)^0.5*z(158)^2); - z(375) = z(111)*z(373)/(z(157)^0.5*z(158)^2); - z(376) = z(72)*z(367) - z(50)*z(73); - z(377) = z(112)*z(373)/(z(157)^0.5*z(158)^2); - z(378) = z(72)*z(369) - z(52)*z(73); - z(379) = par.TrunkLen*z(373)/(z(157)^0.5*z(158)^2); - z(380) = z(44)*z(73) - z(43)*z(72); - z(381) = par.ForearmLen*z(373)/(z(157)^0.5*z(158)^2); - z(382) = par.ShankLen*z(373)/(z(157)^0.5*z(158)^2); - z(383) = par.ThighLen*z(373)/(z(157)^0.5*z(158)^2); - z(384) = z(1)*z(376) + z(2)*z(378); - z(385) = z(9)*z(376) + z(11)*z(378); - z(386) = z(73)*z(172)*z(355) + z(74)*z(167)*z(352) + z(75)*z(167)*z(355) + z(76)*z(168)*z(352) + z(77)*z(168)*z(355) + z(78)*z(123)*z(171) + z(78)*z(167)*z(368) + z(78)*z(168)*z(370) + z(108)*z(167)*z(376) + z(108)*z(168)*z(378) + z(108)*z(171)*z(380) + z(121)*z(171)*z(352) + z(123)*z(171)*z(355) + 0.5*Fc*z(78)*z(381) + 0.5*Fc*z(72)*z(78)*z(374) + 0.5*Fc*z(78)*z(113)*z(382) + 0.5*Fc*z(78)*z(117)*z(383) + 0.5*Fc*z(108)*z(115)*z(382) + 0.5*Fc*z(108)*z(119)*z(383) - z(166)*z(352) - z(72)*z(172)*z(352) - z(78)*z(169)*z(371) - z(78)*z(170)*z(372) - z(108)*z(169)*z(384) - z(108)*z(170)*z(385) - z(113)*z(169)*z(352) - z(115)*z(169)*z(355) - z(117)*z(170)*z(352) - z(119)*z(170)*z(355) - 0.5*Fc*z(73)*z(108)*z(374) - 0.5*Fc*z(74)*z(78)*z(375) - 0.5*Fc*z(75)*z(108)*z(375) - 0.5*Fc*z(76)*z(78)*z(377) - 0.5*Fc*z(77)*z(108)*z(377) - 0.5*Fc*z(78)*z(121)*z(379) - 0.5*Fc*z(108)*z(123)*z(379) - z(95)*(z(76)*z(352)+z(77)*z(355)+z(78)*z(370)+z(87)*z(378)) - z(99)*(z(51)*z(56)+z(52)*z(53)+z(52)*z(351)+z(59)*z(369)); - z(387) = -z(53)*z(72) - z(67)*z(73); - z(388) = -z(72)*z(71) - z(73)*z(63); - z(389) = par.ForearmMass*(z(78)*z(91)+z(83)*z(94)+z(87)*z(388)+z(387)*z(91)); - z(390) = par.ForearmMass*(z(78)*z(83)+z(87)*z(387)); - z(391) = -z(54)*z(72) - z(68)*z(73); - z(392) = par.ForearmMass*(z(78)*z(84)+z(79)*z(83)+z(87)*z(391)+z(88)*z(387)); - z(393) = z(55)*z(72) - z(69)*z(73); - z(394) = par.ForearmMass*(z(78)*z(85)+z(80)*z(83)+z(87)*z(393)+z(89)*z(387)); - z(395) = par.ForearmMass*(z(81)*z(83)+z(86)*z(387)+par.UpparmLen*z(72)*z(78)-par.UpparmLen*z(73)*z(87)); - z(396) = 2*z(137)*z(115) + 2*z(138)*z(119) - 2*z(139)*z(73) - 2*z(145)*z(123) - 2*z(146)*z(75) - 2*z(147)*z(77); - z(397) = par.UpparmLen*z(396)/(z(157)^0.5*z(158)^2); - z(398) = z(111)*z(396)/(z(157)^0.5*z(158)^2); - z(399) = -z(49)*z(72) - z(50)*z(73); - z(400) = z(112)*z(396)/(z(157)^0.5*z(158)^2); - z(401) = -z(51)*z(72) - z(52)*z(73); - z(402) = par.TrunkLen*z(396)/(z(157)^0.5*z(158)^2); - z(403) = par.ForearmLen*z(396)/(z(157)^0.5*z(158)^2); - z(404) = par.ShankLen*z(396)/(z(157)^0.5*z(158)^2); - z(405) = par.ThighLen*z(396)/(z(157)^0.5*z(158)^2); - z(406) = z(1)*z(399) + z(2)*z(401); - z(407) = z(9)*z(399) + z(11)*z(401); - z(408) = z(72)*z(108)*z(172) + z(73)*z(78)*z(172) + z(73)*z(172)*z(387) + z(74)*z(83)*z(167) + z(75)*z(78)*z(167) + z(75)*z(167)*z(387) + z(76)*z(83)*z(168) + z(77)*z(78)*z(168) + z(77)*z(168)*z(387) + z(78)*z(123)*z(171) + z(83)*z(121)*z(171) + z(108)*z(167)*z(399) + z(108)*z(168)*z(401) + z(108)*z(171)*z(380) + z(123)*z(171)*z(387) + 0.5*Fc*z(78)*z(403) + 0.5*Fc*z(72)*z(78)*z(397) + 0.5*Fc*z(78)*z(113)*z(404) + 0.5*Fc*z(78)*z(117)*z(405) + 0.5*Fc*z(108)*z(115)*z(404) + 0.5*Fc*z(108)*z(119)*z(405) - z(83)*z(166) - z(72)*z(83)*z(172) - z(78)*z(115)*z(169) - z(78)*z(119)*z(170) - z(83)*z(113)*z(169) - z(83)*z(117)*z(170) - z(108)*z(169)*z(406) - z(108)*z(170)*z(407) - z(115)*z(169)*z(387) - z(119)*z(170)*z(387) - 0.5*Fc*z(73)*z(108)*z(397) - 0.5*Fc*z(74)*z(78)*z(398) - 0.5*Fc*z(75)*z(108)*z(398) - 0.5*Fc*z(76)*z(78)*z(400) - 0.5*Fc*z(77)*z(108)*z(400) - 0.5*Fc*z(78)*z(121)*z(402) - 0.5*Fc*z(108)*z(123)*z(402) - z(95)*(z(76)*z(83)+z(77)*z(78)+z(77)*z(387)+z(87)*z(401)); - z(409) = z(74)*z(79)*z(168) + z(75)*z(109)*z(168) + z(79)*z(167)*z(243) + z(109)*z(167)*z(253) + 0.5*Fc*z(79)*z(259) + 0.5*Fc*z(72)*z(79)*z(251) + 0.5*Fc*z(79)*z(113)*z(260) + 0.5*Fc*z(79)*z(117)*z(261) + 0.5*Fc*z(109)*z(115)*z(260) + 0.5*Fc*z(109)*z(119)*z(261) + par.ThighLen*(z(10)*z(106)+z(10)*z(264)-z(9)*z(258)-z(182)*z(105)) - z(175)*z(10) - z(79)*z(169)*z(244) - z(79)*z(170)*z(245) - z(109)*z(169)*z(262) - z(109)*z(170)*z(263) - 0.5*Fc*z(73)*z(109)*z(251) - 0.5*Fc*z(74)*z(79)*z(252) - 0.5*Fc*z(75)*z(109)*z(252) - 0.5*Fc*z(76)*z(79)*z(254) - 0.5*Fc*z(77)*z(109)*z(254) - 0.5*Fc*z(79)*z(121)*z(255) - 0.5*Fc*z(109)*z(123)*z(255) - z(95)*(z(74)*z(79)+z(75)*z(88)) - z(98)*(z(26)*z(45)+z(31)*z(46)) - z(99)*(z(49)*z(54)+z(50)*z(60)); - z(410) = z(233)*z(201) + par.TrunkInertia*z(187)*z(236) + z(205)*z(7)*z(6) + par.ForearmMass*(z(79)*z(275)+z(88)*z(277)) + par.TrunkMass*(z(26)*z(271)+z(31)*z(272)) + par.UpparmMass*(z(54)*z(273)+z(60)*z(274)); - z(411) = z(74)*z(79)*z(168) + z(75)*z(109)*z(168) + z(79)*z(167)*z(243) + z(109)*z(167)*z(253) + 0.5*Fc*z(79)*z(297) + 0.5*Fc*z(72)*z(79)*z(291) + 0.5*Fc*z(79)*z(113)*z(298) + 0.5*Fc*z(79)*z(117)*z(299) + 0.5*Fc*z(109)*z(115)*z(298) + 0.5*Fc*z(109)*z(119)*z(299) + par.ThighLen*(z(10)*z(106)+z(10)*z(301)-z(9)*z(296)-z(182)*z(105)) - z(175)*z(10) - z(79)*z(169)*z(285) - z(79)*z(170)*z(245) - z(109)*z(169)*z(300) - z(109)*z(170)*z(263) - 0.5*Fc*z(73)*z(109)*z(291) - 0.5*Fc*z(74)*z(79)*z(292) - 0.5*Fc*z(75)*z(109)*z(292) - 0.5*Fc*z(76)*z(79)*z(293) - 0.5*Fc*z(77)*z(109)*z(293) - 0.5*Fc*z(79)*z(121)*z(294) - 0.5*Fc*z(109)*z(123)*z(294) - z(95)*(z(74)*z(79)+z(75)*z(88)) - z(98)*(z(26)*z(45)+z(31)*z(46)) - z(99)*(z(49)*z(54)+z(50)*z(60)); - z(412) = z(303)*z(201) + par.TrunkInertia*z(187)*z(306) + par.ForearmMass*(z(79)*z(314)+z(88)*z(316)+z(321)*z(94)+z(322)*z(91)) + par.UpparmMass*(z(54)*z(312)+z(60)*z(313)+z(319)*z(66)-z(320)*z(63)) + par.TrunkMass*(z(26)*z(34)+z(31)*z(311)+par.ThighLen*z(23)*z(38)-par.ThighLen*z(24)*z(34)); - z(413) = par.ThighLen*par.TrunkMass; - z(414) = z(199)*z(303) + par.TrunkInertia*z(187)*z(303) + 2*par.ForearmMass*(z(79)*z(321)+z(88)*z(322)) + 2*par.UpparmMass*(z(54)*z(319)-z(60)*z(320)) + 2*z(413)*(z(23)*z(26)-z(24)*z(31)); - z(415) = z(200)*z(303) + par.TrunkInertia*z(187)*z(324) + z(413)*z(24)*z(30) + par.ForearmMass*(z(80)*z(321)+z(89)*z(322)) - par.UpparmMass*(z(55)*z(319)+z(61)*z(320)); - z(416) = par.ForearmMass*(z(81)*z(321)+z(86)*z(322)) - z(209)*z(320); - z(417) = z(73)*z(172)*z(322) + z(74)*z(167)*z(321) + z(75)*z(167)*z(322) + z(76)*z(168)*z(321) + z(77)*z(168)*z(322) + z(79)*z(167)*z(329) + z(79)*z(168)*z(332) + z(109)*z(167)*z(341) + z(109)*z(168)*z(343) + z(121)*z(171)*z(321) + z(123)*z(171)*z(322) + 0.5*Fc*z(79)*z(345) + 0.5*Fc*z(72)*z(79)*z(339) + 0.5*Fc*z(79)*z(113)*z(346) + 0.5*Fc*z(79)*z(117)*z(347) + 0.5*Fc*z(109)*z(115)*z(346) + 0.5*Fc*z(109)*z(119)*z(347) + z(99)*(z(52)*z(320)-z(51)*z(319)-z(54)*z(330)-z(60)*z(331)) - z(166)*z(321) - z(72)*z(172)*z(321) - z(79)*z(169)*z(333) - z(79)*z(170)*z(334) - z(109)*z(169)*z(348) - z(109)*z(170)*z(349) - z(113)*z(169)*z(321) - z(115)*z(169)*z(322) - z(117)*z(170)*z(321) - z(119)*z(170)*z(322) - 0.5*Fc*z(73)*z(109)*z(339) - 0.5*Fc*z(74)*z(79)*z(340) - 0.5*Fc*z(75)*z(109)*z(340) - 0.5*Fc*z(76)*z(79)*z(342) - 0.5*Fc*z(77)*z(109)*z(342) - 0.5*Fc*z(79)*z(121)*z(344) - 0.5*Fc*z(109)*z(123)*z(344) - z(95)*(z(76)*z(321)+z(77)*z(322)+z(79)*z(332)+z(88)*z(343)) - z(98)*(z(26)*z(48)+z(31)*z(186)+par.ThighLen*z(23)*z(47)-par.ThighLen*z(24)*z(48)); - z(418) = par.ForearmMass*(z(79)*z(354)+z(88)*z(356)+z(360)*z(94)+z(361)*z(91)) + par.UpparmMass*(z(54)*z(63)+z(57)*z(66)+z(60)*z(353)+z(359)*z(63)); - z(419) = 2*par.ForearmMass*(z(79)*z(360)+z(88)*z(361)) + 2*par.UpparmMass*(z(54)*z(57)+z(60)*z(359)); - z(420) = -par.ForearmMass*(z(79)*z(363)-z(80)*z(360)-z(88)*z(364)-z(89)*z(361)) - par.UpparmMass*(z(55)*z(57)+z(39)*z(43)*z(54)-z(61)*z(359)-z(39)*z(44)*z(60)); - z(421) = z(209)*z(359) + par.ForearmMass*(z(81)*z(360)+z(86)*z(361)); - z(422) = z(73)*z(172)*z(361) + z(74)*z(167)*z(360) + z(75)*z(167)*z(361) + z(76)*z(168)*z(360) + z(77)*z(168)*z(361) + z(79)*z(123)*z(171) + z(79)*z(167)*z(368) + z(79)*z(168)*z(370) + z(109)*z(167)*z(376) + z(109)*z(168)*z(378) + z(109)*z(171)*z(380) + z(121)*z(171)*z(360) + z(123)*z(171)*z(361) + 0.5*Fc*z(79)*z(381) + 0.5*Fc*z(72)*z(79)*z(374) + 0.5*Fc*z(79)*z(113)*z(382) + 0.5*Fc*z(79)*z(117)*z(383) + 0.5*Fc*z(109)*z(115)*z(382) + 0.5*Fc*z(109)*z(119)*z(383) - z(166)*z(360) - z(72)*z(172)*z(360) - z(79)*z(169)*z(371) - z(79)*z(170)*z(372) - z(109)*z(169)*z(384) - z(109)*z(170)*z(385) - z(113)*z(169)*z(360) - z(115)*z(169)*z(361) - z(117)*z(170)*z(360) - z(119)*z(170)*z(361) - 0.5*Fc*z(73)*z(109)*z(374) - 0.5*Fc*z(74)*z(79)*z(375) - 0.5*Fc*z(75)*z(109)*z(375) - 0.5*Fc*z(76)*z(79)*z(377) - 0.5*Fc*z(77)*z(109)*z(377) - 0.5*Fc*z(79)*z(121)*z(379) - 0.5*Fc*z(109)*z(123)*z(379) - z(95)*(z(76)*z(360)+z(77)*z(361)+z(79)*z(370)+z(88)*z(378)) - z(99)*(z(51)*z(57)+z(52)*z(54)+z(52)*z(359)+z(60)*z(369)); - z(423) = par.ForearmMass*(z(79)*z(91)+z(84)*z(94)+z(88)*z(388)+z(391)*z(91)); - z(424) = par.ForearmMass*(z(79)*z(84)+z(88)*z(391)); - z(425) = par.ForearmMass*(z(79)*z(85)+z(80)*z(84)+z(88)*z(393)+z(89)*z(391)); - z(426) = par.ForearmMass*(z(81)*z(84)+z(86)*z(391)+par.UpparmLen*z(72)*z(79)-par.UpparmLen*z(73)*z(88)); - z(427) = z(72)*z(109)*z(172) + z(73)*z(79)*z(172) + z(73)*z(172)*z(391) + z(74)*z(84)*z(167) + z(75)*z(79)*z(167) + z(75)*z(167)*z(391) + z(76)*z(84)*z(168) + z(77)*z(79)*z(168) + z(77)*z(168)*z(391) + z(79)*z(123)*z(171) + z(84)*z(121)*z(171) + z(109)*z(167)*z(399) + z(109)*z(168)*z(401) + z(109)*z(171)*z(380) + z(123)*z(171)*z(391) + 0.5*Fc*z(79)*z(403) + 0.5*Fc*z(72)*z(79)*z(397) + 0.5*Fc*z(79)*z(113)*z(404) + 0.5*Fc*z(79)*z(117)*z(405) + 0.5*Fc*z(109)*z(115)*z(404) + 0.5*Fc*z(109)*z(119)*z(405) - z(84)*z(166) - z(72)*z(84)*z(172) - z(79)*z(115)*z(169) - z(79)*z(119)*z(170) - z(84)*z(113)*z(169) - z(84)*z(117)*z(170) - z(109)*z(169)*z(406) - z(109)*z(170)*z(407) - z(115)*z(169)*z(391) - z(119)*z(170)*z(391) - 0.5*Fc*z(73)*z(109)*z(397) - 0.5*Fc*z(74)*z(79)*z(398) - 0.5*Fc*z(75)*z(109)*z(398) - 0.5*Fc*z(76)*z(79)*z(400) - 0.5*Fc*z(77)*z(109)*z(400) - 0.5*Fc*z(79)*z(121)*z(402) - 0.5*Fc*z(109)*z(123)*z(402) - z(95)*(z(76)*z(84)+z(77)*z(79)+z(77)*z(391)+z(88)*z(401)); - z(428) = par.TrunkInertia*z(188)*z(236) + 2*z(46)*(z(48)+z(184))*z(201); - z(429) = par.TrunkInertia*z(188)*z(233) + 2*z(46)*z(199)*(z(48)+z(184)); - z(430) = 2*z(188)*z(239) + 2*z(46)*z(200)*(z(48)+z(184)); - z(431) = z(98)*z(30)*z(46) + z(74)*z(80)*z(168) + z(75)*z(110)*z(168) + z(80)*z(167)*z(243) + z(110)*z(167)*z(253) + 0.5*Fc*z(80)*z(259) + 0.5*Fc*z(72)*z(80)*z(251) + 0.5*Fc*z(80)*z(113)*z(260) + 0.5*Fc*z(80)*z(117)*z(261) + 0.5*Fc*z(110)*z(115)*z(260) + 0.5*Fc*z(110)*z(119)*z(261) + z(99)*(z(49)*z(55)-z(50)*z(61)) - z(80)*z(169)*z(244) - z(80)*z(170)*z(245) - z(110)*z(169)*z(262) - z(110)*z(170)*z(263) - 0.5*Fc*z(73)*z(110)*z(251) - 0.5*Fc*z(74)*z(80)*z(252) - 0.5*Fc*z(75)*z(110)*z(252) - 0.5*Fc*z(76)*z(80)*z(254) - 0.5*Fc*z(77)*z(110)*z(254) - 0.5*Fc*z(80)*z(121)*z(255) - 0.5*Fc*z(110)*z(123)*z(255) - z(95)*(z(74)*z(80)+z(75)*z(89)); - z(432) = par.TrunkInertia*z(188)*z(236) + 2*z(46)*(z(48)+z(184))*z(201) + par.ForearmMass*(z(80)*z(275)+z(89)*z(277)) - par.TrunkMass*z(30)*z(272) - par.UpparmMass*(z(55)*z(273)-z(61)*z(274)); - z(433) = par.TrunkInertia*z(188)*z(233) + par.TrunkMass*z(30)*z(267) + 2*z(46)*z(199)*(z(48)+z(184)) + par.ForearmMass*(z(80)*z(270)+z(89)*z(276)) - par.UpparmMass*(z(55)*z(268)-z(61)*z(269)); - z(434) = z(98)*z(30)*z(46) + z(74)*z(80)*z(168) + z(75)*z(110)*z(168) + z(80)*z(167)*z(243) + z(110)*z(167)*z(253) + 0.5*Fc*z(80)*z(297) + 0.5*Fc*z(72)*z(80)*z(291) + 0.5*Fc*z(80)*z(113)*z(298) + 0.5*Fc*z(80)*z(117)*z(299) + 0.5*Fc*z(110)*z(115)*z(298) + 0.5*Fc*z(110)*z(119)*z(299) + z(99)*(z(49)*z(55)-z(50)*z(61)) - z(80)*z(169)*z(285) - z(80)*z(170)*z(245) - z(110)*z(169)*z(300) - z(110)*z(170)*z(263) - 0.5*Fc*z(73)*z(110)*z(291) - 0.5*Fc*z(74)*z(80)*z(292) - 0.5*Fc*z(75)*z(110)*z(292) - 0.5*Fc*z(76)*z(80)*z(293) - 0.5*Fc*z(77)*z(110)*z(293) - 0.5*Fc*z(80)*z(121)*z(294) - 0.5*Fc*z(110)*z(123)*z(294) - z(95)*(z(74)*z(80)+z(75)*z(89)); - z(435) = z(324)*z(201) + par.TrunkInertia*z(188)*z(306) + par.ForearmMass*(z(80)*z(314)+z(89)*z(316)) - par.TrunkMass*z(30)*z(311) - par.UpparmMass*(z(55)*z(312)-z(61)*z(313)); - z(436) = z(199)*z(324) + par.TrunkInertia*z(188)*z(303) + par.ForearmMass*(z(80)*z(310)+z(89)*z(315)) - par.TrunkMass*z(30)*z(307) - par.UpparmMass*(z(55)*z(308)-z(61)*z(309)); - z(437) = z(199)*z(324) + par.TrunkInertia*z(188)*z(303) + z(413)*z(24)*z(30) + par.ForearmMass*(z(80)*z(321)+z(89)*z(322)) - par.UpparmMass*(z(55)*z(319)+z(61)*z(320)); - z(438) = z(324)*(z(200)+par.TrunkInertia*z(188)); - z(439) = z(98)*z(30)*z(186) + z(80)*z(167)*z(329) + z(80)*z(168)*z(332) + z(110)*z(167)*z(341) + z(110)*z(168)*z(343) + 0.5*Fc*z(80)*z(345) + 0.5*Fc*z(72)*z(80)*z(339) + 0.5*Fc*z(80)*z(113)*z(346) + 0.5*Fc*z(80)*z(117)*z(347) + 0.5*Fc*z(110)*z(115)*z(346) + 0.5*Fc*z(110)*z(119)*z(347) + z(99)*(z(55)*z(330)-z(61)*z(331)) - z(80)*z(169)*z(333) - z(80)*z(170)*z(334) - z(110)*z(169)*z(348) - z(110)*z(170)*z(349) - 0.5*Fc*z(73)*z(110)*z(339) - 0.5*Fc*z(74)*z(80)*z(340) - 0.5*Fc*z(75)*z(110)*z(340) - 0.5*Fc*z(76)*z(80)*z(342) - 0.5*Fc*z(77)*z(110)*z(342) - 0.5*Fc*z(80)*z(121)*z(344) - 0.5*Fc*z(110)*z(123)*z(344) - z(95)*(z(80)*z(332)+z(89)*z(343)); - z(440) = -par.ForearmMass*(z(363)*z(94)-z(80)*z(354)-z(89)*z(356)-z(364)*z(91)) - par.UpparmMass*(z(55)*z(63)+z(39)*z(43)*z(66)-z(61)*z(353)-z(39)*z(44)*z(63)); - z(441) = 2*par.UpparmMass*z(39)*(z(43)*z(55)+z(44)*z(61)) - 2*par.ForearmMass*(z(80)*z(363)-z(89)*z(364)); - z(442) = z(209)*z(39)*z(44) - par.ForearmMass*(z(81)*z(363)-z(86)*z(364)); - z(443) = z(166)*z(363) + z(72)*z(172)*z(363) + z(73)*z(172)*z(364) + z(75)*z(167)*z(364) + z(77)*z(168)*z(364) + z(80)*z(123)*z(171) + z(80)*z(167)*z(368) + z(80)*z(168)*z(370) + z(110)*z(167)*z(376) + z(110)*z(168)*z(378) + z(110)*z(171)*z(380) + z(113)*z(169)*z(363) + z(117)*z(170)*z(363) + z(123)*z(171)*z(364) + 0.5*Fc*z(80)*z(381) + 0.5*Fc*z(72)*z(80)*z(374) + 0.5*Fc*z(80)*z(113)*z(382) + 0.5*Fc*z(80)*z(117)*z(383) + 0.5*Fc*z(110)*z(115)*z(382) + 0.5*Fc*z(110)*z(119)*z(383) + z(95)*(z(76)*z(363)-z(77)*z(364)-z(80)*z(370)-z(89)*z(378)) + z(99)*(z(52)*z(55)+z(39)*z(43)*z(51)-z(61)*z(369)-z(39)*z(44)*z(52)) - z(74)*z(167)*z(363) - z(76)*z(168)*z(363) - z(80)*z(169)*z(371) - z(80)*z(170)*z(372) - z(110)*z(169)*z(384) - z(110)*z(170)*z(385) - z(115)*z(169)*z(364) - z(119)*z(170)*z(364) - z(121)*z(171)*z(363) - 0.5*Fc*z(73)*z(110)*z(374) - 0.5*Fc*z(74)*z(80)*z(375) - 0.5*Fc*z(75)*z(110)*z(375) - 0.5*Fc*z(76)*z(80)*z(377) - 0.5*Fc*z(77)*z(110)*z(377) - 0.5*Fc*z(80)*z(121)*z(379) - 0.5*Fc*z(110)*z(123)*z(379); - z(444) = par.ForearmMass*(z(80)*z(91)+z(85)*z(94)+z(89)*z(388)+z(393)*z(91)); - z(445) = par.ForearmMass*(z(80)*z(85)+z(89)*z(393)); - z(446) = par.ForearmMass*(z(81)*z(85)+z(86)*z(393)+par.UpparmLen*z(72)*z(80)-par.UpparmLen*z(73)*z(89)); - z(447) = z(72)*z(110)*z(172) + z(73)*z(80)*z(172) + z(73)*z(172)*z(393) + z(74)*z(85)*z(167) + z(75)*z(80)*z(167) + z(75)*z(167)*z(393) + z(76)*z(85)*z(168) + z(77)*z(80)*z(168) + z(77)*z(168)*z(393) + z(80)*z(123)*z(171) + z(85)*z(121)*z(171) + z(110)*z(167)*z(399) + z(110)*z(168)*z(401) + z(110)*z(171)*z(380) + z(123)*z(171)*z(393) + 0.5*Fc*z(80)*z(403) + 0.5*Fc*z(72)*z(80)*z(397) + 0.5*Fc*z(80)*z(113)*z(404) + 0.5*Fc*z(80)*z(117)*z(405) + 0.5*Fc*z(110)*z(115)*z(404) + 0.5*Fc*z(110)*z(119)*z(405) - z(85)*z(166) - z(72)*z(85)*z(172) - z(80)*z(115)*z(169) - z(80)*z(119)*z(170) - z(85)*z(113)*z(169) - z(85)*z(117)*z(170) - z(110)*z(169)*z(406) - z(110)*z(170)*z(407) - z(115)*z(169)*z(393) - z(119)*z(170)*z(393) - 0.5*Fc*z(73)*z(110)*z(397) - 0.5*Fc*z(74)*z(80)*z(398) - 0.5*Fc*z(75)*z(110)*z(398) - 0.5*Fc*z(76)*z(80)*z(400) - 0.5*Fc*z(77)*z(110)*z(400) - 0.5*Fc*z(80)*z(121)*z(402) - 0.5*Fc*z(110)*z(123)*z(402) - z(95)*(z(76)*z(85)+z(77)*z(80)+z(77)*z(393)+z(89)*z(401)); - z(448) = z(74)*z(81)*z(168) + z(75)*z(107)*z(168) + z(81)*z(167)*z(243) + z(107)*z(167)*z(253) + 0.5*Fc*z(81)*z(259) + 0.5*Fc*z(72)*z(81)*z(251) + 0.5*Fc*z(81)*z(113)*z(260) + 0.5*Fc*z(81)*z(117)*z(261) + 0.5*Fc*z(107)*z(115)*z(260) + 0.5*Fc*z(107)*z(119)*z(261) - z(178)*z(50) - z(81)*z(169)*z(244) - z(81)*z(170)*z(245) - z(107)*z(169)*z(262) - z(107)*z(170)*z(263) - 0.5*Fc*z(73)*z(107)*z(251) - 0.5*Fc*z(74)*z(81)*z(252) - 0.5*Fc*z(75)*z(107)*z(252) - 0.5*Fc*z(76)*z(81)*z(254) - 0.5*Fc*z(77)*z(107)*z(254) - 0.5*Fc*z(81)*z(121)*z(255) - 0.5*Fc*z(107)*z(123)*z(255) - z(95)*(z(74)*z(81)+z(75)*z(86)); - z(449) = z(209)*z(274) + par.ForearmMass*(z(81)*z(275)+z(86)*z(277)); - z(450) = z(74)*z(81)*z(168) + z(75)*z(107)*z(168) + z(81)*z(167)*z(243) + z(107)*z(167)*z(253) + 0.5*Fc*z(81)*z(297) + 0.5*Fc*z(72)*z(81)*z(291) + 0.5*Fc*z(81)*z(113)*z(298) + 0.5*Fc*z(81)*z(117)*z(299) + 0.5*Fc*z(107)*z(115)*z(298) + 0.5*Fc*z(107)*z(119)*z(299) - z(178)*z(50) - z(81)*z(169)*z(285) - z(81)*z(170)*z(245) - z(107)*z(169)*z(300) - z(107)*z(170)*z(263) - 0.5*Fc*z(73)*z(107)*z(291) - 0.5*Fc*z(74)*z(81)*z(292) - 0.5*Fc*z(75)*z(107)*z(292) - 0.5*Fc*z(76)*z(81)*z(293) - 0.5*Fc*z(77)*z(107)*z(293) - 0.5*Fc*z(81)*z(121)*z(294) - 0.5*Fc*z(107)*z(123)*z(294) - z(95)*(z(74)*z(81)+z(75)*z(86)); - z(451) = z(209)*z(313) + par.ForearmMass*(z(81)*z(314)+z(86)*z(316)); - z(452) = z(81)*z(167)*z(329) + z(81)*z(168)*z(332) + z(107)*z(167)*z(341) + z(107)*z(168)*z(343) + 0.5*Fc*z(81)*z(345) + 0.5*Fc*z(72)*z(81)*z(339) + 0.5*Fc*z(81)*z(113)*z(346) + 0.5*Fc*z(81)*z(117)*z(347) + 0.5*Fc*z(107)*z(115)*z(346) + 0.5*Fc*z(107)*z(119)*z(347) - z(178)*z(331) - z(81)*z(169)*z(333) - z(81)*z(170)*z(334) - z(107)*z(169)*z(348) - z(107)*z(170)*z(349) - 0.5*Fc*z(73)*z(107)*z(339) - 0.5*Fc*z(74)*z(81)*z(340) - 0.5*Fc*z(75)*z(107)*z(340) - 0.5*Fc*z(76)*z(81)*z(342) - 0.5*Fc*z(77)*z(107)*z(342) - 0.5*Fc*z(81)*z(121)*z(344) - 0.5*Fc*z(107)*z(123)*z(344) - z(95)*(z(81)*z(332)+z(86)*z(343)); - z(453) = z(209)*z(353) + par.ForearmMass*(z(81)*z(354)+z(86)*z(356)); - z(454) = z(81)*z(123)*z(171) + z(81)*z(167)*z(368) + z(81)*z(168)*z(370) + z(107)*z(167)*z(376) + z(107)*z(168)*z(378) + z(107)*z(171)*z(380) + 0.5*Fc*z(81)*z(381) + 0.5*Fc*z(72)*z(81)*z(374) + 0.5*Fc*z(81)*z(113)*z(382) + 0.5*Fc*z(81)*z(117)*z(383) + 0.5*Fc*z(107)*z(115)*z(382) + 0.5*Fc*z(107)*z(119)*z(383) - z(178)*z(369) - z(81)*z(169)*z(371) - z(81)*z(170)*z(372) - z(107)*z(169)*z(384) - z(107)*z(170)*z(385) - 0.5*Fc*z(73)*z(107)*z(374) - 0.5*Fc*z(74)*z(81)*z(375) - 0.5*Fc*z(75)*z(107)*z(375) - 0.5*Fc*z(76)*z(81)*z(377) - 0.5*Fc*z(77)*z(107)*z(377) - 0.5*Fc*z(81)*z(121)*z(379) - 0.5*Fc*z(107)*z(123)*z(379) - z(95)*(z(81)*z(370)+z(86)*z(378)); - z(455) = par.ForearmMass*(z(81)*z(91)+z(86)*z(388)+par.UpparmLen*z(72)*z(94)-par.UpparmLen*z(73)*z(91)); - z(456) = par.ForearmMass*par.UpparmLen; - z(457) = z(456)*(z(72)*z(81)-z(73)*z(86)); - z(458) = z(72)*z(107)*z(172) + z(73)*z(81)*z(172) + z(75)*z(81)*z(167) + z(77)*z(81)*z(168) + z(81)*z(123)*z(171) + z(107)*z(167)*z(399) + z(107)*z(168)*z(401) + z(107)*z(171)*z(380) + 0.5*Fc*z(81)*z(403) + par.UpparmLen*z(72)*z(74)*z(167) + par.UpparmLen*z(72)*z(76)*z(168) + par.UpparmLen*z(72)*z(121)*z(171) + par.UpparmLen*z(73)*z(115)*z(169) + par.UpparmLen*z(73)*z(119)*z(170) + 0.5*Fc*z(72)*z(81)*z(397) + 0.5*Fc*z(81)*z(113)*z(404) + 0.5*Fc*z(81)*z(117)*z(405) + 0.5*Fc*z(107)*z(115)*z(404) + 0.5*Fc*z(107)*z(119)*z(405) - par.UpparmLen*z(72)*z(166) - z(81)*z(115)*z(169) - z(81)*z(119)*z(170) - z(107)*z(169)*z(406) - z(107)*z(170)*z(407) - par.UpparmLen*z(72)*z(113)*z(169) - par.UpparmLen*z(72)*z(117)*z(170) - par.UpparmLen*z(73)*z(75)*z(167) - par.UpparmLen*z(73)*z(77)*z(168) - par.UpparmLen*z(73)*z(123)*z(171) - par.UpparmLen*z(172)*z(72)^2 - par.UpparmLen*z(172)*z(73)^2 - 0.5*Fc*z(73)*z(107)*z(397) - 0.5*Fc*z(74)*z(81)*z(398) - 0.5*Fc*z(75)*z(107)*z(398) - 0.5*Fc*z(76)*z(81)*z(400) - 0.5*Fc*z(77)*z(107)*z(400) - 0.5*Fc*z(81)*z(121)*z(402) - 0.5*Fc*z(107)*z(123)*z(402) - z(95)*(z(77)*z(81)+z(86)*z(401)+par.UpparmLen*z(72)*z(76)-par.UpparmLen*z(73)*z(77)); - z(459) = 0.5*par.ForearmLen*(2*z(75)*z(168)+2*z(167)*z(253)+Fc*z(115)*z(260)+Fc*z(119)*z(261)-2*z(169)*z(262)-2*z(170)*z(263)-Fc*z(73)*z(251)-Fc*z(75)*z(252)-Fc*z(77)*z(254)-Fc*z(123)*z(255)) - z(180)*z(75); - z(460) = 0.5*par.ForearmLen*(2*z(75)*z(168)+2*z(167)*z(253)+Fc*z(115)*z(298)+Fc*z(119)*z(299)-2*z(169)*z(300)-2*z(170)*z(263)-Fc*z(73)*z(291)-Fc*z(75)*z(292)-Fc*z(77)*z(293)-Fc*z(123)*z(294)) - z(180)*z(75); - z(461) = 0.5*par.ForearmLen*(2*z(167)*z(341)+2*z(168)*z(343)+Fc*z(115)*z(346)+Fc*z(119)*z(347)-2*z(169)*z(348)-2*z(170)*z(349)-Fc*z(73)*z(339)-Fc*z(75)*z(340)-Fc*z(77)*z(342)-Fc*z(123)*z(344)) - z(180)*z(343); - z(462) = 0.5*par.ForearmLen*(2*z(167)*z(376)+2*z(168)*z(378)+2*z(171)*z(380)+Fc*z(115)*z(382)+Fc*z(119)*z(383)-2*z(169)*z(384)-2*z(170)*z(385)-Fc*z(73)*z(374)-Fc*z(75)*z(375)-Fc*z(77)*z(377)-Fc*z(123)*z(379)) - z(180)*z(378); - z(463) = 0.5*par.ForearmLen*(2*z(72)*z(172)+2*z(167)*z(399)+2*z(168)*z(401)+2*z(171)*z(380)+Fc*z(115)*z(404)+Fc*z(119)*z(405)-2*z(169)*z(406)-2*z(170)*z(407)-Fc*z(73)*z(397)-Fc*z(75)*z(398)-Fc*z(77)*z(400)-Fc*z(123)*z(402)) - z(180)*z(401); - z(464) = (z(137)*z(244)+z(138)*z(245)+z(141)*z(246)+z(142)*z(248)+z(143)*z(183)+z(144)*z(45)+z(149)*z(2)-z(146)*z(243)-z(147)*z(74)-z(148)*z(249)-z(150)*z(1)-z(152)*z(10)-z(153)*z(9)-z(155)*z(241)-z(156)*z(49))/(z(136)+2*z(137)*z(113)+2*z(138)*z(117)+2*z(139)*z(72)+2*z(140)*z(7)+2*z(141)*z(128)+2*z(142)*z(132)+2*z(143)*z(45)+2*z(144)*z(47)-2*z(145)*z(121)-2*z(146)*z(74)-2*z(147)*z(76)-2*z(148)*z(124)-2*z(149)*z(1)-2*z(150)*z(2)-2*z(151)*z(23)-2*z(152)*z(9)-2*z(153)*z(11)-2*z(154)*z(43)-2*z(155)*z(49)-2*z(156)*z(51))^0.5; - z(465) = (z(137)*z(285)+z(138)*z(245)+z(141)*z(286)+z(142)*z(288)+z(143)*z(183)+z(144)*z(45)-z(140)*z(8)-z(146)*z(243)-z(147)*z(74)-z(148)*z(289)-z(152)*z(10)-z(153)*z(9)-z(155)*z(241)-z(156)*z(49))/(z(136)+2*z(137)*z(113)+2*z(138)*z(117)+2*z(139)*z(72)+2*z(140)*z(7)+2*z(141)*z(128)+2*z(142)*z(132)+2*z(143)*z(45)+2*z(144)*z(47)-2*z(145)*z(121)-2*z(146)*z(74)-2*z(147)*z(76)-2*z(148)*z(124)-2*z(149)*z(1)-2*z(150)*z(2)-2*z(151)*z(23)-2*z(152)*z(9)-2*z(153)*z(11)-2*z(154)*z(43)-2*z(155)*z(49)-2*z(156)*z(51))^0.5; - z(466) = (z(137)*z(333)+z(138)*z(334)+z(141)*z(335)+z(142)*z(337)+z(143)*z(46)+z(144)*z(48)+z(151)*z(24)-z(146)*z(329)-z(147)*z(332)-z(148)*z(125)-z(155)*z(327)-z(156)*z(330))/(z(136)+2*z(137)*z(113)+2*z(138)*z(117)+2*z(139)*z(72)+2*z(140)*z(7)+2*z(141)*z(128)+2*z(142)*z(132)+2*z(143)*z(45)+2*z(144)*z(47)-2*z(145)*z(121)-2*z(146)*z(74)-2*z(147)*z(76)-2*z(148)*z(124)-2*z(149)*z(1)-2*z(150)*z(2)-2*z(151)*z(23)-2*z(152)*z(9)-2*z(153)*z(11)-2*z(154)*z(43)-2*z(155)*z(49)-2*z(156)*z(51))^0.5; - z(467) = (z(137)*z(371)+z(138)*z(372)+z(141)*z(129)+z(142)*z(133)+z(154)*z(44)-z(145)*z(123)-z(146)*z(368)-z(147)*z(370)-z(155)*z(50)-z(156)*z(52))/(z(136)+2*z(137)*z(113)+2*z(138)*z(117)+2*z(139)*z(72)+2*z(140)*z(7)+2*z(141)*z(128)+2*z(142)*z(132)+2*z(143)*z(45)+2*z(144)*z(47)-2*z(145)*z(121)-2*z(146)*z(74)-2*z(147)*z(76)-2*z(148)*z(124)-2*z(149)*z(1)-2*z(150)*z(2)-2*z(151)*z(23)-2*z(152)*z(9)-2*z(153)*z(11)-2*z(154)*z(43)-2*z(155)*z(49)-2*z(156)*z(51))^0.5; - z(468) = par.ForearmLen*(par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))/(z(136)+2*z(137)*z(113)+2*z(138)*z(117)+2*z(139)*z(72)+2*z(140)*z(7)+2*z(141)*z(128)+2*z(142)*z(132)+2*z(143)*z(45)+2*z(144)*z(47)-2*z(145)*z(121)-2*z(146)*z(74)-2*z(147)*z(76)-2*z(148)*z(124)-2*z(149)*z(1)-2*z(150)*z(2)-2*z(151)*z(23)-2*z(152)*z(9)-2*z(153)*z(11)-2*z(154)*z(43)-2*z(155)*z(49)-2*z(156)*z(51))^0.5; - z(469) = z(237) + z(238)*q1pp + z(238)*q2pp + z(240)*q3pp - z(265); - z(470) = z(278) + z(280)*q1pp + z(282)*q2pp + z(283)*q3pp + z(284)*q4pp + z(211)*z(276)*q5pp - z(302); - z(471) = z(317) + z(318)*q1pp + z(323)*q2pp + z(325)*q3pp + z(326)*q4pp + z(211)*z(315)*q5pp - z(350); - z(472) = z(357) + z(358)*q1pp + z(362)*q2pp + z(365)*q3pp + z(366)*q4pp + z(211)*z(355)*q5pp - z(386); - z(473) = z(389) + z(392)*q2pp + z(394)*q3pp + z(395)*q4pp + 2*z(390)*q1pp + z(211)*z(387)*q5pp - z(408); - z(474) = z(237) + z(238)*q1pp + z(238)*q2pp + z(240)*q3pp - z(409); - z(475) = z(410) + z(238)*q2pp + z(240)*q3pp + z(282)*q1pp - z(411); - z(476) = z(412) + z(323)*q1pp + z(414)*q2pp + z(415)*q3pp + z(416)*q4pp + z(211)*z(322)*q5pp - z(417); - z(477) = z(418) + z(362)*q1pp + z(419)*q2pp + z(420)*q3pp + z(421)*q4pp + z(211)*z(361)*q5pp - z(422); - z(478) = z(423) + z(392)*q1pp + z(425)*q3pp + z(426)*q4pp + 2*z(424)*q2pp + z(211)*z(391)*q5pp - z(427); - z(479) = z(428) + z(429)*q1pp + z(429)*q2pp + z(430)*q3pp - z(431); - z(480) = z(432) + z(429)*q2pp + z(430)*q3pp + z(433)*q1pp - z(434); - z(481) = z(435) + z(436)*q1pp + z(437)*q2pp + z(438)*q3pp - z(439); - z(482) = z(440) + z(365)*q1pp + z(420)*q2pp + z(441)*q3pp + z(442)*q4pp + z(211)*z(364)*q5pp - z(443); - z(483) = z(444) + z(394)*q1pp + z(425)*q2pp + z(446)*q4pp + 2*z(445)*q3pp + z(211)*z(393)*q5pp - z(447); - z(484) = z(449) + z(284)*q1pp - z(450); - z(485) = z(451) + z(326)*q1pp + z(416)*q2pp - z(452); - z(486) = z(453) + z(366)*q1pp + z(421)*q2pp + z(442)*q3pp - z(454); - z(487) = par.UpparmLen*z(211); - z(488) = z(455) + z(395)*q1pp + z(426)*q2pp + z(446)*q3pp + 2*z(457)*q4pp - z(458) - z(487)*z(73)*q5pp; - z(489) = z(211)*z(277) + z(211)*z(276)*q1pp - z(460); - z(490) = z(211)*z(316) + z(211)*z(315)*q1pp + z(211)*z(322)*q2pp - z(461); - z(491) = z(211)*z(356) + z(211)*z(355)*q1pp + z(211)*z(361)*q2pp + z(211)*z(364)*q3pp - z(462); - z(492) = z(211)*z(388) + z(211)*z(387)*q1pp + z(211)*z(391)*q2pp + z(211)*z(393)*q3pp - z(463) - z(487)*z(73)*q4pp; - z(493) = z(45)*z(46)*q1p + z(45)*z(46)*q2p + z(46)*z(232)*q1p + z(46)*z(232)*q2p + z(48)*z(183)*q1p + z(48)*z(183)*q2p + z(183)*z(184)*q1p + z(183)*z(184)*q2p + 2*z(46)*z(48)*q3p + 2*z(46)*z(184)*q3p + z(45)*z(194) + z(46)*z(197) + z(48)*z(192) + z(183)*z(195); + z(333) = -z(23)*z(22) - z(24)*z(16); + z(334) = z(43)*z(34) + z(44)*z(333); + z(335) = z(43)*z(333) - z(44)*z(34); + z(336) = z(72)*z(334) + z(73)*z(335); + z(337) = z(72)*z(331) - z(73)*z(330); + z(338) = z(72)*z(335) - z(73)*z(334); + z(339) = z(325)*z(237) + par.TrunkInertia*z(223)*z(328) + par.ForearmMass*(z(78)*z(336)+z(87)*z(338)+z(332)*z(94)+z(337)*z(91)) + par.TrunkMass*(z(25)*z(34)+z(28)*z(38)+z(32)*z(333)+z(329)*z(34)) + par.UpparmMass*(z(53)*z(334)+z(59)*z(335)+z(330)*z(66)+z(331)*z(63)); + z(340) = z(235)*z(325) + par.TrunkInertia*z(223)*z(325) + 2*par.ForearmMass*(z(78)*z(332)+z(87)*z(337)) + 2*par.TrunkMass*(z(25)*z(28)+z(32)*z(329)) + 2*par.UpparmMass*(z(53)*z(330)+z(59)*z(331)); + z(341) = par.ThighLen*(z(23)*z(43)-z(24)*z(44)); + z(342) = par.ThighLen*(z(23)*z(44)+z(24)*z(43)); + z(343) = z(72)*z(341) - z(73)*z(342); + z(344) = -z(72)*z(342) - z(73)*z(341); + z(345) = z(235)*z(325) + par.TrunkInertia*z(223)*z(325) + par.ForearmMass*(z(78)*z(343)+z(79)*z(332)+z(87)*z(344)+z(88)*z(337)) + par.TrunkMass*(z(26)*z(28)+z(31)*z(329)+par.ThighLen*z(23)*z(25)-par.ThighLen*z(24)*z(32)) - par.UpparmMass*(z(59)*z(342)-z(53)*z(341)-z(54)*z(330)-z(60)*z(331)); + z(346) = 2*z(46)*z(139) + 2*z(48)*z(148); + z(347) = z(236)*z(325) + par.TrunkInertia*z(223)*z(346) + par.ForearmMass*(z(80)*z(332)+z(89)*z(337)) - par.TrunkMass*z(30)*z(329) - par.UpparmMass*(z(55)*z(330)-z(61)*z(331)); + z(348) = z(245)*z(331) + par.ForearmMass*(z(81)*z(332)+z(86)*z(337)); + z(349) = 2*z(172)*z(156) + 2*z(173)*z(160) + 2*z(174)*z(162) + 2*z(176)*z(169) + 2*z(177)*z(46) + 2*z(178)*z(48) + 2*z(191)*z(24) - 2*z(179)*z(146) - 2*z(180)*z(153) - 2*z(181)*z(125) - 2*z(185)*z(140) - 2*z(186)*z(149); + z(350) = par.UpparmLen*z(349)/(z(198)^0.5*z(199)^2); + z(351) = z(111)*z(349)/(z(198)^0.5*z(199)^2); + z(352) = z(72)*z(143) - z(73)*z(140); + z(353) = z(112)*z(349)/(z(198)^0.5*z(199)^2); + z(354) = z(72)*z(150) - z(73)*z(149); + z(355) = par.TrunkLen*z(349)/(z(198)^0.5*z(199)^2); + z(356) = par.ForearmLen*z(349)/(z(198)^0.5*z(199)^2); + z(357) = par.ShankLen*z(349)/(z(198)^0.5*z(199)^2); + z(358) = par.ThighLen*z(349)/(z(198)^0.5*z(199)^2); + z(359) = z(1)*z(352) + z(2)*z(354); + z(360) = z(9)*z(352) + z(11)*z(354); + z(361) = z(73)*z(213)*z(337) + z(74)*z(208)*z(332) + z(75)*z(208)*z(337) + z(76)*z(209)*z(332) + z(77)*z(209)*z(337) + z(78)*z(146)*z(208) + z(78)*z(153)*z(209) + z(108)*z(208)*z(352) + z(108)*z(209)*z(354) + z(121)*z(212)*z(332) + z(123)*z(212)*z(337) + 0.5*Fc*z(78)*z(356) + 0.5*Fc*z(72)*z(78)*z(350) + 0.5*Fc*z(78)*z(113)*z(357) + 0.5*Fc*z(78)*z(117)*z(358) + 0.5*Fc*z(108)*z(115)*z(357) + 0.5*Fc*z(108)*z(119)*z(358) - z(207)*z(332) - z(72)*z(213)*z(332) - z(78)*z(156)*z(210) - z(78)*z(160)*z(211) - z(108)*z(210)*z(359) - z(108)*z(211)*z(360) - z(113)*z(210)*z(332) - z(115)*z(210)*z(337) - z(117)*z(211)*z(332) - z(119)*z(211)*z(337) - 0.5*Fc*z(73)*z(108)*z(350) - 0.5*Fc*z(74)*z(78)*z(351) - 0.5*Fc*z(75)*z(108)*z(351) - 0.5*Fc*z(76)*z(78)*z(353) - 0.5*Fc*z(77)*z(108)*z(353) - 0.5*Fc*z(78)*z(121)*z(355) - 0.5*Fc*z(108)*z(123)*z(355) - z(95)*(z(76)*z(332)+z(77)*z(337)+z(78)*z(153)+z(87)*z(354)) - z(98)*(z(25)*z(48)+z(28)*z(47)+z(32)*z(148)+z(48)*z(329)) - z(99)*(z(51)*z(330)+z(52)*z(331)+z(53)*z(149)+z(59)*z(150)); + z(362) = -z(25)*z(43) - z(41)*z(44); + z(363) = z(56)*z(72) + z(73)*z(362); + z(364) = -z(43)*z(42) - z(44)*z(34); + z(365) = z(72)*z(63) + z(73)*z(364); + z(366) = z(72)*z(362) - z(56)*z(73); + z(367) = z(72)*z(364) - z(73)*z(63); + z(368) = par.ForearmMass*(z(78)*z(365)+z(87)*z(367)+z(363)*z(94)+z(366)*z(91)) + par.UpparmMass*(z(53)*z(63)+z(56)*z(66)+z(59)*z(364)+z(362)*z(63)); + z(369) = 2*par.ForearmMass*(z(78)*z(363)+z(87)*z(366)) + 2*par.UpparmMass*(z(53)*z(56)+z(59)*z(362)); + z(370) = -z(26)*z(43) - z(40)*z(44); + z(371) = z(57)*z(72) + z(73)*z(370); + z(372) = z(72)*z(370) - z(57)*z(73); + z(373) = par.ForearmMass*(z(78)*z(371)+z(79)*z(363)+z(87)*z(372)+z(88)*z(366)) + par.UpparmMass*(z(53)*z(57)+z(54)*z(56)+z(59)*z(370)+z(60)*z(362)); + z(374) = z(39)*(z(43)*z(72)-z(44)*z(73)); + z(375) = z(39)*(z(43)*z(73)+z(44)*z(72)); + z(376) = -par.ForearmMass*(z(78)*z(374)-z(80)*z(363)-z(87)*z(375)-z(89)*z(366)) - par.UpparmMass*(z(55)*z(56)+z(39)*z(43)*z(53)-z(61)*z(362)-z(39)*z(44)*z(59)); + z(377) = z(245)*z(362) + par.ForearmMass*(z(81)*z(363)+z(86)*z(366)); + z(378) = 2*z(172)*z(155) + 2*z(173)*z(159) + 2*z(174)*z(129) + 2*z(176)*z(133) + 2*z(192)*z(44) - 2*z(179)*z(145) - 2*z(180)*z(152) - 2*z(185)*z(50) - 2*z(186)*z(52) - 2*z(190)*z(123); + z(379) = par.UpparmLen*z(378)/(z(198)^0.5*z(199)^2); + z(380) = z(111)*z(378)/(z(198)^0.5*z(199)^2); + z(381) = z(72)*z(144) - z(50)*z(73); + z(382) = z(112)*z(378)/(z(198)^0.5*z(199)^2); + z(383) = z(72)*z(151) - z(52)*z(73); + z(384) = par.TrunkLen*z(378)/(z(198)^0.5*z(199)^2); + z(385) = z(44)*z(73) - z(43)*z(72); + z(386) = par.ForearmLen*z(378)/(z(198)^0.5*z(199)^2); + z(387) = par.ShankLen*z(378)/(z(198)^0.5*z(199)^2); + z(388) = par.ThighLen*z(378)/(z(198)^0.5*z(199)^2); + z(389) = z(1)*z(381) + z(2)*z(383); + z(390) = z(9)*z(381) + z(11)*z(383); + z(391) = z(73)*z(213)*z(366) + z(74)*z(208)*z(363) + z(75)*z(208)*z(366) + z(76)*z(209)*z(363) + z(77)*z(209)*z(366) + z(78)*z(123)*z(212) + z(78)*z(145)*z(208) + z(78)*z(152)*z(209) + z(108)*z(208)*z(381) + z(108)*z(209)*z(383) + z(108)*z(212)*z(385) + z(121)*z(212)*z(363) + z(123)*z(212)*z(366) + 0.5*Fc*z(78)*z(386) + 0.5*Fc*z(72)*z(78)*z(379) + 0.5*Fc*z(78)*z(113)*z(387) + 0.5*Fc*z(78)*z(117)*z(388) + 0.5*Fc*z(108)*z(115)*z(387) + 0.5*Fc*z(108)*z(119)*z(388) - z(207)*z(363) - z(72)*z(213)*z(363) - z(78)*z(155)*z(210) - z(78)*z(159)*z(211) - z(108)*z(210)*z(389) - z(108)*z(211)*z(390) - z(113)*z(210)*z(363) - z(115)*z(210)*z(366) - z(117)*z(211)*z(363) - z(119)*z(211)*z(366) - 0.5*Fc*z(73)*z(108)*z(379) - 0.5*Fc*z(74)*z(78)*z(380) - 0.5*Fc*z(75)*z(108)*z(380) - 0.5*Fc*z(76)*z(78)*z(382) - 0.5*Fc*z(77)*z(108)*z(382) - 0.5*Fc*z(78)*z(121)*z(384) - 0.5*Fc*z(108)*z(123)*z(384) - z(95)*(z(76)*z(363)+z(77)*z(366)+z(78)*z(152)+z(87)*z(383)) - z(99)*(z(51)*z(56)+z(52)*z(53)+z(52)*z(362)+z(59)*z(151)); + z(392) = -z(53)*z(72) - z(67)*z(73); + z(393) = -z(72)*z(71) - z(73)*z(63); + z(394) = par.ForearmMass*(z(78)*z(91)+z(83)*z(94)+z(87)*z(393)+z(392)*z(91)); + z(395) = par.ForearmMass*(z(78)*z(83)+z(87)*z(392)); + z(396) = -z(54)*z(72) - z(68)*z(73); + z(397) = par.ForearmMass*(z(78)*z(84)+z(79)*z(83)+z(87)*z(396)+z(88)*z(392)); + z(398) = z(55)*z(72) - z(69)*z(73); + z(399) = par.ForearmMass*(z(78)*z(85)+z(80)*z(83)+z(87)*z(398)+z(89)*z(392)); + z(400) = par.ForearmMass*(z(81)*z(83)+z(86)*z(392)+par.UpparmLen*z(72)*z(78)-par.UpparmLen*z(73)*z(87)); + z(401) = 2*z(172)*z(115) + 2*z(173)*z(119) - 2*z(179)*z(75) - 2*z(180)*z(77) - 2*z(188)*z(73) - 2*z(190)*z(123); + z(402) = par.UpparmLen*z(401)/(z(198)^0.5*z(199)^2); + z(403) = z(111)*z(401)/(z(198)^0.5*z(199)^2); + z(404) = -z(49)*z(72) - z(50)*z(73); + z(405) = z(112)*z(401)/(z(198)^0.5*z(199)^2); + z(406) = -z(51)*z(72) - z(52)*z(73); + z(407) = par.TrunkLen*z(401)/(z(198)^0.5*z(199)^2); + z(408) = par.ForearmLen*z(401)/(z(198)^0.5*z(199)^2); + z(409) = par.ShankLen*z(401)/(z(198)^0.5*z(199)^2); + z(410) = par.ThighLen*z(401)/(z(198)^0.5*z(199)^2); + z(411) = z(1)*z(404) + z(2)*z(406); + z(412) = z(9)*z(404) + z(11)*z(406); + z(413) = z(72)*z(108)*z(213) + z(73)*z(78)*z(213) + z(73)*z(213)*z(392) + z(74)*z(83)*z(208) + z(75)*z(78)*z(208) + z(75)*z(208)*z(392) + z(76)*z(83)*z(209) + z(77)*z(78)*z(209) + z(77)*z(209)*z(392) + z(78)*z(123)*z(212) + z(83)*z(121)*z(212) + z(108)*z(208)*z(404) + z(108)*z(209)*z(406) + z(108)*z(212)*z(385) + z(123)*z(212)*z(392) + 0.5*Fc*z(78)*z(408) + 0.5*Fc*z(72)*z(78)*z(402) + 0.5*Fc*z(78)*z(113)*z(409) + 0.5*Fc*z(78)*z(117)*z(410) + 0.5*Fc*z(108)*z(115)*z(409) + 0.5*Fc*z(108)*z(119)*z(410) - z(83)*z(207) - z(72)*z(83)*z(213) - z(78)*z(115)*z(210) - z(78)*z(119)*z(211) - z(83)*z(113)*z(210) - z(83)*z(117)*z(211) - z(108)*z(210)*z(411) - z(108)*z(211)*z(412) - z(115)*z(210)*z(392) - z(119)*z(211)*z(392) - 0.5*Fc*z(73)*z(108)*z(402) - 0.5*Fc*z(74)*z(78)*z(403) - 0.5*Fc*z(75)*z(108)*z(403) - 0.5*Fc*z(76)*z(78)*z(405) - 0.5*Fc*z(77)*z(108)*z(405) - 0.5*Fc*z(78)*z(121)*z(407) - 0.5*Fc*z(108)*z(123)*z(407) - z(95)*(z(76)*z(83)+z(77)*z(78)+z(77)*z(392)+z(87)*z(406)); + z(414) = z(74)*z(79)*z(209) + z(75)*z(109)*z(209) + z(79)*z(147)*z(208) + z(109)*z(208)*z(280) + 0.5*Fc*z(79)*z(286) + 0.5*Fc*z(72)*z(79)*z(278) + 0.5*Fc*z(79)*z(113)*z(287) + 0.5*Fc*z(79)*z(117)*z(288) + 0.5*Fc*z(109)*z(115)*z(287) + 0.5*Fc*z(109)*z(119)*z(288) + par.ThighLen*(z(10)*z(106)+z(10)*z(291)-z(9)*z(285)-z(136)*z(105)) - z(216)*z(10) - z(79)*z(154)*z(210) - z(79)*z(158)*z(211) - z(109)*z(210)*z(289) - z(109)*z(211)*z(290) - 0.5*Fc*z(73)*z(109)*z(278) - 0.5*Fc*z(74)*z(79)*z(279) - 0.5*Fc*z(75)*z(109)*z(279) - 0.5*Fc*z(76)*z(79)*z(281) - 0.5*Fc*z(77)*z(109)*z(281) - 0.5*Fc*z(79)*z(121)*z(282) - 0.5*Fc*z(109)*z(123)*z(282) - z(95)*(z(74)*z(79)+z(75)*z(88)) - z(98)*(z(26)*z(45)+z(31)*z(46)) - z(99)*(z(49)*z(54)+z(50)*z(60)); + z(415) = z(269)*z(237) + par.TrunkInertia*z(223)*z(272) + z(241)*z(7)*z(6) + par.ForearmMass*(z(79)*z(302)+z(88)*z(304)) + par.TrunkMass*(z(26)*z(298)+z(31)*z(299)) + par.UpparmMass*(z(54)*z(300)+z(60)*z(301)); + z(416) = z(74)*z(79)*z(209) + z(75)*z(109)*z(209) + z(79)*z(147)*z(208) + z(109)*z(208)*z(280) + 0.5*Fc*z(79)*z(319) + 0.5*Fc*z(72)*z(79)*z(313) + 0.5*Fc*z(79)*z(113)*z(320) + 0.5*Fc*z(79)*z(117)*z(321) + 0.5*Fc*z(109)*z(115)*z(320) + 0.5*Fc*z(109)*z(119)*z(321) + par.ThighLen*(z(10)*z(106)+z(10)*z(323)-z(9)*z(318)-z(136)*z(105)) - z(216)*z(10) - z(79)*z(157)*z(210) - z(79)*z(158)*z(211) - z(109)*z(210)*z(322) - z(109)*z(211)*z(290) - 0.5*Fc*z(73)*z(109)*z(313) - 0.5*Fc*z(74)*z(79)*z(314) - 0.5*Fc*z(75)*z(109)*z(314) - 0.5*Fc*z(76)*z(79)*z(315) - 0.5*Fc*z(77)*z(109)*z(315) - 0.5*Fc*z(79)*z(121)*z(316) - 0.5*Fc*z(109)*z(123)*z(316) - z(95)*(z(74)*z(79)+z(75)*z(88)) - z(98)*(z(26)*z(45)+z(31)*z(46)) - z(99)*(z(49)*z(54)+z(50)*z(60)); + z(417) = z(325)*z(237) + par.TrunkInertia*z(223)*z(328) + par.ForearmMass*(z(79)*z(336)+z(88)*z(338)+z(343)*z(94)+z(344)*z(91)) + par.UpparmMass*(z(54)*z(334)+z(60)*z(335)+z(341)*z(66)-z(342)*z(63)) + par.TrunkMass*(z(26)*z(34)+z(31)*z(333)+par.ThighLen*z(23)*z(38)-par.ThighLen*z(24)*z(34)); + z(418) = par.ThighLen*par.TrunkMass; + z(419) = z(235)*z(325) + par.TrunkInertia*z(223)*z(325) + 2*par.ForearmMass*(z(79)*z(343)+z(88)*z(344)) + 2*par.UpparmMass*(z(54)*z(341)-z(60)*z(342)) + 2*z(418)*(z(23)*z(26)-z(24)*z(31)); + z(420) = z(236)*z(325) + par.TrunkInertia*z(223)*z(346) + z(418)*z(24)*z(30) + par.ForearmMass*(z(80)*z(343)+z(89)*z(344)) - par.UpparmMass*(z(55)*z(341)+z(61)*z(342)); + z(421) = par.ForearmMass*(z(81)*z(343)+z(86)*z(344)) - z(245)*z(342); + z(422) = z(73)*z(213)*z(344) + z(74)*z(208)*z(343) + z(75)*z(208)*z(344) + z(76)*z(209)*z(343) + z(77)*z(209)*z(344) + z(79)*z(146)*z(208) + z(79)*z(153)*z(209) + z(109)*z(208)*z(352) + z(109)*z(209)*z(354) + z(121)*z(212)*z(343) + z(123)*z(212)*z(344) + 0.5*Fc*z(79)*z(356) + 0.5*Fc*z(72)*z(79)*z(350) + 0.5*Fc*z(79)*z(113)*z(357) + 0.5*Fc*z(79)*z(117)*z(358) + 0.5*Fc*z(109)*z(115)*z(357) + 0.5*Fc*z(109)*z(119)*z(358) + z(99)*(z(52)*z(342)-z(51)*z(341)-z(54)*z(149)-z(60)*z(150)) - z(207)*z(343) - z(72)*z(213)*z(343) - z(79)*z(156)*z(210) - z(79)*z(160)*z(211) - z(109)*z(210)*z(359) - z(109)*z(211)*z(360) - z(113)*z(210)*z(343) - z(115)*z(210)*z(344) - z(117)*z(211)*z(343) - z(119)*z(211)*z(344) - 0.5*Fc*z(73)*z(109)*z(350) - 0.5*Fc*z(74)*z(79)*z(351) - 0.5*Fc*z(75)*z(109)*z(351) - 0.5*Fc*z(76)*z(79)*z(353) - 0.5*Fc*z(77)*z(109)*z(353) - 0.5*Fc*z(79)*z(121)*z(355) - 0.5*Fc*z(109)*z(123)*z(355) - z(95)*(z(76)*z(343)+z(77)*z(344)+z(79)*z(153)+z(88)*z(354)) - z(98)*(z(26)*z(48)+z(31)*z(148)+par.ThighLen*z(23)*z(47)-par.ThighLen*z(24)*z(48)); + z(423) = par.ForearmMass*(z(79)*z(365)+z(88)*z(367)+z(371)*z(94)+z(372)*z(91)) + par.UpparmMass*(z(54)*z(63)+z(57)*z(66)+z(60)*z(364)+z(370)*z(63)); + z(424) = 2*par.ForearmMass*(z(79)*z(371)+z(88)*z(372)) + 2*par.UpparmMass*(z(54)*z(57)+z(60)*z(370)); + z(425) = -par.ForearmMass*(z(79)*z(374)-z(80)*z(371)-z(88)*z(375)-z(89)*z(372)) - par.UpparmMass*(z(55)*z(57)+z(39)*z(43)*z(54)-z(61)*z(370)-z(39)*z(44)*z(60)); + z(426) = z(245)*z(370) + par.ForearmMass*(z(81)*z(371)+z(86)*z(372)); + z(427) = z(73)*z(213)*z(372) + z(74)*z(208)*z(371) + z(75)*z(208)*z(372) + z(76)*z(209)*z(371) + z(77)*z(209)*z(372) + z(79)*z(123)*z(212) + z(79)*z(145)*z(208) + z(79)*z(152)*z(209) + z(109)*z(208)*z(381) + z(109)*z(209)*z(383) + z(109)*z(212)*z(385) + z(121)*z(212)*z(371) + z(123)*z(212)*z(372) + 0.5*Fc*z(79)*z(386) + 0.5*Fc*z(72)*z(79)*z(379) + 0.5*Fc*z(79)*z(113)*z(387) + 0.5*Fc*z(79)*z(117)*z(388) + 0.5*Fc*z(109)*z(115)*z(387) + 0.5*Fc*z(109)*z(119)*z(388) - z(207)*z(371) - z(72)*z(213)*z(371) - z(79)*z(155)*z(210) - z(79)*z(159)*z(211) - z(109)*z(210)*z(389) - z(109)*z(211)*z(390) - z(113)*z(210)*z(371) - z(115)*z(210)*z(372) - z(117)*z(211)*z(371) - z(119)*z(211)*z(372) - 0.5*Fc*z(73)*z(109)*z(379) - 0.5*Fc*z(74)*z(79)*z(380) - 0.5*Fc*z(75)*z(109)*z(380) - 0.5*Fc*z(76)*z(79)*z(382) - 0.5*Fc*z(77)*z(109)*z(382) - 0.5*Fc*z(79)*z(121)*z(384) - 0.5*Fc*z(109)*z(123)*z(384) - z(95)*(z(76)*z(371)+z(77)*z(372)+z(79)*z(152)+z(88)*z(383)) - z(99)*(z(51)*z(57)+z(52)*z(54)+z(52)*z(370)+z(60)*z(151)); + z(428) = par.ForearmMass*(z(79)*z(91)+z(84)*z(94)+z(88)*z(393)+z(396)*z(91)); + z(429) = par.ForearmMass*(z(79)*z(84)+z(88)*z(396)); + z(430) = par.ForearmMass*(z(79)*z(85)+z(80)*z(84)+z(88)*z(398)+z(89)*z(396)); + z(431) = par.ForearmMass*(z(81)*z(84)+z(86)*z(396)+par.UpparmLen*z(72)*z(79)-par.UpparmLen*z(73)*z(88)); + z(432) = z(72)*z(109)*z(213) + z(73)*z(79)*z(213) + z(73)*z(213)*z(396) + z(74)*z(84)*z(208) + z(75)*z(79)*z(208) + z(75)*z(208)*z(396) + z(76)*z(84)*z(209) + z(77)*z(79)*z(209) + z(77)*z(209)*z(396) + z(79)*z(123)*z(212) + z(84)*z(121)*z(212) + z(109)*z(208)*z(404) + z(109)*z(209)*z(406) + z(109)*z(212)*z(385) + z(123)*z(212)*z(396) + 0.5*Fc*z(79)*z(408) + 0.5*Fc*z(72)*z(79)*z(402) + 0.5*Fc*z(79)*z(113)*z(409) + 0.5*Fc*z(79)*z(117)*z(410) + 0.5*Fc*z(109)*z(115)*z(409) + 0.5*Fc*z(109)*z(119)*z(410) - z(84)*z(207) - z(72)*z(84)*z(213) - z(79)*z(115)*z(210) - z(79)*z(119)*z(211) - z(84)*z(113)*z(210) - z(84)*z(117)*z(211) - z(109)*z(210)*z(411) - z(109)*z(211)*z(412) - z(115)*z(210)*z(396) - z(119)*z(211)*z(396) - 0.5*Fc*z(73)*z(109)*z(402) - 0.5*Fc*z(74)*z(79)*z(403) - 0.5*Fc*z(75)*z(109)*z(403) - 0.5*Fc*z(76)*z(79)*z(405) - 0.5*Fc*z(77)*z(109)*z(405) - 0.5*Fc*z(79)*z(121)*z(407) - 0.5*Fc*z(109)*z(123)*z(407) - z(95)*(z(76)*z(84)+z(77)*z(79)+z(77)*z(396)+z(88)*z(406)); + z(433) = par.TrunkInertia*z(224)*z(272) + 2*z(46)*(z(48)+z(138))*z(237); + z(434) = par.TrunkInertia*z(224)*z(269) + 2*z(46)*z(235)*(z(48)+z(138)); + z(435) = 2*z(224)*z(275) + 2*z(46)*z(236)*(z(48)+z(138)); + z(436) = z(98)*z(30)*z(46) + z(74)*z(80)*z(209) + z(75)*z(110)*z(209) + z(80)*z(147)*z(208) + z(110)*z(208)*z(280) + 0.5*Fc*z(80)*z(286) + 0.5*Fc*z(72)*z(80)*z(278) + 0.5*Fc*z(80)*z(113)*z(287) + 0.5*Fc*z(80)*z(117)*z(288) + 0.5*Fc*z(110)*z(115)*z(287) + 0.5*Fc*z(110)*z(119)*z(288) + z(99)*(z(49)*z(55)-z(50)*z(61)) - z(80)*z(154)*z(210) - z(80)*z(158)*z(211) - z(110)*z(210)*z(289) - z(110)*z(211)*z(290) - 0.5*Fc*z(73)*z(110)*z(278) - 0.5*Fc*z(74)*z(80)*z(279) - 0.5*Fc*z(75)*z(110)*z(279) - 0.5*Fc*z(76)*z(80)*z(281) - 0.5*Fc*z(77)*z(110)*z(281) - 0.5*Fc*z(80)*z(121)*z(282) - 0.5*Fc*z(110)*z(123)*z(282) - z(95)*(z(74)*z(80)+z(75)*z(89)); + z(437) = par.TrunkInertia*z(224)*z(272) + 2*z(46)*(z(48)+z(138))*z(237) + par.ForearmMass*(z(80)*z(302)+z(89)*z(304)) - par.TrunkMass*z(30)*z(299) - par.UpparmMass*(z(55)*z(300)-z(61)*z(301)); + z(438) = par.TrunkInertia*z(224)*z(269) + par.TrunkMass*z(30)*z(294) + 2*z(46)*z(235)*(z(48)+z(138)) + par.ForearmMass*(z(80)*z(297)+z(89)*z(303)) - par.UpparmMass*(z(55)*z(295)-z(61)*z(296)); + z(439) = z(98)*z(30)*z(46) + z(74)*z(80)*z(209) + z(75)*z(110)*z(209) + z(80)*z(147)*z(208) + z(110)*z(208)*z(280) + 0.5*Fc*z(80)*z(319) + 0.5*Fc*z(72)*z(80)*z(313) + 0.5*Fc*z(80)*z(113)*z(320) + 0.5*Fc*z(80)*z(117)*z(321) + 0.5*Fc*z(110)*z(115)*z(320) + 0.5*Fc*z(110)*z(119)*z(321) + z(99)*(z(49)*z(55)-z(50)*z(61)) - z(80)*z(157)*z(210) - z(80)*z(158)*z(211) - z(110)*z(210)*z(322) - z(110)*z(211)*z(290) - 0.5*Fc*z(73)*z(110)*z(313) - 0.5*Fc*z(74)*z(80)*z(314) - 0.5*Fc*z(75)*z(110)*z(314) - 0.5*Fc*z(76)*z(80)*z(315) - 0.5*Fc*z(77)*z(110)*z(315) - 0.5*Fc*z(80)*z(121)*z(316) - 0.5*Fc*z(110)*z(123)*z(316) - z(95)*(z(74)*z(80)+z(75)*z(89)); + z(440) = z(346)*z(237) + par.TrunkInertia*z(224)*z(328) + par.ForearmMass*(z(80)*z(336)+z(89)*z(338)) - par.TrunkMass*z(30)*z(333) - par.UpparmMass*(z(55)*z(334)-z(61)*z(335)); + z(441) = z(235)*z(346) + par.TrunkInertia*z(224)*z(325) + par.ForearmMass*(z(80)*z(332)+z(89)*z(337)) - par.TrunkMass*z(30)*z(329) - par.UpparmMass*(z(55)*z(330)-z(61)*z(331)); + z(442) = z(235)*z(346) + par.TrunkInertia*z(224)*z(325) + z(418)*z(24)*z(30) + par.ForearmMass*(z(80)*z(343)+z(89)*z(344)) - par.UpparmMass*(z(55)*z(341)+z(61)*z(342)); + z(443) = z(346)*(z(236)+par.TrunkInertia*z(224)); + z(444) = z(98)*z(30)*z(148) + z(80)*z(146)*z(208) + z(80)*z(153)*z(209) + z(110)*z(208)*z(352) + z(110)*z(209)*z(354) + 0.5*Fc*z(80)*z(356) + 0.5*Fc*z(72)*z(80)*z(350) + 0.5*Fc*z(80)*z(113)*z(357) + 0.5*Fc*z(80)*z(117)*z(358) + 0.5*Fc*z(110)*z(115)*z(357) + 0.5*Fc*z(110)*z(119)*z(358) + z(99)*(z(55)*z(149)-z(61)*z(150)) - z(80)*z(156)*z(210) - z(80)*z(160)*z(211) - z(110)*z(210)*z(359) - z(110)*z(211)*z(360) - 0.5*Fc*z(73)*z(110)*z(350) - 0.5*Fc*z(74)*z(80)*z(351) - 0.5*Fc*z(75)*z(110)*z(351) - 0.5*Fc*z(76)*z(80)*z(353) - 0.5*Fc*z(77)*z(110)*z(353) - 0.5*Fc*z(80)*z(121)*z(355) - 0.5*Fc*z(110)*z(123)*z(355) - z(95)*(z(80)*z(153)+z(89)*z(354)); + z(445) = -par.ForearmMass*(z(374)*z(94)-z(80)*z(365)-z(89)*z(367)-z(375)*z(91)) - par.UpparmMass*(z(55)*z(63)+z(39)*z(43)*z(66)-z(61)*z(364)-z(39)*z(44)*z(63)); + z(446) = 2*par.UpparmMass*z(39)*(z(43)*z(55)+z(44)*z(61)) - 2*par.ForearmMass*(z(80)*z(374)-z(89)*z(375)); + z(447) = z(245)*z(39)*z(44) - par.ForearmMass*(z(81)*z(374)-z(86)*z(375)); + z(448) = z(207)*z(374) + z(72)*z(213)*z(374) + z(73)*z(213)*z(375) + z(75)*z(208)*z(375) + z(77)*z(209)*z(375) + z(80)*z(123)*z(212) + z(80)*z(145)*z(208) + z(80)*z(152)*z(209) + z(110)*z(208)*z(381) + z(110)*z(209)*z(383) + z(110)*z(212)*z(385) + z(113)*z(210)*z(374) + z(117)*z(211)*z(374) + z(123)*z(212)*z(375) + 0.5*Fc*z(80)*z(386) + 0.5*Fc*z(72)*z(80)*z(379) + 0.5*Fc*z(80)*z(113)*z(387) + 0.5*Fc*z(80)*z(117)*z(388) + 0.5*Fc*z(110)*z(115)*z(387) + 0.5*Fc*z(110)*z(119)*z(388) + z(95)*(z(76)*z(374)-z(77)*z(375)-z(80)*z(152)-z(89)*z(383)) + z(99)*(z(52)*z(55)+z(39)*z(43)*z(51)-z(61)*z(151)-z(39)*z(44)*z(52)) - z(74)*z(208)*z(374) - z(76)*z(209)*z(374) - z(80)*z(155)*z(210) - z(80)*z(159)*z(211) - z(110)*z(210)*z(389) - z(110)*z(211)*z(390) - z(115)*z(210)*z(375) - z(119)*z(211)*z(375) - z(121)*z(212)*z(374) - 0.5*Fc*z(73)*z(110)*z(379) - 0.5*Fc*z(74)*z(80)*z(380) - 0.5*Fc*z(75)*z(110)*z(380) - 0.5*Fc*z(76)*z(80)*z(382) - 0.5*Fc*z(77)*z(110)*z(382) - 0.5*Fc*z(80)*z(121)*z(384) - 0.5*Fc*z(110)*z(123)*z(384); + z(449) = par.ForearmMass*(z(80)*z(91)+z(85)*z(94)+z(89)*z(393)+z(398)*z(91)); + z(450) = par.ForearmMass*(z(80)*z(85)+z(89)*z(398)); + z(451) = par.ForearmMass*(z(81)*z(85)+z(86)*z(398)+par.UpparmLen*z(72)*z(80)-par.UpparmLen*z(73)*z(89)); + z(452) = z(72)*z(110)*z(213) + z(73)*z(80)*z(213) + z(73)*z(213)*z(398) + z(74)*z(85)*z(208) + z(75)*z(80)*z(208) + z(75)*z(208)*z(398) + z(76)*z(85)*z(209) + z(77)*z(80)*z(209) + z(77)*z(209)*z(398) + z(80)*z(123)*z(212) + z(85)*z(121)*z(212) + z(110)*z(208)*z(404) + z(110)*z(209)*z(406) + z(110)*z(212)*z(385) + z(123)*z(212)*z(398) + 0.5*Fc*z(80)*z(408) + 0.5*Fc*z(72)*z(80)*z(402) + 0.5*Fc*z(80)*z(113)*z(409) + 0.5*Fc*z(80)*z(117)*z(410) + 0.5*Fc*z(110)*z(115)*z(409) + 0.5*Fc*z(110)*z(119)*z(410) - z(85)*z(207) - z(72)*z(85)*z(213) - z(80)*z(115)*z(210) - z(80)*z(119)*z(211) - z(85)*z(113)*z(210) - z(85)*z(117)*z(211) - z(110)*z(210)*z(411) - z(110)*z(211)*z(412) - z(115)*z(210)*z(398) - z(119)*z(211)*z(398) - 0.5*Fc*z(73)*z(110)*z(402) - 0.5*Fc*z(74)*z(80)*z(403) - 0.5*Fc*z(75)*z(110)*z(403) - 0.5*Fc*z(76)*z(80)*z(405) - 0.5*Fc*z(77)*z(110)*z(405) - 0.5*Fc*z(80)*z(121)*z(407) - 0.5*Fc*z(110)*z(123)*z(407) - z(95)*(z(76)*z(85)+z(77)*z(80)+z(77)*z(398)+z(89)*z(406)); + z(453) = z(74)*z(81)*z(209) + z(75)*z(107)*z(209) + z(81)*z(147)*z(208) + z(107)*z(208)*z(280) + 0.5*Fc*z(81)*z(286) + 0.5*Fc*z(72)*z(81)*z(278) + 0.5*Fc*z(81)*z(113)*z(287) + 0.5*Fc*z(81)*z(117)*z(288) + 0.5*Fc*z(107)*z(115)*z(287) + 0.5*Fc*z(107)*z(119)*z(288) - z(219)*z(50) - z(81)*z(154)*z(210) - z(81)*z(158)*z(211) - z(107)*z(210)*z(289) - z(107)*z(211)*z(290) - 0.5*Fc*z(73)*z(107)*z(278) - 0.5*Fc*z(74)*z(81)*z(279) - 0.5*Fc*z(75)*z(107)*z(279) - 0.5*Fc*z(76)*z(81)*z(281) - 0.5*Fc*z(77)*z(107)*z(281) - 0.5*Fc*z(81)*z(121)*z(282) - 0.5*Fc*z(107)*z(123)*z(282) - z(95)*(z(74)*z(81)+z(75)*z(86)); + z(454) = z(245)*z(301) + par.ForearmMass*(z(81)*z(302)+z(86)*z(304)); + z(455) = z(74)*z(81)*z(209) + z(75)*z(107)*z(209) + z(81)*z(147)*z(208) + z(107)*z(208)*z(280) + 0.5*Fc*z(81)*z(319) + 0.5*Fc*z(72)*z(81)*z(313) + 0.5*Fc*z(81)*z(113)*z(320) + 0.5*Fc*z(81)*z(117)*z(321) + 0.5*Fc*z(107)*z(115)*z(320) + 0.5*Fc*z(107)*z(119)*z(321) - z(219)*z(50) - z(81)*z(157)*z(210) - z(81)*z(158)*z(211) - z(107)*z(210)*z(322) - z(107)*z(211)*z(290) - 0.5*Fc*z(73)*z(107)*z(313) - 0.5*Fc*z(74)*z(81)*z(314) - 0.5*Fc*z(75)*z(107)*z(314) - 0.5*Fc*z(76)*z(81)*z(315) - 0.5*Fc*z(77)*z(107)*z(315) - 0.5*Fc*z(81)*z(121)*z(316) - 0.5*Fc*z(107)*z(123)*z(316) - z(95)*(z(74)*z(81)+z(75)*z(86)); + z(456) = z(245)*z(335) + par.ForearmMass*(z(81)*z(336)+z(86)*z(338)); + z(457) = z(81)*z(146)*z(208) + z(81)*z(153)*z(209) + z(107)*z(208)*z(352) + z(107)*z(209)*z(354) + 0.5*Fc*z(81)*z(356) + 0.5*Fc*z(72)*z(81)*z(350) + 0.5*Fc*z(81)*z(113)*z(357) + 0.5*Fc*z(81)*z(117)*z(358) + 0.5*Fc*z(107)*z(115)*z(357) + 0.5*Fc*z(107)*z(119)*z(358) - z(219)*z(150) - z(81)*z(156)*z(210) - z(81)*z(160)*z(211) - z(107)*z(210)*z(359) - z(107)*z(211)*z(360) - 0.5*Fc*z(73)*z(107)*z(350) - 0.5*Fc*z(74)*z(81)*z(351) - 0.5*Fc*z(75)*z(107)*z(351) - 0.5*Fc*z(76)*z(81)*z(353) - 0.5*Fc*z(77)*z(107)*z(353) - 0.5*Fc*z(81)*z(121)*z(355) - 0.5*Fc*z(107)*z(123)*z(355) - z(95)*(z(81)*z(153)+z(86)*z(354)); + z(458) = z(245)*z(364) + par.ForearmMass*(z(81)*z(365)+z(86)*z(367)); + z(459) = z(81)*z(123)*z(212) + z(81)*z(145)*z(208) + z(81)*z(152)*z(209) + z(107)*z(208)*z(381) + z(107)*z(209)*z(383) + z(107)*z(212)*z(385) + 0.5*Fc*z(81)*z(386) + 0.5*Fc*z(72)*z(81)*z(379) + 0.5*Fc*z(81)*z(113)*z(387) + 0.5*Fc*z(81)*z(117)*z(388) + 0.5*Fc*z(107)*z(115)*z(387) + 0.5*Fc*z(107)*z(119)*z(388) - z(219)*z(151) - z(81)*z(155)*z(210) - z(81)*z(159)*z(211) - z(107)*z(210)*z(389) - z(107)*z(211)*z(390) - 0.5*Fc*z(73)*z(107)*z(379) - 0.5*Fc*z(74)*z(81)*z(380) - 0.5*Fc*z(75)*z(107)*z(380) - 0.5*Fc*z(76)*z(81)*z(382) - 0.5*Fc*z(77)*z(107)*z(382) - 0.5*Fc*z(81)*z(121)*z(384) - 0.5*Fc*z(107)*z(123)*z(384) - z(95)*(z(81)*z(152)+z(86)*z(383)); + z(460) = par.ForearmMass*(z(81)*z(91)+z(86)*z(393)+par.UpparmLen*z(72)*z(94)-par.UpparmLen*z(73)*z(91)); + z(461) = par.ForearmMass*par.UpparmLen; + z(462) = z(461)*(z(72)*z(81)-z(73)*z(86)); + z(463) = z(72)*z(107)*z(213) + z(73)*z(81)*z(213) + z(75)*z(81)*z(208) + z(77)*z(81)*z(209) + z(81)*z(123)*z(212) + z(107)*z(208)*z(404) + z(107)*z(209)*z(406) + z(107)*z(212)*z(385) + 0.5*Fc*z(81)*z(408) + par.UpparmLen*z(72)*z(74)*z(208) + par.UpparmLen*z(72)*z(76)*z(209) + par.UpparmLen*z(72)*z(121)*z(212) + par.UpparmLen*z(73)*z(115)*z(210) + par.UpparmLen*z(73)*z(119)*z(211) + 0.5*Fc*z(72)*z(81)*z(402) + 0.5*Fc*z(81)*z(113)*z(409) + 0.5*Fc*z(81)*z(117)*z(410) + 0.5*Fc*z(107)*z(115)*z(409) + 0.5*Fc*z(107)*z(119)*z(410) - par.UpparmLen*z(72)*z(207) - z(81)*z(115)*z(210) - z(81)*z(119)*z(211) - z(107)*z(210)*z(411) - z(107)*z(211)*z(412) - par.UpparmLen*z(72)*z(113)*z(210) - par.UpparmLen*z(72)*z(117)*z(211) - par.UpparmLen*z(73)*z(75)*z(208) - par.UpparmLen*z(73)*z(77)*z(209) - par.UpparmLen*z(73)*z(123)*z(212) - par.UpparmLen*z(213)*z(72)^2 - par.UpparmLen*z(213)*z(73)^2 - 0.5*Fc*z(73)*z(107)*z(402) - 0.5*Fc*z(74)*z(81)*z(403) - 0.5*Fc*z(75)*z(107)*z(403) - 0.5*Fc*z(76)*z(81)*z(405) - 0.5*Fc*z(77)*z(107)*z(405) - 0.5*Fc*z(81)*z(121)*z(407) - 0.5*Fc*z(107)*z(123)*z(407) - z(95)*(z(77)*z(81)+z(86)*z(406)+par.UpparmLen*z(72)*z(76)-par.UpparmLen*z(73)*z(77)); + z(464) = 0.5*par.ForearmLen*(2*z(75)*z(209)+2*z(208)*z(280)+Fc*z(115)*z(287)+Fc*z(119)*z(288)-2*z(210)*z(289)-2*z(211)*z(290)-Fc*z(73)*z(278)-Fc*z(75)*z(279)-Fc*z(77)*z(281)-Fc*z(123)*z(282)) - z(221)*z(75); + z(465) = 0.5*par.ForearmLen*(2*z(75)*z(209)+2*z(208)*z(280)+Fc*z(115)*z(320)+Fc*z(119)*z(321)-2*z(210)*z(322)-2*z(211)*z(290)-Fc*z(73)*z(313)-Fc*z(75)*z(314)-Fc*z(77)*z(315)-Fc*z(123)*z(316)) - z(221)*z(75); + z(466) = 0.5*par.ForearmLen*(2*z(208)*z(352)+2*z(209)*z(354)+Fc*z(115)*z(357)+Fc*z(119)*z(358)-2*z(210)*z(359)-2*z(211)*z(360)-Fc*z(73)*z(350)-Fc*z(75)*z(351)-Fc*z(77)*z(353)-Fc*z(123)*z(355)) - z(221)*z(354); + z(467) = 0.5*par.ForearmLen*(2*z(208)*z(381)+2*z(209)*z(383)+2*z(212)*z(385)+Fc*z(115)*z(387)+Fc*z(119)*z(388)-2*z(210)*z(389)-2*z(211)*z(390)-Fc*z(73)*z(379)-Fc*z(75)*z(380)-Fc*z(77)*z(382)-Fc*z(123)*z(384)) - z(221)*z(383); + z(468) = 0.5*par.ForearmLen*(2*z(72)*z(213)+2*z(208)*z(404)+2*z(209)*z(406)+2*z(212)*z(385)+Fc*z(115)*z(409)+Fc*z(119)*z(410)-2*z(210)*z(411)-2*z(211)*z(412)-Fc*z(73)*z(402)-Fc*z(75)*z(403)-Fc*z(77)*z(405)-Fc*z(123)*z(407)) - z(221)*z(406); + z(469) = z(273) + z(274)*q1pp + z(274)*q2pp + z(276)*q3pp - z(292); + z(470) = z(305) + z(307)*q1pp + z(309)*q2pp + z(310)*q3pp + z(311)*q4pp + z(247)*z(303)*q5pp - z(324); + z(471) = z(339) + z(340)*q1pp + z(345)*q2pp + z(347)*q3pp + z(348)*q4pp + z(247)*z(337)*q5pp - z(361); + z(472) = z(368) + z(369)*q1pp + z(373)*q2pp + z(376)*q3pp + z(377)*q4pp + z(247)*z(366)*q5pp - z(391); + z(473) = z(394) + z(397)*q2pp + z(399)*q3pp + z(400)*q4pp + 2*z(395)*q1pp + z(247)*z(392)*q5pp - z(413); + z(474) = z(273) + z(274)*q1pp + z(274)*q2pp + z(276)*q3pp - z(414); + z(475) = z(415) + z(274)*q2pp + z(276)*q3pp + z(309)*q1pp - z(416); + z(476) = z(417) + z(345)*q1pp + z(419)*q2pp + z(420)*q3pp + z(421)*q4pp + z(247)*z(344)*q5pp - z(422); + z(477) = z(423) + z(373)*q1pp + z(424)*q2pp + z(425)*q3pp + z(426)*q4pp + z(247)*z(372)*q5pp - z(427); + z(478) = z(428) + z(397)*q1pp + z(430)*q3pp + z(431)*q4pp + 2*z(429)*q2pp + z(247)*z(396)*q5pp - z(432); + z(479) = z(433) + z(434)*q1pp + z(434)*q2pp + z(435)*q3pp - z(436); + z(480) = z(437) + z(434)*q2pp + z(435)*q3pp + z(438)*q1pp - z(439); + z(481) = z(440) + z(441)*q1pp + z(442)*q2pp + z(443)*q3pp - z(444); + z(482) = z(445) + z(376)*q1pp + z(425)*q2pp + z(446)*q3pp + z(447)*q4pp + z(247)*z(375)*q5pp - z(448); + z(483) = z(449) + z(399)*q1pp + z(430)*q2pp + z(451)*q4pp + 2*z(450)*q3pp + z(247)*z(398)*q5pp - z(452); + z(484) = z(454) + z(311)*q1pp - z(455); + z(485) = z(456) + z(348)*q1pp + z(421)*q2pp - z(457); + z(486) = z(458) + z(377)*q1pp + z(426)*q2pp + z(447)*q3pp - z(459); + z(487) = par.UpparmLen*z(247); + z(488) = z(460) + z(400)*q1pp + z(431)*q2pp + z(451)*q3pp + 2*z(462)*q4pp - z(463) - z(487)*z(73)*q5pp; + z(489) = z(247)*z(304) + z(247)*z(303)*q1pp - z(465); + z(490) = z(247)*z(338) + z(247)*z(337)*q1pp + z(247)*z(344)*q2pp - z(466); + z(491) = z(247)*z(367) + z(247)*z(366)*q1pp + z(247)*z(372)*q2pp + z(247)*z(375)*q3pp - z(467); + z(492) = z(247)*z(393) + z(247)*z(392)*q1pp + z(247)*z(396)*q2pp + z(247)*z(398)*q3pp - z(468) - z(487)*z(73)*q4pp; + z(493) = z(45)*z(46)*q1p + z(45)*z(46)*q2p + z(46)*z(268)*q1p + z(46)*z(268)*q2p + z(48)*z(137)*q1p + z(48)*z(137)*q2p + z(137)*z(138)*q1p + z(137)*z(138)*q2p + 2*z(46)*z(48)*q3p + 2*z(46)*z(138)*q3p + z(45)*z(230) + z(46)*z(233) + z(48)*z(228) + z(137)*z(231); z(494) = z(7)*(par.ShankLen*q1p+z(5)); z(495) = -z(21) - z(494) - par.ThighLen*z(18); z(496) = z(8)*(par.ShankLen*q1p+z(5)); @@ -547,7 +550,7 @@ z(506) = -z(17) - z(494) - par.ThighCM*z(18); z(507) = par.TrunkCM*q1p + par.TrunkCM*q2p + z(30)*q3p + z(497) + par.TrunkCM*(z(36)+z(37)); z(508) = z(500) - z(64) - par.UpparmCM*z(65); - z(509) = par.TrunkInertia*z(187)*z(493) + par.ForearmMass*(z(78)*z(504)+z(87)*z(505)) + par.ThighMass*(z(12)*z(506)+z(14)*z(496)) + par.TrunkMass*(z(25)*z(507)+z(32)*z(499)) + par.UpparmMass*(z(53)*z(508)+z(59)*z(502)); + z(509) = par.TrunkInertia*z(223)*z(493) + par.ForearmMass*(z(78)*z(504)+z(87)*z(505)) + par.ThighMass*(z(12)*z(506)+z(14)*z(496)) + par.TrunkMass*(z(25)*z(507)+z(32)*z(499)) + par.UpparmMass*(z(53)*z(508)+z(59)*z(502)); z(510) = par.a*par.Cseat; z(511) = z(510)*z(103)/z(102)^0.5; z(512) = z(9)*z(12)*z(511) + z(10)*z(20)*z(511) - par.Cseat*z(103)*(z(9)*z(20)+z(11)*z(12))/z(102)^0.5; @@ -562,10 +565,10 @@ z(521) = z(72)*z(518) - z(73)*z(517); z(522) = par.TrunkCM*q1p + par.TrunkCM*q2p + z(30)*q3p + par.TrunkCM*(z(36)+z(37)) - z(513); z(523) = z(516) - z(64) - par.UpparmCM*z(65); - z(524) = par.TrunkInertia*z(187)*z(493) + par.ForearmMass*(z(78)*z(520)+z(87)*z(521)) + par.TrunkMass*(z(25)*z(522)+z(32)*z(515)) + par.UpparmMass*(z(53)*z(523)+z(59)*z(518)) - par.ThighMass*z(12)*(z(17)+par.ThighCM*z(18)); + z(524) = par.TrunkInertia*z(223)*z(493) + par.ForearmMass*(z(78)*z(520)+z(87)*z(521)) + par.TrunkMass*(z(25)*z(522)+z(32)*z(515)) + par.UpparmMass*(z(53)*z(523)+z(59)*z(518)) - par.ThighMass*z(12)*(z(17)+par.ThighCM*z(18)); z(525) = z(510)*z(104)/z(102)^0.5; z(526) = z(9)*z(12)*z(525) + z(10)*z(20)*z(525) - par.Cseat*z(104)*(z(9)*z(20)+z(11)*z(12))/z(102)^0.5; - z(527) = z(45)*z(186)*q1p + z(45)*z(186)*q2p + z(46)*z(48)*q1p + z(46)*z(48)*q2p + z(46)*z(184)*q1p + z(46)*z(184)*q2p + z(183)*z(185)*q1p + z(183)*z(185)*q2p + 2*z(46)*z(185)*q3p + 2*z(48)*z(186)*q3p + 2*z(46)*z(195) + 2*z(48)*z(194); + z(527) = z(45)*z(148)*q1p + z(45)*z(148)*q2p + z(46)*z(48)*q1p + z(46)*z(48)*q2p + z(46)*z(138)*q1p + z(46)*z(138)*q2p + z(137)*z(139)*q1p + z(137)*z(139)*q2p + 2*z(46)*z(139)*q3p + 2*z(48)*z(148)*q3p + 2*z(46)*z(231) + 2*z(48)*z(230); z(528) = (1+z(29))*(par.TrunkLen*q1p+par.TrunkLen*q2p+z(39)*q3p) + z(39)*(z(36)+z(37)); z(529) = z(43)*z(528) - z(70) - par.UpparmLen*z(65); z(530) = z(72)*z(529) - z(44)*z(73)*z(528); @@ -573,53 +576,160 @@ z(532) = -z(73)*z(529) - z(44)*z(72)*z(528); z(533) = (1+z(29))*(par.TrunkCM*q1p+par.TrunkCM*q2p+z(30)*q3p) + z(30)*(z(36)+z(37)); z(534) = z(43)*z(528) - z(64) - par.UpparmCM*z(65); - z(535) = par.TrunkInertia*z(187)*z(527) + par.TrunkMass*z(25)*z(533) + par.ForearmMass*(z(78)*z(531)+z(87)*z(532)) + par.UpparmMass*(z(53)*z(534)-z(44)*z(59)*z(528)); + z(535) = par.TrunkInertia*z(223)*z(527) + par.TrunkMass*z(25)*z(533) + par.ForearmMass*(z(78)*z(531)+z(87)*z(532)) + par.UpparmMass*(z(53)*z(534)-z(44)*z(59)*z(528)); z(536) = z(72)*(z(70)+par.UpparmLen*z(65)); z(537) = -z(92) - z(536) - par.ForearmCM*z(93); z(538) = z(73)*(z(70)+par.UpparmLen*z(65)); z(539) = par.ForearmMass*(z(78)*z(537)+z(87)*z(538)) - par.UpparmMass*z(53)*(z(64)+par.UpparmCM*z(65)); z(540) = par.ForearmMass*z(78)*(z(92)+par.ForearmCM*z(93)); - z(541) = z(205)*z(496) + par.TrunkInertia*z(187)*z(493) + par.ForearmMass*(z(79)*z(504)+z(88)*z(505)) + par.TrunkMass*(z(26)*z(507)+z(31)*z(499)) + par.UpparmMass*(z(54)*z(508)+z(60)*z(502)); + z(541) = z(241)*z(496) + par.TrunkInertia*z(223)*z(493) + par.ForearmMass*(z(79)*z(504)+z(88)*z(505)) + par.TrunkMass*(z(26)*z(507)+z(31)*z(499)) + par.UpparmMass*(z(54)*z(508)+z(60)*z(502)); z(542) = par.ThighLen*(z(10)*z(511)-par.Cseat*z(9)*z(103)/z(102)^0.5); - z(543) = par.TrunkInertia*z(187)*z(493) + par.ForearmMass*(z(79)*z(520)+z(88)*z(521)) + par.TrunkMass*(z(26)*z(522)+z(31)*z(515)) + par.UpparmMass*(z(54)*z(523)+z(60)*z(518)); + z(543) = par.TrunkInertia*z(223)*z(493) + par.ForearmMass*(z(79)*z(520)+z(88)*z(521)) + par.TrunkMass*(z(26)*z(522)+z(31)*z(515)) + par.UpparmMass*(z(54)*z(523)+z(60)*z(518)); z(544) = par.ThighLen*(z(10)*z(525)-par.Cseat*z(9)*z(104)/z(102)^0.5); - z(545) = par.TrunkInertia*z(187)*z(527) + par.TrunkMass*z(26)*z(533) + par.ForearmMass*(z(79)*z(531)+z(88)*z(532)) + par.UpparmMass*(z(54)*z(534)-z(44)*z(60)*z(528)); + z(545) = par.TrunkInertia*z(223)*z(527) + par.TrunkMass*z(26)*z(533) + par.ForearmMass*(z(79)*z(531)+z(88)*z(532)) + par.UpparmMass*(z(54)*z(534)-z(44)*z(60)*z(528)); z(546) = par.ForearmMass*(z(79)*z(537)+z(88)*z(538)) - par.UpparmMass*z(54)*(z(64)+par.UpparmCM*z(65)); z(547) = par.ForearmMass*z(79)*(z(92)+par.ForearmCM*z(93)); - z(548) = par.TrunkInertia*z(188)*z(493) + par.ForearmMass*(z(80)*z(504)+z(89)*z(505)) - par.TrunkMass*z(30)*z(499) - par.UpparmMass*(z(55)*z(508)-z(61)*z(502)); - z(549) = par.TrunkInertia*z(188)*z(493) + par.ForearmMass*(z(80)*z(520)+z(89)*z(521)) - par.TrunkMass*z(30)*z(515) - par.UpparmMass*(z(55)*z(523)-z(61)*z(518)); - z(550) = par.TrunkInertia*z(188)*z(527) + par.ForearmMass*(z(80)*z(531)+z(89)*z(532)) - par.UpparmMass*(z(55)*z(534)+z(44)*z(61)*z(528)); + z(548) = par.TrunkInertia*z(224)*z(493) + par.ForearmMass*(z(80)*z(504)+z(89)*z(505)) - par.TrunkMass*z(30)*z(499) - par.UpparmMass*(z(55)*z(508)-z(61)*z(502)); + z(549) = par.TrunkInertia*z(224)*z(493) + par.ForearmMass*(z(80)*z(520)+z(89)*z(521)) - par.TrunkMass*z(30)*z(515) - par.UpparmMass*(z(55)*z(523)-z(61)*z(518)); + z(550) = par.TrunkInertia*z(224)*z(527) + par.ForearmMass*(z(80)*z(531)+z(89)*z(532)) - par.UpparmMass*(z(55)*z(534)+z(44)*z(61)*z(528)); z(551) = par.ForearmMass*(z(80)*z(537)+z(89)*z(538)) + par.UpparmMass*z(55)*(z(64)+par.UpparmCM*z(65)); z(552) = par.ForearmMass*z(80)*(z(92)+par.ForearmCM*z(93)); - z(553) = z(209)*z(502) + par.ForearmMass*(z(81)*z(504)+z(86)*z(505)); - z(554) = z(209)*z(518) + par.ForearmMass*(z(81)*z(520)+z(86)*z(521)); - z(555) = par.ForearmMass*(z(81)*z(531)+z(86)*z(532)) - z(209)*z(44)*z(528); + z(553) = z(245)*z(502) + par.ForearmMass*(z(81)*z(504)+z(86)*z(505)); + z(554) = z(245)*z(518) + par.ForearmMass*(z(81)*z(520)+z(86)*z(521)); + z(555) = par.ForearmMass*(z(81)*z(531)+z(86)*z(532)) - z(245)*z(44)*z(528); z(556) = par.ForearmMass*(z(81)*z(537)+z(86)*z(538)); z(557) = par.ForearmMass*z(81)*(z(92)+par.ForearmCM*z(93)); z(558) = z(509) - z(512); z(559) = z(524) - z(526); z(560) = z(541) - z(542); z(561) = z(543) - z(544); - z(562) = z(211)*z(505); - z(563) = z(211)*z(521); - z(564) = z(211)*z(532); - z(565) = z(211)*z(538); - z(566) = z(73)*z(108)*z(165) + z(74)*z(78)*z(160) + z(75)*z(108)*z(160) + z(76)*z(78)*z(161) + z(77)*z(108)*z(161) + z(78)*z(121)*z(164) + z(108)*z(123)*z(164) - z(78)*z(159) - z(72)*z(78)*z(165) - z(78)*z(113)*z(162) - z(78)*z(117)*z(163) - z(108)*z(115)*z(162) - z(108)*z(119)*z(163); - z(567) = z(73)*z(109)*z(165) + z(74)*z(79)*z(160) + z(75)*z(109)*z(160) + z(76)*z(79)*z(161) + z(77)*z(109)*z(161) + z(79)*z(121)*z(164) + z(109)*z(123)*z(164) - z(79)*z(159) - z(72)*z(79)*z(165) - z(79)*z(113)*z(162) - z(79)*z(117)*z(163) - z(109)*z(115)*z(162) - z(109)*z(119)*z(163); - z(568) = z(73)*z(110)*z(165) + z(74)*z(80)*z(160) + z(75)*z(110)*z(160) + z(76)*z(80)*z(161) + z(77)*z(110)*z(161) + z(80)*z(121)*z(164) + z(110)*z(123)*z(164) - z(80)*z(159) - z(72)*z(80)*z(165) - z(80)*z(113)*z(162) - z(80)*z(117)*z(163) - z(110)*z(115)*z(162) - z(110)*z(119)*z(163); - z(569) = z(73)*z(107)*z(165) + z(74)*z(81)*z(160) + z(75)*z(107)*z(160) + z(76)*z(81)*z(161) + z(77)*z(107)*z(161) + z(81)*z(121)*z(164) + z(107)*z(123)*z(164) - z(81)*z(159) - z(72)*z(81)*z(165) - z(81)*z(113)*z(162) - z(81)*z(117)*z(163) - z(107)*z(115)*z(162) - z(107)*z(119)*z(163); - z(570) = par.ForearmLen*(z(115)*z(162)+z(119)*z(163)-z(73)*z(165)-z(75)*z(160)-z(77)*z(161)-z(123)*z(164)); + z(562) = z(247)*z(505); + z(563) = z(247)*z(521); + z(564) = z(247)*z(532); + z(565) = z(247)*z(538); + z(566) = z(73)*z(108)*z(206) + z(74)*z(78)*z(201) + z(75)*z(108)*z(201) + z(76)*z(78)*z(202) + z(77)*z(108)*z(202) + z(78)*z(121)*z(205) + z(108)*z(123)*z(205) - z(78)*z(200) - z(72)*z(78)*z(206) - z(78)*z(113)*z(203) - z(78)*z(117)*z(204) - z(108)*z(115)*z(203) - z(108)*z(119)*z(204); + z(567) = z(73)*z(109)*z(206) + z(74)*z(79)*z(201) + z(75)*z(109)*z(201) + z(76)*z(79)*z(202) + z(77)*z(109)*z(202) + z(79)*z(121)*z(205) + z(109)*z(123)*z(205) - z(79)*z(200) - z(72)*z(79)*z(206) - z(79)*z(113)*z(203) - z(79)*z(117)*z(204) - z(109)*z(115)*z(203) - z(109)*z(119)*z(204); + z(568) = z(73)*z(110)*z(206) + z(74)*z(80)*z(201) + z(75)*z(110)*z(201) + z(76)*z(80)*z(202) + z(77)*z(110)*z(202) + z(80)*z(121)*z(205) + z(110)*z(123)*z(205) - z(80)*z(200) - z(72)*z(80)*z(206) - z(80)*z(113)*z(203) - z(80)*z(117)*z(204) - z(110)*z(115)*z(203) - z(110)*z(119)*z(204); + z(569) = z(73)*z(107)*z(206) + z(74)*z(81)*z(201) + z(75)*z(107)*z(201) + z(76)*z(81)*z(202) + z(77)*z(107)*z(202) + z(81)*z(121)*z(205) + z(107)*z(123)*z(205) - z(81)*z(200) - z(72)*z(81)*z(206) - z(81)*z(113)*z(203) - z(81)*z(117)*z(204) - z(107)*z(115)*z(203) - z(107)*z(119)*z(204); + z(570) = par.ForearmLen*(z(115)*z(203)+z(119)*z(204)-z(73)*z(206)-z(75)*z(201)-z(77)*z(202)-z(123)*z(205)); + z(571) = z(11)*z(23) - z(24)*z(136); + z(572) = z(43)*z(268) + z(44)*z(571); + z(573) = z(43)*z(571) - z(44)*z(268); + z(574) = z(72)*z(572) + z(73)*z(573); + z(575) = z(1)*(z(74)+z(574)) - z(2)*(z(76)+z(147)); + z(576) = z(9)*z(574) + z(10)*z(76) + z(11)*z(147) + z(74)*z(136) + 2*z(9)*z(74) + 2*z(10)*z(147); + z(577) = z(1)*(z(49)+z(572)) - z(2)*(z(51)+z(141)); + z(578) = z(1)*(z(51)+z(141)) + z(2)*(z(49)+z(572)); + z(579) = z(7)*z(577) - z(8)*z(578); + z(580) = z(1)*(z(45)+z(268)) - z(2)*(z(47)+z(137)); + z(581) = ((z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))^2-(z(172)*z(575)+z(173)*z(576)+z(174)*z(577)+z(175)*z(1)+z(176)*z(579)+z(177)*z(268)+z(178)*z(137)+z(182)*z(2)-z(179)*z(574)-z(180)*z(147)-z(181)*z(580)-z(183)*z(136)-z(184)*z(10)-z(185)*z(572)-z(186)*z(141))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(582) = z(1)*(z(74)+z(574)); + z(583) = z(1)*(z(49)+z(572)); + z(584) = z(2)*(z(49)+z(572)); + z(585) = z(7)*z(583) - z(7)*z(164) - z(8)*z(161) - z(8)*z(584); + z(586) = z(1)*(z(45)+z(268)); + z(587) = ((z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))-(z(172)*z(582)+z(173)*z(576)+z(174)*z(583)+z(176)*z(585)+z(177)*z(268)+z(178)*z(137)-z(179)*z(574)-z(180)*z(147)-z(181)*z(586)-z(183)*z(136)-z(184)*z(10)-z(185)*z(572)-z(186)*z(141))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(588) = par.ForearmLen*((par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))-(par.ShankLen*z(289)+par.ThighLen*z(290)-z(111)*z(280)-z(112)*z(75))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(589) = -z(10)*z(23) - z(24)*z(136); + z(590) = z(43)*z(138) + z(44)*z(589); + z(591) = z(43)*z(589) - z(44)*z(138); + z(592) = z(72)*z(590) + z(73)*z(591); + z(593) = z(1)*(z(48)+z(138)); + z(594) = z(1)*(z(153)+z(592)); + z(595) = z(9)*z(153) + z(9)*z(592) + z(10)*z(146) + z(11)*z(146); + z(596) = z(1)*(z(149)+z(590)); + z(597) = z(2)*(z(149)+z(590)); + z(598) = z(7)*z(596) - z(8)*z(597); + z(599) = ((z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))+(z(172)*z(594)+z(173)*z(595)+z(174)*z(596)+z(176)*z(598)+z(177)*z(138)+z(178)*z(46)-z(179)*z(592)-z(180)*z(146)-z(181)*z(593)-z(185)*z(590)-z(186)*z(140))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(600) = -z(43)*z(137) - z(44)*z(138); + z(601) = z(72)*z(142) + z(73)*z(600); + z(602) = z(1)*(z(152)+z(601)); + z(603) = z(9)*z(152) + z(9)*z(601) + z(10)*z(145) + z(11)*z(145); + z(604) = z(1)*(z(52)+z(142)); + z(605) = z(2)*(z(52)+z(142)); + z(606) = z(7)*z(604) - z(8)*z(605); + z(607) = ((z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))+(z(172)*z(602)+z(173)*z(603)+z(174)*z(604)+z(176)*z(606)-z(179)*z(601)-z(180)*z(145)-z(185)*z(142)-z(186)*z(50))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(608) = z(599)*q3p + z(607)*q4p - z(581)*q1p - z(587)*q2p - z(588)*q5p; + z(609) = z(1)*z(7)*(z(49)+z(572)) - z(7)*z(164) - z(8)*z(161) - z(2)*z(8)*(z(49)+z(572)); + z(610) = ((z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))-(z(173)*z(576)+z(176)*z(609)+z(177)*z(268)+z(178)*z(137)+z(172)*z(1)*(z(74)+z(574))+z(174)*z(1)*(z(49)+z(572))-z(179)*z(574)-z(180)*z(147)-z(183)*z(136)-z(184)*z(10)-z(185)*z(572)-z(186)*z(141)-z(181)*z(1)*(z(45)+z(268)))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(611) = z(1)*z(574) + z(2)*z(147); + z(612) = z(1)*z(572) + z(2)*z(141); + z(613) = z(1)*z(141) - z(2)*z(572); + z(614) = z(7)*z(612) + z(8)*z(613) + 2*z(7)*z(165) - 2*z(8)*z(163) - z(7)*z(128) - z(8)*z(130); + z(615) = z(1)*z(268) + z(2)*z(137); + z(616) = ((z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))^2-(z(172)*z(611)+z(173)*z(576)+z(174)*z(612)+z(176)*z(614)+z(177)*z(268)+z(178)*z(137)-z(179)*z(574)-z(180)*z(147)-z(181)*z(615)-z(183)*z(136)-z(184)*z(10)-z(185)*z(572)-z(186)*z(141)-z(189)*z(7))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(617) = par.ForearmLen*((par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))*(z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))-(par.ShankLen*z(322)+par.ThighLen*z(290)-z(111)*z(280)-z(112)*z(75))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(618) = z(1)*z(138) + z(2)*z(46); + z(619) = z(1)*z(592) + z(2)*z(146); + z(620) = z(1)*z(590) + z(2)*z(140); + z(621) = z(1)*z(140) - z(2)*z(590); + z(622) = z(7)*z(166) + z(7)*z(620) + z(8)*z(621) - z(8)*z(162); + z(623) = ((z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))*(z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))+(z(172)*z(619)+z(173)*z(595)+z(174)*z(620)+z(176)*z(622)+z(177)*z(138)+z(178)*z(46)-z(179)*z(592)-z(180)*z(146)-z(181)*z(618)-z(185)*z(590)-z(186)*z(140))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(624) = z(1)*z(601) + z(2)*z(145); + z(625) = z(1)*z(142) + z(2)*z(50); + z(626) = z(1)*z(50) - z(2)*z(142); + z(627) = z(7)*z(131) + z(7)*z(625) + z(8)*z(626) - z(8)*z(129); + z(628) = ((z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))*(z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))+(z(172)*z(624)+z(173)*z(603)+z(174)*z(625)+z(176)*z(627)-z(179)*z(601)-z(180)*z(145)-z(185)*z(142)-z(186)*z(50))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(629) = z(623)*q3p + z(628)*q4p - z(610)*q1p - z(616)*q2p - z(617)*q5p; + z(630) = (z(149)+z(590))*(z(1)*z(7)-z(2)*z(8)); + z(631) = ((z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))+(z(173)*z(595)+z(176)*z(630)+z(177)*z(138)+z(178)*z(46)+z(172)*z(1)*(z(153)+z(592))+z(174)*z(1)*(z(149)+z(590))-z(179)*z(592)-z(180)*z(146)-z(185)*z(590)-z(186)*z(140)-z(181)*z(1)*(z(48)+z(138)))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(632) = par.ForearmLen*((par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))*(z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))+(par.ShankLen*z(359)+par.ThighLen*z(360)-z(111)*z(352)-z(112)*z(354))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(633) = z(9)*z(24) - z(10)*z(23); + z(634) = z(43)*z(139) + z(44)*z(633); + z(635) = z(43)*z(633) - z(44)*z(139); + z(636) = z(72)*z(634) + z(73)*z(635); + z(637) = z(11)*z(24) - z(9)*z(23); + z(638) = z(43)*z(148) + z(44)*z(637); + z(639) = z(43)*z(637) - z(44)*z(148); + z(640) = z(72)*z(638) + z(73)*z(639); + z(641) = z(1)*z(139) + z(2)*z(148); + z(642) = z(1)*z(636) + z(2)*z(640); + z(643) = z(9)*z(636) + z(11)*z(640); + z(644) = z(1)*z(634) + z(2)*z(638); + z(645) = z(1)*z(638) - z(2)*z(634); + z(646) = z(7)*z(644) + z(8)*z(645); + z(647) = ((z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))^2+(z(179)*z(636)+z(180)*z(640)+z(181)*z(641)+z(185)*z(634)+z(186)*z(638)-z(172)*z(642)-z(173)*z(643)-z(174)*z(644)-z(176)*z(646)-z(177)*z(139)-z(178)*z(148)-z(191)*z(23))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(648) = -z(43)*z(46) - z(44)*z(139); + z(649) = z(72)*z(143) + z(73)*z(648); + z(650) = -z(43)*z(48) - z(44)*z(148); + z(651) = z(72)*z(150) + z(73)*z(650); + z(652) = z(1)*z(649) + z(2)*z(651); + z(653) = z(9)*z(649) + z(11)*z(651); + z(654) = z(1)*z(143) + z(2)*z(150); + z(655) = z(1)*z(150) - z(2)*z(143); + z(656) = z(7)*z(654) + z(8)*z(655); + z(657) = ((z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))*(z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))-(z(172)*z(652)+z(173)*z(653)+z(174)*z(654)+z(176)*z(656)-z(179)*z(649)-z(180)*z(651)-z(185)*z(143)-z(186)*z(150))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(658) = z(623)*q2p + z(631)*q1p + z(632)*q5p - z(647)*q3p - z(657)*q4p; + z(659) = (z(52)+z(142))*(z(1)*z(7)-z(2)*z(8)); + z(660) = ((z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))-(z(179)*z(601)+z(180)*z(145)+z(185)*z(142)+z(186)*z(50)-z(173)*z(603)-z(176)*z(659)-z(172)*z(1)*(z(152)+z(601))-z(174)*z(1)*(z(52)+z(142)))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(661) = par.ForearmLen*((par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))*(z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))+(par.ShankLen*z(389)+par.ThighLen*z(390)-par.TrunkLen*z(385)-z(111)*z(381)-z(112)*z(383))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(662) = z(44)*z(45) - z(43)*z(46); + z(663) = z(72)*z(144) + z(73)*z(662); + z(664) = z(44)*z(47) - z(43)*z(48); + z(665) = z(72)*z(151) + z(73)*z(664); + z(666) = z(1)*z(663) + z(2)*z(665); + z(667) = z(9)*z(663) + z(11)*z(665); + z(668) = z(1)*z(144) + z(2)*z(151); + z(669) = z(1)*z(151) - z(2)*z(144); + z(670) = z(7)*z(668) + z(8)*z(669); + z(671) = ((z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))^2+(z(179)*z(663)+z(180)*z(665)+z(185)*z(144)+z(186)*z(151)+z(190)*z(385)-z(172)*z(666)-z(173)*z(667)-z(174)*z(668)-z(176)*z(670)-z(192)*z(43))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(672) = z(628)*q2p + z(660)*q1p + z(661)*q5p - z(657)*q3p - z(671)*q4p; + z(673) = ((z(172)*z(115)+z(173)*z(119)-z(179)*z(75)-z(180)*z(77)-z(188)*z(73)-z(190)*z(123))*(z(172)*z(154)+z(173)*z(158)+z(174)*z(161)+z(175)*z(2)+z(176)*z(168)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(170)-z(182)*z(1)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49))+(z(179)*z(280)+z(180)*z(75)-z(173)*z(290)-z(172)*z(1)*(z(77)+z(280)))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(674) = ((z(172)*z(115)+z(173)*z(119)-z(179)*z(75)-z(180)*z(77)-z(188)*z(73)-z(190)*z(123))*(z(172)*z(157)+z(173)*z(158)+z(174)*z(163)+z(176)*z(167)+z(177)*z(137)+z(178)*z(45)-z(179)*z(147)-z(180)*z(74)-z(181)*z(171)-z(183)*z(10)-z(184)*z(9)-z(185)*z(141)-z(186)*z(49)-z(189)*z(8))-(z(172)*z(322)+z(173)*z(290)-z(179)*z(280)-z(180)*z(75))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(675) = par.ForearmLen*((par.ShankLen*z(115)+par.ThighLen*z(119)-par.TrunkLen*z(123)-par.UpparmLen*z(73)-z(111)*z(75)-z(112)*z(77))*(z(172)*z(115)+z(173)*z(119)-z(179)*z(75)-z(180)*z(77)-z(188)*z(73)-z(190)*z(123))-(par.ShankLen*z(411)+par.ThighLen*z(412)-par.TrunkLen*z(385)-par.UpparmLen*z(72)-z(111)*z(404)-z(112)*z(406))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(676) = ((z(172)*z(115)+z(173)*z(119)-z(179)*z(75)-z(180)*z(77)-z(188)*z(73)-z(190)*z(123))*(z(179)*z(146)+z(180)*z(153)+z(181)*z(125)+z(185)*z(140)+z(186)*z(149)-z(172)*z(156)-z(173)*z(160)-z(174)*z(162)-z(176)*z(169)-z(177)*z(46)-z(178)*z(48)-z(191)*z(24))+(z(172)*z(359)+z(173)*z(360)-z(179)*z(352)-z(180)*z(354))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(677) = ((z(172)*z(115)+z(173)*z(119)-z(179)*z(75)-z(180)*z(77)-z(188)*z(73)-z(190)*z(123))*(z(179)*z(145)+z(180)*z(152)+z(185)*z(50)+z(186)*z(52)+z(190)*z(123)-z(172)*z(155)-z(173)*z(159)-z(174)*z(129)-z(176)*z(133)-z(192)*z(44))+(z(172)*z(389)+z(173)*z(390)-z(179)*z(381)-z(180)*z(383)-z(190)*z(385))*(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43)))/(z(187)+2*z(172)*z(113)+2*z(173)*z(117)+2*z(174)*z(128)+2*z(176)*z(132)+2*z(177)*z(45)+2*z(178)*z(47)+2*z(188)*z(72)+2*z(189)*z(7)-2*z(175)*z(1)-2*z(179)*z(74)-2*z(180)*z(76)-2*z(181)*z(124)-2*z(182)*z(2)-2*z(183)*z(9)-2*z(184)*z(11)-2*z(185)*z(49)-2*z(186)*z(51)-2*z(190)*z(121)-2*z(191)*z(23)-2*z(192)*z(43))^1.5; + z(678) = z(676)*q3p + z(677)*q4p - z(673)*q1p - z(674)*q2p - z(675)*q5p; %=========================================================================== - f(1) = z(213) + z(203)*q1pp + z(206)*q2pp + z(207)*q3pp + z(210)*q4pp + z(212)*q5pp - z(174); - f(2) = z(219) + z(206)*q1pp + z(215)*q2pp + z(216)*q3pp + z(217)*q4pp + z(218)*q5pp - z(176); - f(3) = z(225) + z(220)*q1pp + z(221)*q2pp + z(222)*q3pp + z(223)*q4pp + z(224)*q5pp - z(177); - f(4) = z(229) + z(210)*q1pp + z(217)*q2pp + z(223)*q3pp + z(227)*q4pp + z(228)*q5pp - z(179); - f(5) = z(231) + z(230)*q5pp + z(212)*q1pp + z(218)*q2pp + z(224)*q3pp + z(228)*q4pp - z(181); - f(6) = L; + f(1) = z(249) + z(239)*q1pp + z(242)*q2pp + z(243)*q3pp + z(246)*q4pp + z(248)*q5pp - z(215); + f(2) = z(255) + z(242)*q1pp + z(251)*q2pp + z(252)*q3pp + z(253)*q4pp + z(254)*q5pp - z(217); + f(3) = z(261) + z(256)*q1pp + z(257)*q2pp + z(258)*q3pp + z(259)*q4pp + z(260)*q5pp - z(218); + f(4) = z(265) + z(246)*q1pp + z(253)*q2pp + z(259)*q3pp + z(263)*q4pp + z(264)*q5pp - z(220); + f(5) = z(267) + z(266)*q5pp + z(248)*q1pp + z(254)*q2pp + z(260)*q3pp + z(264)*q4pp - z(222); df_dq(1,1) = z(469); df_dq(1,2) = z(470); df_dq(1,3) = z(471); @@ -635,21 +745,16 @@ df_dq(3,3) = z(481); df_dq(3,4) = z(482); df_dq(3,5) = z(483); - df_dq(4,1) = -z(448); + df_dq(4,1) = -z(453); df_dq(4,2) = z(484); df_dq(4,3) = z(485); df_dq(4,4) = z(486); df_dq(4,5) = z(488); - df_dq(5,1) = -z(459); + df_dq(5,1) = -z(464); df_dq(5,2) = z(489); df_dq(5,3) = z(490); df_dq(5,4) = z(491); df_dq(5,5) = z(492); - df_dq(6,1) = z(464); - df_dq(6,2) = z(465); - df_dq(6,3) = z(466); - df_dq(6,4) = z(467); - df_dq(6,5) = z(468); df_dqd(1,1) = z(558); df_dqd(1,2) = z(559); df_dqd(1,3) = z(535); @@ -675,47 +780,46 @@ df_dqd(5,3) = z(564); df_dqd(5,4) = z(565); df_dqd(5,5) = 0; - df_dqd(6,1) = 0; - df_dqd(6,2) = 0; - df_dqd(6,3) = 0; - df_dqd(6,4) = 0; - df_dqd(6,5) = 0; - df_dqdd(1,1) = z(203); - df_dqdd(1,2) = z(206); - df_dqdd(1,3) = z(207); - df_dqdd(1,4) = z(210); - df_dqdd(1,5) = z(212); - df_dqdd(2,1) = z(206); - df_dqdd(2,2) = z(215); - df_dqdd(2,3) = z(216); - df_dqdd(2,4) = z(217); - df_dqdd(2,5) = z(218); - df_dqdd(3,1) = z(220); - df_dqdd(3,2) = z(221); - df_dqdd(3,3) = z(222); - df_dqdd(3,4) = z(223); - df_dqdd(3,5) = z(224); - df_dqdd(4,1) = z(210); - df_dqdd(4,2) = z(217); - df_dqdd(4,3) = z(223); - df_dqdd(4,4) = z(227); - df_dqdd(4,5) = z(228); - df_dqdd(5,1) = z(212); - df_dqdd(5,2) = z(218); - df_dqdd(5,3) = z(224); - df_dqdd(5,4) = z(228); - df_dqdd(5,5) = z(230); - df_dqdd(6,1) = 0; - df_dqdd(6,2) = 0; - df_dqdd(6,3) = 0; - df_dqdd(6,4) = 0; - df_dqdd(6,5) = 0; + df_dqdd(1,1) = z(239); + df_dqdd(1,2) = z(242); + df_dqdd(1,3) = z(243); + df_dqdd(1,4) = z(246); + df_dqdd(1,5) = z(248); + df_dqdd(2,1) = z(242); + df_dqdd(2,2) = z(251); + df_dqdd(2,3) = z(252); + df_dqdd(2,4) = z(253); + df_dqdd(2,5) = z(254); + df_dqdd(3,1) = z(256); + df_dqdd(3,2) = z(257); + df_dqdd(3,3) = z(258); + df_dqdd(3,4) = z(259); + df_dqdd(3,5) = z(260); + df_dqdd(4,1) = z(246); + df_dqdd(4,2) = z(253); + df_dqdd(4,3) = z(259); + df_dqdd(4,4) = z(263); + df_dqdd(4,5) = z(264); + df_dqdd(5,1) = z(248); + df_dqdd(5,2) = z(254); + df_dqdd(5,3) = z(260); + df_dqdd(5,4) = z(264); + df_dqdd(5,5) = z(266); df_dFc(1) = -z(566); df_dFc(2) = -z(567); df_dFc(3) = -z(568); df_dFc(4) = -z(569); df_dFc(5) = z(570); - df_dFc(6) = 0; + dL_dq(1,1) = z(193); + dL_dq(1,2) = z(196); + dL_dq(1,3) = -z(194); + dL_dq(1,4) = -z(195); + dL_dq(1,5) = z(197); + dLdot_dq(1,1) = z(608); + dLdot_dq(1,2) = z(629); + dLdot_dq(1,3) = z(658); + dLdot_dq(1,4) = z(672); + dLdot_dq(1,5) = z(678); stick(1,1) = par.Xankle; stick(1,2) = par.Yankle; stick(2,1) = par.Xankle + par.ShankLen*z(1); From 9fc0fa7e6a29ce7615192ab7d967ced1306d21b2 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Fri, 16 Feb 2018 11:45:26 -0500 Subject: [PATCH 10/23] tmp.avi removed and added to .gitignore --- model/.gitignore | 1 + model/tmp.avi | Bin 2376408 -> 0 bytes 2 files changed, 1 insertion(+) delete mode 100644 model/tmp.avi diff --git a/model/.gitignore 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zzPVHTom<7I{q~HyErL-qo-nG&0Hb=&o;S6BqaLHKKFX-E*BKSnGU^_t`BVEj?DbrF zo`l2ap;Oi8T-{I>Ok+th65WXG~`69k964?`9ABn7tuaiXHjjxwPUWBik zM9#<8Pa@0X>nM?@iTn&-hlzX> zUyq5*j<3r^?!nh*BKP6zG?5MQ^_s}$__|HxOZfUtPzU-ya3jIaMhZo&HiB5%U`0U~e2`vM|A#rp#yFT?u;BCp2#1tRC- zeFKq~;r#=V~sV2k%3O zdM|gM2^S%9wL|E{ST3u@ji&iYw&)E$T4_dMC8wSe?;VEc%MY%AiQ59 zas%Es5m^QApNM=I@1uzP5bvjmJO}Tqi0p>Zlc?;eL68Spb4-#1r?+c0Sh4+Uj@&1v>m+(H4$gFrjNn|&?uO#vZyuT#!9=y*a@-w2}#QOy~yzeBoN8tS@ zkvZ``l*o>FKT6~>ye}oP65gK@`4Zlz5_wFC(T@^&C*HRb`4Qf~5?LDWV~Knk?`MhJ zgZH&W-i-IRM81vpxkR3h_q#+sjQ71nuEqObBCFtiFp;m|{Vyq_jAH{Mqh*%|MziClsA*+f>t`)wj$#QSa{ z58?eckxlVFoX9zNKTc$Eye}uR58j^>`5oS;6L}5ZuM;^D@7syYiudnC-iP<`L@vSm zc_Pc>eLazb@&2C3eR!WwWJA2)C-ObK?SaRiY&@#6_1Z^Dl&hh Date: Fri, 16 Feb 2018 13:13:39 -0500 Subject: [PATCH 11/23] Simple change The name of one of the output was not the name it used in the function. --- model/dynfun.m | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/model/dynfun.m b/model/dynfun.m index 7317c9c..73ad812 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -1,4 +1,4 @@ - function [f, dfdx, dfdxdot, dfdu, L, dLdq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix + function [f, dfdx, dfdxdot, dfdu, L, Ldot] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix % The 13 dynamics equations of the system, in the form % f(x, dx/dt, u) = 0 % where x contains the 13 state variables and u are the 5 joint torques @@ -38,6 +38,9 @@ [z, dz_dq, dz_dqd, dz_dqdd, dz_dFc, L, dL_dq, dLdot_dq] = rowerdynamics(q,qd,qdd,x(13),model.parameters);% inverse dynamics so gives us the z(torques) Ldot = dL_dq * qd; + + + % multibody dynamics f(8:12) = z - u; dfdx(8:12, 2:6) = dz_dq; From 5b5379912c9a471b45b120a73b14e0f0b0ffc06e Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Tue, 20 Feb 2018 16:24:51 -0500 Subject: [PATCH 12/23] mytest.m now tests dynfun.m and rowerdynamics.m --- model/dynfun.m | 2 +- model/makerowerdynamics.m | 2 +- model/mytest.m | 104 +++++++++++++++++++++++++++++++++++++- model/rowerdynamics.m | 4 +- 4 files changed, 107 insertions(+), 5 deletions(-) diff --git a/model/dynfun.m b/model/dynfun.m index 7317c9c..91ffc0e 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -1,4 +1,4 @@ - function [f, dfdx, dfdxdot, dfdu, L, dLdq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix + function [f, dfdx, dfdxdot, dfdu, L, dL_dq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix % The 13 dynamics equations of the system, in the form % f(x, dx/dt, u) = 0 % where x contains the 13 state variables and u are the 5 joint torques diff --git a/model/makerowerdynamics.m b/model/makerowerdynamics.m index 0b28382..0fa1645 100644 --- a/model/makerowerdynamics.m +++ b/model/makerowerdynamics.m @@ -99,7 +99,7 @@ fprintf(fid2,' df_dq = sparse(df_dq);\n'); fprintf(fid2,' df_dqd = sparse(df_dqd);\n'); fprintf(fid2,' df_dqdd = sparse(df_dqdd);\n'); - fprintf(fid2,' df_dFc = sparse(df_dFc);\n'); + fprintf(fid2,' df_dFc = transpose(sparse(df_dFc));\n'); fprintf(fid2,'\nend \n'); fclose(fid2); diff --git a/model/mytest.m b/model/mytest.m index 440b7ef..a3bcd92 100644 --- a/model/mytest.m +++ b/model/mytest.m @@ -5,6 +5,96 @@ addpath('../tools'); [~,~,~, model.parameters] = datainterp2; + + % test the derivatives of dynfun.m + disp('Testing dynfun.m'); + x = rand(13,1); + xd = rand(13,1); + u = rand(5,1); + [f, df_dx, df_dxd, df_du, L, dL_dq] = dynfun(x, xd, u); + df_dx_num = zeros(13,13); + df_dxd_num = zeros(13,13); + df_du_num = zeros(13,5); + dL_dq_num = zeros(1,5); + hh = 1e-7; + for i = 1:13 + save = x(i); + x(i) = x(i) + hh; + [fh,~,~,~,Lh] = dynfun(x, xd, u); + df_dx_num(:,i) = (fh - f)/hh; + if (i>=2) && (i<=6) + dL_dq_num(1,i-1) = (Lh - L)/hh; + end + x(i) = save; + %--------------------- + save = xd(i); + xd(i) = xd(i) + hh; + fh = dynfun(x, xd, u); + df_dxd_num(:,i) = (fh - f)/hh; + xd(i) = save; + end + for i = 1:5 + save = u(i); + u(i) = u(i) + hh; + fh = dynfun(x, xd, u); + df_du_num(:,i) = (fh - f)/hh; + u(i) = save; + end + fprintf('Max. error in df_dx: '); matcompare(df_dx, df_dx_num); + fprintf('Max. error in df_dxd: '); matcompare(df_dxd, df_dxd_num); + fprintf('Max. error in df_du: '); matcompare(df_du, df_du_num); + fprintf('Max. error in dL_dq: '); matcompare(dL_dq, dL_dq_num); + + + % test the derivatives of rowerdynamics.m + disp('Testing rowerdynamics.m...'); + q = rand(5,1); + qd = rand(5,1); + qdd = rand(5,1); + Fc = rand(1,1); + [f, df_dq, df_dqd, df_dqdd, df_dFc, L, dL_dq, dLdot_dq] = rowerdynamics(q,qd,qdd,Fc,model.parameters); + df_dq_num = zeros(5,5); + df_dqd_num = zeros(5,5); + df_dqdd_num = zeros(5,5); + df_dFc_num = zeros(5,1); + dL_dq_num = zeros(1,5); + dLdot_dq_num = zeros(1,5); + Ldot = dL_dq * qd; + hh = 1e-7; + for i = 1:5 + save = q(i); + q(i) = q(i) + hh; + [fh,~,~,~,~,Lh,dL_dqh] = rowerdynamics(q,qd,qdd,Fc,model.parameters); + df_dq_num(:,i) = (fh - f)/hh; + dL_dq_num(:,i) = (Lh - L)/hh; + Ldoth = dL_dqh * qd; + dLdot_dq_num(:,i) = (Ldoth - Ldot)/hh; + q(i) = save; + %----------------------- + save = qd(i); + qd(i) = qd(i) + hh; + fh = rowerdynamics(q,qd,qdd,Fc,model.parameters); + df_dqd_num(:,i) = (fh - f)/hh; + qd(i) = save; + %----------------------- + save = qdd(i); + qdd(i) = qdd(i) + hh; + fh = rowerdynamics(q,qd,qdd,Fc,model.parameters); + df_dqdd_num(:,i) = (fh - f)/hh; + qdd(i) = save; + end + save = Fc; + Fc = Fc + hh; + fh = rowerdynamics(q,qd,qdd,Fc,model.parameters); + df_dFc_num(:,1) = (fh - f)/hh; + Fc = save; + fprintf('Max. error in df_dq: '); matcompare(df_dq, df_dq_num); + fprintf('Max. error in df_dqd: '); matcompare(df_dqd, df_dqd_num); + fprintf('Max. error in df_dqdd: '); matcompare(df_dqdd, df_dqdd_num); + fprintf('Max. error in df_dFc: '); matcompare(df_dFc, df_dFc_num); + fprintf('Max. error in dL_dq: '); matcompare(dL_dq, dL_dq_num); + fprintf('Max. error in dLdot_dq: '); matcompare(dLdot_dq, dLdot_dq_num); + keyboard % choose a suitable initial condition: realistic joint angles, and choose flywheel position y(1) % to be equal to the L that comes from these joint angles @@ -86,4 +176,16 @@ end end -%======================================================================= +%==================================================================== + function matcompare(a,b) + % compares two matrices and prints element that has greatest difference + if (size(a,1) == 1) + irow = 1; + [maxerr,icol] = max(abs(a-b)); + else + [maxerr,irow] = max(abs(a-b)); + [maxerr,icol] = max(maxerr); + irow = irow(icol); + end + fprintf('%9.6f at %d %d (%9.6f vs. %9.6f)\n', full(maxerr), irow, icol, full(a(irow,icol)), full(b(irow,icol))); + end diff --git a/model/rowerdynamics.m b/model/rowerdynamics.m index 12da1ce..43f2452 100644 --- a/model/rowerdynamics.m +++ b/model/rowerdynamics.m @@ -1,4 +1,4 @@ -% This file was generated by makerowerdynamics.m on 15-Feb-2018 19:25:34 +% This file was generated by makerowerdynamics.m on 20-Feb-2018 16:03:12 function [f, df_dq, df_dqd, df_dqdd, df_dFc, L, dL_dq, dLdot_dq, stick] = rowerdynamics(q,qd,qdd,Fc,par); % % Input: @@ -838,6 +838,6 @@ df_dq = sparse(df_dq); df_dqd = sparse(df_dqd); df_dqdd = sparse(df_dqdd); - df_dFc = sparse(df_dFc); + df_dFc = transpose(sparse(df_dFc)); end From 5ab4d83f5c9cb422aa53bc6a2a46a9ea8e48e005 Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Tue, 20 Feb 2018 16:31:03 -0500 Subject: [PATCH 13/23] Changed dynfun.m --- model/dynfun.m | 7 ------- 1 file changed, 7 deletions(-) diff --git a/model/dynfun.m b/model/dynfun.m index 7397183..b233e36 100644 --- a/model/dynfun.m +++ b/model/dynfun.m @@ -1,8 +1,4 @@ -<<<<<<< HEAD function [f, dfdx, dfdxdot, dfdu, L, dL_dq] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix -======= - function [f, dfdx, dfdxdot, dfdu, L, Ldot] = dynfun(x, xdot, u)%dLdx (x2 to 6 which are the angles) dLdq 1 by 5 matrix ->>>>>>> origin/model-with-CRM-damper % The 13 dynamics equations of the system, in the form % f(x, dx/dt, u) = 0 % where x contains the 13 state variables and u are the 5 joint torques @@ -41,10 +37,7 @@ % using inverse dynamics and also the wrist-sprocket length L [z, dz_dq, dz_dqd, dz_dqdd, dz_dFc, L, dL_dq, dLdot_dq] = rowerdynamics(q,qd,qdd,x(13),model.parameters);% inverse dynamics so gives us the z(torques) Ldot = dL_dq * qd; - - - % multibody dynamics f(8:12) = z - u; dfdx(8:12, 2:6) = dz_dq; From 7398461dd4bf22143d8070c566c1f9a8add4689a Mon Sep 17 00:00:00 2001 From: Frohani Date: Tue, 20 Feb 2018 16:42:34 -0500 Subject: [PATCH 14/23] Chnaged the number of task task constraint was changed from 3 to 2. (Removed the flwheel position constraint) --- main.m => main/main.m | 12 +++---- optimizer/optimize.m | 77 +++++++++++++++++++++++++++++++++++++++---- 2 files changed, 76 insertions(+), 13 deletions(-) rename main.m => main/main.m (77%) diff --git a/main.m b/main/main.m similarity index 77% rename from main.m rename to main/main.m index bedd033..c926431 100644 --- a/main.m +++ b/main/main.m @@ -7,14 +7,14 @@ % Add that folder plus all subfolders to the path. % mkdir('optimizer') -% addpath(genpath('optimizer')) -% addpath(genpath('model')) -% addpath(genpath('tools')) -% addpath(genpath('data')) + addpath(genpath('optimizer')) + addpath(genpath('model')) + addpath(genpath('tools')) + addpath(genpath('data')) - problem.initialguess = 'sim'; - problem.N = 70; % number of collocation points + problem.initialguess = 'simulation'; + problem.N = 4; % number of collocation points % problem.initialguess = 'midpoint'; % problem.N = 4; % number of collocation points % model.task.Lmin = 0.2077; % min and max of cable lenght from the data diff --git a/optimizer/optimize.m b/optimizer/optimize.m index 2212b96..aafd7b1 100644 --- a/optimizer/optimize.m +++ b/optimizer/optimize.m @@ -106,7 +106,10 @@ model.iper = 2:model.nx; model.npar = numel(p_lb); model.nper = numel(model.iper); - model.ntask = 2; % number of constraints for task when doing predictive simulation (cable length) + model.ntask = 2; % number of constraints for task when doing predictive simulation (cable length) +% model.ntask = 3; % number of constraints for task when doing predictive simulation (intial and final cable length + + %flywheel postion should be equal to the max cable length at tmax + intial flywheel postion should be equal to the intial cable length ) + % collocation grid and unknowns model.Nvarpernode = model.nx + model.nu ; % number of unknowns per node model.Nconpernode = model.nx ; % number of constraint equations per node (number of dynamic equations) @@ -360,6 +363,8 @@ x0 = X(1:model.nx); [~,~,~,~,L0] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between final and initial cable length c(end-1) +% c(end-model.ntask) = L0 - model.task.Lmin; % difference between final and initial cable length c(end-2) + % % task constraint for the max cable length tmax = X(end-model.npar+1); @@ -370,9 +375,17 @@ xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - c(end) = Ltmax - model.task.Lmax; % difference between final and initial cable length + c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length +% c(end-1) = Ltmax - model.task.Lmax; % difference between the time that cable length is max(from the previous simulation results) and maximum cable length -d +% % task constraint for the flywheel position +% flywheel_pos1 = xi1(1); +% flywheel_pos2 = xi2(1); +% flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; +% c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position + +% init_flywheel_pos = x0(1); +% c(end-model.ntask+4) = init_flywheel_pos - model.task.Lmin; % difference between final and initial cable length c(end-1) @@ -438,6 +451,35 @@ J(model.Nconpernode*(model.N-1)+(1:npercon) , ifirst) = speye(npercon); J(model.Nconpernode*(model.N-1)+(1:npercon) , ilast) = -speye(npercon); +% % task constraint for the min cable length +% x0 = X(1:model.nx); +% [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) +% c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data +% J(end-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) +% % +% % task constraint for the max cable length +% tmax = X(end-model.npar+1); +% i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei +% +% f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % +% +% xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i +% [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point +% +% xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 +% [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point +% +% Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes +% c(end) = Ltmax - model.task.Lmax; % difference between final and initial cable length +% +% % J(end , end-model.npar+1) = f* dLi1dt + (1-f)*dLi2dt; +% J(end , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; +% J(end , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; +% +% dLtmaxdf = Li1 - Li2; +% dfdtmax = 1/(model.time(i+1)-model.time(i)); +% J(end, end) = dLtmaxdf*dfdtmax; + % task constraint for the min cable length x0 = X(1:model.nx); [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) @@ -457,15 +499,36 @@ [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - c(end) = Ltmax - model.task.Lmax; % difference between final and initial cable length + c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between final and initial cable length % J(end , end-model.npar+1) = f* dLi1dt + (1-f)*dLi2dt; - J(end , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; - J(end , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; + J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; + J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; dLtmaxdf = Li1 - Li2; dfdtmax = 1/(model.time(i+1)-model.time(i)); - J(end, end) = dLtmaxdf*dfdtmax; + J(end-model.ntask+2, end-model.ntask+2) = dLtmaxdf*dfdtmax; + + + +% % task constraint for the flywheel position +% flywheel_pos1 = xi1(1); +% flywheel_pos2 = xi2(1); +% flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; +% c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position + +% J(end-model.ntask+3 , (model.nx+model.nu)*(i-1) + 1) = f*xi1(7); +% J(end-model.ntask+3 , (model.nx+model.nu)*i + 1) = (1-f)*xi2(7); +% +% % +% dflywheel_posdf = flywheel_pos1 - flywheel_pos2; +% dfdtmax = 1/(model.time(i+1)-model.time(i)); +% J(end-model.ntask+3, end-model.ntask+3) = dflywheel_posdf*dfdtmax; + +% init_flywheel_pos = x0(1); +% c(end-model.ntask+4) = init_flywheel_pos - model.task.Lmin; % difference between final and initial cable length c(end-1) +% +% J(end-model.ntask+4 , 1 ) = x0(7); % init_flywheel_pos derivetive will be initial flywheel velocity) From 709a8be5542165d4d57ab17ef336a1f753794703 Mon Sep 17 00:00:00 2001 From: Frohani Date: Thu, 8 Mar 2018 10:36:09 -0500 Subject: [PATCH 15/23] Cleaned up code-Tracking using either springor damper in ratchet mechanism The code can work using max and min of cable (for predictive simulation) in main.m. Also it would be possible to use either nonlinear damper or spring in ratchet mechanism. 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zuB&jJUi+6?o%lzsX1EZH3l9OQ)tYcjAhr65z378lWp(L#HU{K19qm1}Yy_AC<|$T#fuPuUGgEMup{Dyd`FAe!RK*A{NjqJMjo%(83HloUg4Q-RbIcS z@vKf`x_<@%_Vc%3zJBrY2|S73JIrm8i@}oqPBQS9U3WsJ*RX7zy4n_gKoP@g0x^bxtPpGh3QRWiAh& zBF>`8F^SBE^2G|!6o!KxsBG(nq(k_kBkFfP)99dZiGUM;@ttdT5)D1=rpIQ&45OK! zM!K>6rB>5nuOxxgs^V85wc7uWT4i^m_R+cf6zJ>$GB>+m_j^exj>is1dk2SY?+K@S zOqI^P5i#2SS4Vm|t29)8lhR#z+~BZ{YZwB{PlI3glGp7oP-lqhj6xpN_G1d8-xDVL zEM~nZr~HYHD;6pdUEy{rR)2VYuJY{uz7X}j0*_c*meyG9yBzsCb@qSMYL;WiSiJl5 z2epbu8U-%n@_vbO38Yq8a00riwf~1&wE$A9lTH6os}BFDRf-Ec)ZklPUd4aZYB0;v z;x3R{P5(=+R?kXlkprpKNxVsJzKHoW*N1!YJfuZM{8J#csvR%94y0CNKd4npl8yT~ tsQ@7iDy}ll{2P|#bT1ZX#qt0d+k^6X#NX9EN>}acY model.time)) == diff(tmax > model.time)); % find the index of Model.time which is just less than tmax: Huawei - f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % - xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i - [~,~,~,~,Li1] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point - xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 - [~,~,~,~,Li2] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length -% c(end-1) = Ltmax - model.task.Lmax; % difference between the time that cable length is max(from the previous simulation results) and maximum cable length - -% % task constraint for the flywheel position + if isfield(model,'task') + % task constraint for the min cable length + x0 = X(1:model.nx); + [~,~,~,~,L0] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) + c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between final and initial cable length c(end-1) + + % task constraint for the max cable length + tmax = X(end-model.npar+1); + i = find(min(diff(tmax > model.time)) == diff(tmax > model.time)); % find the index of Model.time which is just less than tmax: Huawei + f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % + xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i + [~,~,~,~,Li1] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point + xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 + [~,~,~,~,Li2] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point + Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes + c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length + end + +% %task constraint for the flywheel position (in case of using both costraint for flywheel position model.ntask=4 +% %or if using just one of them model.ntask=3 ) % flywheel_pos1 = xi1(1); % flywheel_pos2 = xi2(1); % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position -% init_flywheel_pos = x0(1); -% c(end-model.ntask+4) = init_flywheel_pos - model.task.Lmin; % difference between final and initial cable length c(end-1) - - - - end @@ -397,7 +435,6 @@ function [J] = conjac(X) global model - h = model.h; c = zeros(model.Ncon,1); % initialize the constraints @@ -450,64 +487,30 @@ c(model.Nconpernode*(model.N-1)+(1:npercon)) = X(ifirst) - X(ilast); % node one - the last one J(model.Nconpernode*(model.N-1)+(1:npercon) , ifirst) = speye(npercon); J(model.Nconpernode*(model.N-1)+(1:npercon) , ilast) = -speye(npercon); - -% % task constraint for the min cable length -% x0 = X(1:model.nx); -% [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) -% c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data -% J(end-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) -% % -% % task constraint for the max cable length -% tmax = X(end-model.npar+1); -% i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei -% -% f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % -% -% xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i -% [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point -% -% xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 -% [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point -% -% Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes -% c(end) = Ltmax - model.task.Lmax; % difference between final and initial cable length -% -% % J(end , end-model.npar+1) = f* dLi1dt + (1-f)*dLi2dt; -% J(end , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; -% J(end , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; -% -% dLtmaxdf = Li1 - Li2; -% dfdtmax = 1/(model.time(i+1)-model.time(i)); -% J(end, end) = dLtmaxdf*dfdtmax; - % task constraint for the min cable length - x0 = X(1:model.nx); - [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) - c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data - J(end-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) -% - % task constraint for the max cable length - tmax = X(end-model.npar+1); - i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei - - f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % - - xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i - [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point - - xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 - [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between final and initial cable length - -% J(end , end-model.npar+1) = f* dLi1dt + (1-f)*dLi2dt; - J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; - J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; - - dLtmaxdf = Li1 - Li2; - dfdtmax = 1/(model.time(i+1)-model.time(i)); - J(end-model.ntask+2, end-model.ntask+2) = dLtmaxdf*dfdtmax; + if isfield(model,'task') + + % task constraint for the min cable length + x0 = X(1:model.nx); + [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) + % c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data + J(end-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) + + % task constraint for the max cable length + tmax = X(end-model.npar+1); + i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei + f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % + xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i + [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point + xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 + [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point + Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes + J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; + J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; + dLtmaxdf = Li1 - Li2; + dfdtmax = 1/(model.time(i+1)-model.time(i)); + J(end-model.ntask+2, end) = dLtmaxdf*dfdtmax; + end @@ -516,19 +519,13 @@ % flywheel_pos2 = xi2(1); % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position - -% J(end-model.ntask+3 , (model.nx+model.nu)*(i-1) + 1) = f*xi1(7); -% J(end-model.ntask+3 , (model.nx+model.nu)*i + 1) = (1-f)*xi2(7); -% +% +% J(end-model.ntask+3 , (model.nx+model.nu)*(i-1) + 1) = f; +% J(end-model.ntask+3 , (model.nx+model.nu)*i + 1 ) = (1-f); % % % dflywheel_posdf = flywheel_pos1 - flywheel_pos2; % dfdtmax = 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z4}EXLZ6P&fv-ujgJ^0Cv?Ujs)g}T;ZMMsv2U@4CdXQMqzpv`!ceB5{uVaakDu9Tf1 zt4cVVzNpZ^LVNxCw&KN5bjZtj!-@&iYgSy4a=j7NUekT`#$*xk_{4xd+c}_a)ATyS z0>s*FvMq%7Vyf=_liwCw1HTK?#IBeZD;~Pqv6e>}9KTP`d5tV0dSdu?wk;FFRPrOe z0ZRiTnf_L8-#U<@r-z9ZO4$~%&mmQhUX&)Of%}?{ z7h5x(um|g?`&A8V2(ogSc`rRreu|P7i+G_7q8Gkq(=!DLkaS8Bs3vvq@glAAABCkkrn`MTIs(F7M$IjyZ7#iTn`0@t*3_FnYco5)uu4>P57U} zvq=mwC%jweqQs3H0-xP!_CTghn8>{QlB1$e><02{&bN z%WDPE$1FLZl)4{dZQTts+Vx8xEI6vvRXI;DrND%+#wVAG^H4dmIOv-^9iNsH5Dqjr zfRBpgGj-ps!jC8XY(83u5LD08gtP+#{5^H64w@~7_QtrOCJRek>L4v~@<9tK93L^+ zOdUm(E}pb?Z*4(7Q+{3cg7adZa_(#Y&+sxjf-iNj20L}HxDm8y9nh#xJ4ek9;8zZ2 zx$z~O_}m5W1m6cDgicYoMs*j9jN^>m|7>78B+Fl7gohl*Ry01w#v|L{pp?&?>~#f@ zCB;^h?7W4mZqL$UO3jFug+1S7gjWzB63;cbi8MpO9!|A95q)Cg=`YmS75NZmkaKbE ziJe4}?B%F&FSFL1577RcHh<6+xy?{-}YbTtt0r~ s@>czaJnBO4*ngbo721FE{_naN{x90 + +% options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = 1.5*model.cgain; +% options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath)) = 0.6*model.cgain; + options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(1) ) = 1.5*model.cgain; + options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1)) = 0.78*model.cgain; + if model.nconpath==2 + options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(2) ) = 1.5*model.cgain; + options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 2)) = 0.78*model.cgain; + end + % options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = model.cgain*[0.984587124166634,0.949239382211693,0.940856786460101,0.945733510058762,0.957084562150634,0.972721713834140,0.982509343643580,0.987816947672726,0.990539007860171,0.990227649806674,0.994967362720877,1.00263477046094,1.00334222046470,1.00144009367118,0.997344919254536,0.989714675158803,0.986123385439148,0.977004790375032,0.968045821421840,0.958646052162770,0.948193316336059,0.941418405647705,0.938910094583808,0.924573210865546,0.906861858588330,0.892478320365616,0.881124752664981,0.912010855669652,0.931751477873481,0.944534048076951,0.949628794333322,0.949838966830169,0.948059476679608,0.945912702743256,0.939938348258617,0.930775839376757,0.923109611948986,0.912706410950738,0.907525287589332,0.913178747383131,0.918094181330246,0.925448288060352,0.931908885377663,0.938841859848728,0.947657130474933,0.958560954984599,0.970764124781298,0.984569343535761,0.991153597130201,0.999707630343451,1.00771863848097,1.01451724929020,1.01957971015749,1.02292890754400,1.02408734776336,1.02335939940512,1.02101448675558,1.01703412767700,1.01073978538003,1.00238201602046,0.991859778375628,0.980683771690154,0.972870044715305,0.971611739892830,0.969269605275424,0.965862830792782,0.961891542922626,0.952998931433828,0.948379405406072,0.984587124166634]'; + % options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = model.cgain*[0.984587124166634,0.949239382211693,0.940856786460101,0.945733510058762,0.957084562150634,0.972721713834140,0.982509343643580,0.987816947672726,0.990539007860171,0.990227649806674,0.994967362720877,1.00263477046094,1.00334222046470,1.00144009367118,0.997344919254536,0.989714675158803,0.986123385439148,0.977004790375032,0.968045821421840,0.958646052162770,0.948193316336059,0.941418405647705,0.938910094583808,0.924573210865546,0.906861858588330,0.892478320365616,0.881124752664981,0.912010855669652,0.931751477873481,0.944534048076951,0.949628794333322,0.949838966830169,0.948059476679608,0.945912702743256,0.939938348258617,0.930775839376757,0.923109611948986,0.912706410950738,0.907525287589332,0.913178747383131,0.918094181330246,0.925448288060352,0.931908885377663,0.938841859848728,0.947657130474933,0.958560954984599,0.970764124781298,0.984569343535761,0.991153597130201,0.999707630343451,1.00771863848097,1.01451724929020,1.01957971015749,1.02292890754400,1.02408734776336,1.02335939940512,1.02101448675558,1.01703412767700,1.01073978538003,1.00238201602046,0.991859778375628,0.980683771690154,0.972870044715305,0.971611739892830,0.969269605275424,0.965862830792782,0.961891542922626,0.952998931433828,0.948379405406072,0.984587124166634]'; + % + %917-986 + end + +% model.cl=options.cl ; +% model.cu=options.cu; + + % options.cl(end-model.ntask+2) = 10; + % options.cu(end-model.ntask+2) = 0; + options.ipopt.max_iter = 5000; +% options.ipopt.hessian_approximation = 'limited-memory'; options.ipopt.hessian_approximation = 'limited-memory'; - options.ipopt.tol = 1e-3; + +options.ipopt.tol = 1e-3; % options.ipopt.print_level = 0; [X, info] = ipopt(X0,funcs,options); @@ -260,10 +343,16 @@ f2 = 0; iu = model.nx + (1:model.nu); +% umax = [5,5,5,0.4,0.2]'; +% umax = [1,1,1,0.4,0.2]'; +% umax = [1,1,2,0.4,0.6]'; + +% umax = [1,1,1,1,1]'; +% umax = [2.89,1.18,6.97,1.09,0.57]'; for i = 1:model.N-1 u = X(iu); - f2 = f2 + mean(u.^2); + f2 = f2 + mean((u./model.umax).^2)*1000; iu = iu + model.Nvarpernode; end % iw = 8:12; @@ -292,6 +381,14 @@ % gradient of tracking cost ix = 1:model.nx; +% umax = [5,5,3,0.4,0.2]'; +% umax = [1,1,1,1,1]'; +% umax = [2.89,1.18,6.97,1.09,0.57]'; +% umax = [5,5,5,0.4,0.2]'; +% umax = [1,1,1,0.4,0.2]'; +% umax = [1,1,2,0.4,0.6]'; + + for i = 1:model.N-1 iy = ix(model.itrack)'; y = X(iy); @@ -310,7 +407,7 @@ for i = 1:model.N-1 u = X(iu); % f2 = f2 + mean(u.^2); - g(iu) = g(iu) + model.Weffort * 2*u ; + g(iu) = g(iu) + model.Weffort * 2*u*1000./(model.umax.^2) ; g(iu)=g(iu)/(model.N-1)/model.nu; %g(iu)=g(iu)/model.nu; iu = iu + model.Nvarpernode; @@ -364,7 +461,22 @@ % the difference is we have to have seperate x and u h = model.h; + load('Cons.mat') c = zeros(model.Ncon,1); % initialize the constraints + % c = a; % initialize the constraints + + if model.nconpath == 2 +% c = [a;a(end)]; +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = 0.8014; + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; + end + + par.Yankle = 0.5182; + par.ForearmLen = 0.2355; + par.ShankLen = 0.4252; + par.ThighLen = 0.4009; + par.UpparmLen = 0.2856; + par.TrunkLen = 0.4312; % dynamics constraints ix1 = 1:model.nx; % index for the state variables of node 1 @@ -385,9 +497,9 @@ % use Backward Euler formula or Midpoint Euler formula as dynamics constraint if strcmp(model.discretization, 'BE') - c(ic) = dynfun(x2 , (x2-x1)/h, u2); + c(ic) = dynfun(x2 , (x2-x1)/h, u2)/model.dyngain; else - c(ic) = dynfun((x1+x2)/2 , (x2-x1)/h, (u1+u2)/2); + c(ic) = dynfun((x1+x2)/2 , (x2-x1)/h, (u1+u2)/2)/model.dyngain; end ix1 = ix1 + model.Nvarpernode; @@ -403,13 +515,13 @@ npercon = numel(ifirst); c(model.Nconpernode*(model.N-1)+(1:npercon)) = ... - X(ifirst) - X(ilast); % node one - the last one + X(ifirst) - X(ilast); % node one - the last one 989-914 - if isfield(model,'task') + if isfield(model,'task') % task constraint for the min cable length x0 = X(1:model.nx); [~,~,~,~,L0] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) - c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between final and initial cable length c(end-1) + c(model.ncondyn + model.ncontaskper + 1) = L0 - model.task.Lmin; % difference between final and initial cable length c(model.Ncon-1) % task constraint for the max cable length tmax = X(end-model.npar+1); @@ -419,19 +531,64 @@ [~,~,~,~,Li1] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length - end - -% %task constraint for the flywheel position (in case of using both costraint for flywheel position model.ntask=4 -% %or if using just one of them model.ntask=3 ) -% flywheel_pos1 = xi1(1); -% flywheel_pos2 = xi2(1); -% flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; -% c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position - - + + Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length + if model.nconpath>0 +% for i = 1:model.N +% for i = 1:model.nconpath + for i = 38 + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); +% q = [q1,q2,q3,q4,q5]';%trasnpose +% % +% qddot = zeros(5,1); +% qdot = zeros(5,1); +% +% % F(:,i) = X((model.nx+model.nu)*(i-1)+13);%zero for this also +% F = 0; +% +% [~,~,~,~,~,~,~,~,stick] = rowerdynamics(q,qdot,qddot,F,model.parameters); +% wrist(i) = stick (6,2)';%keep the wrist higher than a constant value(so we dont need to use hip) + % wristXmine(i) = par.Yankle - par.ShankLen*sin(-q1(i)) +par.ThighLen*sin(q2(i)+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i))- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i))+... + % par.ForearmLen*sin(+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); + % calculate the vertical cordinate of the wrist + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = (par.Yankle + par.ShankLen*sin(pi-q1) -... + par.ThighLen*sin(q2-pi+q1)+... + par.TrunkLen*sin(-q2-q1-q3+2*pi)- par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... + par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; +% for j=model.N-35 + + + end + if model.nconpath==2 + + for i = 38 + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = (par.Yankle + par.ShankLen*sin(pi-q1) -... + par.ThighLen*sin(q2-pi+q1)+... + par.TrunkLen*sin(-q2-q1-q3+2*pi)- par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... + par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; + end + end + end + end + model.c=c; + plot(model.c) + +% a=c(917:model.Ncon); +% plot(c,'r');hold on;plot(model.cl,'b');hold on;plot(model.cu,'g') end %==================================================================== @@ -440,6 +597,13 @@ global model h = model.h; c = zeros(model.Ncon,1); % initialize the constraints + par.Yankle = 0.5182; + par.ForearmLen = 0.2355; + par.ShankLen = 0.4252; + par.ThighLen = 0.4009; + par.UpparmLen = 0.2856; + par.TrunkLen = 0.4312; + % initialize the sparse Jacobian matrix J = spalloc(model.Ncon,model.Nvar, model.Jnnz); @@ -460,16 +624,17 @@ p = X(model.ip); if strcmp(model.discretization, 'BE') - [~, dfdx, dfdxdot,dfdu] = dynfun(x2, (x2-x1)/h, u2); %?????dLdq - J(ic,ix1) = -dfdxdot/h; - J(ic,ix2) = dfdx + dfdxdot/h; - J(ic, iu2) = dfdu; + [~, dfdx, dfdxdot,dfdu]= dynfun(x2, (x2-x1)/h, u2); %?????dLdq + + J(ic,ix1) = -dfdxdot/h/model.dyngain; + J(ic,ix2) = (dfdx + dfdxdot/h)/model.dyngain; + J(ic, iu2) = dfdu/model.dyngain; else [~, dfdx, dfdxdot,dfdu] = dynfun((x1+x2)/2, (x2-x1)/h, (u1+u2)/2); %?????dLdq - J(ic,ix1) = dfdx/2 - dfdxdot/h; - J(ic,ix2) = dfdx/2 + dfdxdot/h; - J(ic, iu1) = dfdu/2; - J(ic, iu2) = dfdu/2; + J(ic,ix1) = (dfdx/2 - dfdxdot/h)/model.dyngain; + J(ic,ix2) = (dfdx/2 + dfdxdot/h/model.dyngain); + J(ic, iu1) = dfdu/2/model.dyngain; + J(ic, iu2) = dfdu/2/model.dyngain; end % advance ix1 and irow to next node @@ -481,7 +646,7 @@ end % periodicity constraints for states and controls - % dynamics constraints: state periodicity (all variables axcept state 1)and conbtrol periodicity + % state periodicity (all variables axcept state 1)and conbtrol periodicity ifirst = [model.iper model.nx+(1:model.nu)]; ilast = (model.N-1)*model.Nvarpernode + ifirst; npercon = numel(ifirst); @@ -490,49 +655,106 @@ c(model.Nconpernode*(model.N-1)+(1:npercon)) = X(ifirst) - X(ilast); % node one - the last one J(model.Nconpernode*(model.N-1)+(1:npercon) , ifirst) = speye(npercon); J(model.Nconpernode*(model.N-1)+(1:npercon) , ilast) = -speye(npercon); - + if isfield(model,'task') % task constraint for the min cable length x0 = X(1:model.nx); [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) % c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data - J(end-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) + J(model.ncondyn + model.ncontaskper + 1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) % task constraint for the max cable length tmax = X(end-model.npar+1); -% i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei + % i = find( min(diff(tmax > model.time)) == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei i = find( -1 == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei - - f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % + + f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i - [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point + [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes - J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; - J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; - dLtmaxdf = Li1 - Li2; + % Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes + % c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, (model.nx+model.nu)*(i-1) + (2:6)) = (1-f)* dLi1dt ; + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl , (model.nx+model.nu)*i + (2:6)) = f*dLi2dt; + dLtmaxdf = -Li1 + Li2; dfdtmax = 1/(model.time(i+1)-model.time(i)); - J(end-model.ntask+2, end) = dLtmaxdf*dfdtmax; + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, end) = dLtmaxdf*dfdtmax; + + + if model.nconpath>0 + +% for i = 1:model.nconpath + for i = 38 + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); + + % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... + % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... + par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4) +... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+ par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + end + if model.nconpath==2 + for i = 38 + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); + + % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... + % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); +% model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:i) + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... + par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4) +... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+ par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(i-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(i-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + end + end + end end - - -% % task constraint for the flywheel position -% flywheel_pos1 = xi1(1); -% flywheel_pos2 = xi2(1); -% flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; -% c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position -% -% J(end-model.ntask+3 , (model.nx+model.nu)*(i-1) + 1) = f; -% J(end-model.ntask+3 , (model.nx+model.nu)*i + 1 ) = (1-f); -% % -% dflywheel_posdf = flywheel_pos1 - flywheel_pos2; -% dfdtmax = 1/(model.time(i+1)-model.time(i)); -% J(end-model.ntask+3, end) = dflywheel_posdf*dfdtmax; + - end %==================================================================== @@ -581,5 +803,4 @@ function matcompare(a,b) irow = irow(icol); fprintf('%9.6f at %d %d (%9.6f vs. %9.6f)\n', full(maxerr), irow, icol, full(a(irow,icol)), full(b(irow,icol))); end - - + \ No newline at end of file From 018b959636ca6450ee81852ac14ea3fe5b021340 Mon Sep 17 00:00:00 2001 From: Frohani Date: Fri, 11 May 2018 14:02:06 -0400 Subject: [PATCH 19/23] 05112018 --- main/main.m | 6 +++--- main/rowingtest.mat | Bin 54841 -> 50707 bytes optimizer/optimize.m | 33 ++++++++++++--------------------- 3 files changed, 15 insertions(+), 24 deletions(-) diff --git a/main/main.m b/main/main.m index 79397dd..7e3af9b 100644 --- a/main/main.m +++ b/main/main.m @@ -17,12 +17,12 @@ problem.dyngain = 1; % scaling factor for non path constraint problem.np =1; % on/off switch for constraints problem.N = 70; % number of collocation points - % problem.N = 50; % used for derivetive checking +% problem.N = 50; % used for derivetive checking if problem.np == 1 problem.task.Lmin = 0.2077; % min and max of cable lenght from the data problem.task.Lmax = 1.1288; problem.cablecnst = 2; % number of constraints for task when doing predictive simulation (cable length) Lmin & Lmax - problem.nconpath = 2; % Zwrist constraint (depends on the number of nodes can be varies between 0 and model.N) + problem.nconpath = 0; % Zwrist constraint (depends on the number of nodes can be varies between 0 and model.N) problem.ntask = problem.nconpath + problem.cablecnst; % the total number of constraints else problem.ntask = 0; @@ -31,7 +31,7 @@ problem.component = 'spring'; % choose if we want to use damper or spring problem.discretization = 'BE'; % Backward Euler(BE) or Midpoint Euler(ME) discretization problem.tracking = 3; % if 1 tracking the angles only else track all states (but flywheel velocity) - % objective function gains (Wtrack=1 for the tracking and Weffort=1 for predictive simulation) + % objective function gains (Wtrack=1 for the tracking and Weffort=1 for predictive simulation) problem.Wtrack =1; problem.Weffort =0; result = optimize(problem); diff --git a/main/rowingtest.mat b/main/rowingtest.mat index 4ac72f7307ef8af518fd38ac4c66d1f270ce71f2..037a766fbd790bca06f559cd1305038a84f9ce37 100644 GIT binary patch literal 50707 zcmeEtWlS6Z6D96ethg30?(XhZ+}#$6ySuwBjaRZAyX99V6?QcxA;h=VsGMV>FDghN2VgKC9A~6 z@sUj2*}}xt!ko+zz(*$KY(u7K;zh>FO2*2@$HC6W!b--*!pcMTfBAs;?*md+5gq(I 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interpolation of two above nodes c(model.ncondyn + model.ncontaskper + model.ncontaskcbl) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length - if model.nconpath>0 + + if model.nconpath>0 % for i = 1:model.N % for i = 1:model.nconpath for i = 38 @@ -583,7 +584,6 @@ end end end -======= Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length end @@ -595,16 +595,14 @@ % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position - ->>>>>>> e109c3f2d5672b4b3050c1e1f35ca9f7162632ec - + end - model.c=c; - plot(model.c) +% model.c=c; +% plot(model.c) % a=c(917:model.Ncon); % plot(c,'r');hold on;plot(model.cl,'b');hold on;plot(model.cu,'g') -end +% end %==================================================================== function [J] = conjac(X) @@ -677,7 +675,7 @@ x0 = X(1:model.nx); [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) % c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data - J(model.ncondyn + model.ncontaskper + 1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) + J(model.Ncon-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) % task constraint for the max cable length tmax = X(end-model.npar+1); @@ -689,21 +687,14 @@ [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point -<<<<<<< HEAD % Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes % c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, (model.nx+model.nu)*(i-1) + (2:6)) = (1-f)* dLi1dt ; - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl , (model.nx+model.nu)*i + (2:6)) = f*dLi2dt; + J(model.Ncon-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = (1-f)* dLi1dt ; + J(model.Ncon-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = f*dLi2dt; dLtmaxdf = -Li1 + Li2; -======= - Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes - J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; - J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; - dLtmaxdf = Li1 - Li2; ->>>>>>> e109c3f2d5672b4b3050c1e1f35ca9f7162632ec dfdtmax = 1/(model.time(i+1)-model.time(i)); - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, end) = dLtmaxdf*dfdtmax; + J(model.Ncon-model.ntask+2, end) = dLtmaxdf*dfdtmax; if model.nconpath>0 From 3206fd87ee851a899e5822e3a76df71776184d51 Mon Sep 17 00:00:00 2001 From: Frohani Date: Mon, 14 May 2018 11:02:41 -0400 Subject: [PATCH 20/23] Updated 05142018 --- data/Simresult2.mat | Bin 0 -> 9976 bytes main/Cons.mat | Bin 3994 -> 4139 bytes main/main.m | 3 +- main/rowingtest.mat | Bin 50707 -> 54898 bytes optimizer/optimize.m | 293 +++++++++++++++++++++++-------------------- 5 files changed, 155 insertions(+), 141 deletions(-) create mode 100644 data/Simresult2.mat diff --git a/data/Simresult2.mat b/data/Simresult2.mat new file mode 100644 index 0000000000000000000000000000000000000000..7f22d037855b116b182bc32c9ba326af46ee23de GIT binary patch literal 9976 zcma*sQ$r;H0zlzx+cqcLwr$sB+ql^_CQUWjwr$&X-L(6%@B2NS|8NvU)a6A)NjR8( zktm3$Gg{i%Sul_&+nKmoI=a~Nk|>L5$tZHNGmwb6SeUq3n3Fg<@RF#xJCG=tc$2WO 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zoiP-{YR9nZQin!PRMG`E7Qxl-pU;_Udyz=qt*;p!%W&yiNU4`>FZz_$y4`{!V0`uu z6?}Ufk;4t#`KRt)@V7KJ(;ZWS24@6C4NXnq=(XwB^~*a|@rLRB`6&2Vv2PfRannZ|E65}-Vq=cWc z%G7|^zr=iVtSN?C9X@Q045MhnD~PRwZx#+M2zUn`Yex?%BMD;x4p<%A;fgPwL?k&D z7NY;l6rRo=As7x6AyYeGeL#RX*{qRfQHjN-*Np0l+W@0Ol(+~@(rx0A@C;=e2DDnl@2C6zH-a{xvZ)20+QA7j2|&&?{%$-sI3Z*R)w z?xKUg4)Ri23ehXReJ4FqEKtOITyDj>2GZ`8S9`!p#@x!xmSuIQNcMi_TV}^}~E9aP{ma95i^DX>B%Rkah^b;w>i|9T9H*FSLY&U}ms$tQ|ue)591MhX?zS(4}n^eEts7WsY^ zD!N-CsFpW`Y?M-fqC+kGB@xLrlR5%V``y>S>*|b|%Jy4cIs%n~ zipg+fdHCsCiYHPc2rkD6UPo5U{UTR%%rFc0+j{AB9})l5mhP*eLiARAOZ1Xj1=707 zCwJ#UA3FMc>70FB5xjZjo`5A=AB;vh3xPxz%&yo@FL2%m7O^@cGKalD?nxgHp81gg zA4XJ60WTLs=aa$ALsmkbr?zg6*qUP{T`w8By~VYnjFA^o$hY?vOEAF-3u@t;%akugrIdR%*0ciD;BB5odsBhj1Of=j$D-kL z)8q1>tr|V>ku2_IsDsr*wzjVxxMJZiw(swciH8k;TLtBtQxLCBeP?1X4Zi7GVx0Z! zhROrx+L#W=LOTKdz3N{dV$Uf}#cb=vsD8GI_gQ8ITx(eJycOMsR$|S%=Bhj3c$)Oe z-k5L5jg{ff_RvQdbY{FzzvJtiGzMh6eAhv9UWHi1Vf>TcU0Vy0HQYiG=~=k+W@hJg^T+8he9} zc{HOcN0le*(g9dd(mvI*r_zxRvr&1@ITvIGlbkGDD$sgacBSGCN6;&yP(LKdAeO4s zxLDO)EbeV3x!1W0V(HH*NAW{Q*X4q{_QOfQ*A$7>#}1&LG0ek~Ish_Ux`ZXJm*}Ko zmMKMphShBty)ZUTM|z>terXdqKqHx^RcU3Q2;F2+x+MwNsRWJYo~MlyB{UV;+1&4DBLm*kz4so>f`k3owz*&@vb7M%7dPsKz9#!{xrJf$4^}XC zq4S;J>x@wJ%7yip4aF$fuliGXvT6=kE0@Fw@fiS3$|&mKsZ$`+nf2^bqZdXiP!u!< zxXH63Ow=J@Mq{^ zWU8vRk0Ezx`dv(I9B?Ko^(mZTV7{$)iFNWJoag3sp8MeqnzHp*Y~KvS4Dr*V%k*qW z*QwoPndPGU(ReF=s09_XON#P2cM!MWkp|KWUDW&NTCYGL6{9ulIEQo>!#C7bf4M7d z=!qvmOrp30Gzoa+@0*#hB-3r))LD(pXP9O31^q~d%(Jvy8HO31uU=6|EQLHmY9gVn z0;#KODQPkRnk>C+Bx_w!hs59;*>`$KlHM{(&!S?|R38g7gF=u`KT5rOk_FPdd_By+ zu~6XGp5+-IF=!uscq3-|DLQKyOZ;ngA}lI9T%pxRV16AI3pX0eVBTtq>HWL{v>=LoT>2k+0hqK@Z^->CIS`#Yz0AHo0)+&QPmwPNcK%%qv77k} zcrRFLGM4M%^ne53l6()81|(F!wFt#DZ*2$I^m)U)tDS5)7Y%VpMsc2-Dg=$p0QuXQ z{?PZ_E?G6t7_wFmjdi^D#8N(<;EpQE1jo(m^DJr)OoWuJ){FO`b)9iRp)CM1L%D+2)%wRjqc%mX3vb{Fad^h0 zO{FqCRmZ=zsrJVhqvI20vA2+pZS;R!vUEXRLBd$R6C?IF!7n?-o zd~1$P`(PbHS`7_NiQvC-Zg|@vANkO|h_(kB5cj?jW4FL+Rp&!Ui}^Zpoav84A(9LYGJ6>>yDxkw2Wn7E|n6 zAB?LFfk_>IC%)KO6wu35(2tu1;(>B~vCcIZkX_AByR!nNTsr7)` z0#TE3MCN$X-!TsD7deTU+Ssg)+1a)w5n`RU$>Qatr`Q~Su%XAr7T`Ue#nGBOgLDHp z6{gqLQ0cE(!2&L9G@c>nN)KuTb-hE>C58|2OP>UI|G7^D`qHNkzVwNNoX>s8aANvq zk!zX~7SXTrQDIV$$dAL}6nA`J$J~2!SDbr0{y)4cj-3>`Gk3W-{J%Ml|H5(N_Tvuj z?HW5K+d7f#+#NkhJK2uxLUDJqaddH~;BLFw*gKM3+;0 % options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = 1.5*model.cgain; -% options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath)) = 0.6*model.cgain; +% options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath)) = 0.78*model.cgain; options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(1) ) = 1.5*model.cgain; - options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1)) = 0.78*model.cgain; + options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(1)) = 0.78*model.cgain; if model.nconpath==2 options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(2) ) = 1.5*model.cgain; - options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 2)) = 0.78*model.cgain; + options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +(2)) = 0.78*model.cgain; end % options.cu(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = model.cgain*[0.984587124166634,0.949239382211693,0.940856786460101,0.945733510058762,0.957084562150634,0.972721713834140,0.982509343643580,0.987816947672726,0.990539007860171,0.990227649806674,0.994967362720877,1.00263477046094,1.00334222046470,1.00144009367118,0.997344919254536,0.989714675158803,0.986123385439148,0.977004790375032,0.968045821421840,0.958646052162770,0.948193316336059,0.941418405647705,0.938910094583808,0.924573210865546,0.906861858588330,0.892478320365616,0.881124752664981,0.912010855669652,0.931751477873481,0.944534048076951,0.949628794333322,0.949838966830169,0.948059476679608,0.945912702743256,0.939938348258617,0.930775839376757,0.923109611948986,0.912706410950738,0.907525287589332,0.913178747383131,0.918094181330246,0.925448288060352,0.931908885377663,0.938841859848728,0.947657130474933,0.958560954984599,0.970764124781298,0.984569343535761,0.991153597130201,0.999707630343451,1.00771863848097,1.01451724929020,1.01957971015749,1.02292890754400,1.02408734776336,1.02335939940512,1.02101448675558,1.01703412767700,1.01073978538003,1.00238201602046,0.991859778375628,0.980683771690154,0.972870044715305,0.971611739892830,0.969269605275424,0.965862830792782,0.961891542922626,0.952998931433828,0.948379405406072,0.984587124166634]'; % options.cl(model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:model.nconpath) ) = model.cgain*[0.984587124166634,0.949239382211693,0.940856786460101,0.945733510058762,0.957084562150634,0.972721713834140,0.982509343643580,0.987816947672726,0.990539007860171,0.990227649806674,0.994967362720877,1.00263477046094,1.00334222046470,1.00144009367118,0.997344919254536,0.989714675158803,0.986123385439148,0.977004790375032,0.968045821421840,0.958646052162770,0.948193316336059,0.941418405647705,0.938910094583808,0.924573210865546,0.906861858588330,0.892478320365616,0.881124752664981,0.912010855669652,0.931751477873481,0.944534048076951,0.949628794333322,0.949838966830169,0.948059476679608,0.945912702743256,0.939938348258617,0.930775839376757,0.923109611948986,0.912706410950738,0.907525287589332,0.913178747383131,0.918094181330246,0.925448288060352,0.931908885377663,0.938841859848728,0.947657130474933,0.958560954984599,0.970764124781298,0.984569343535761,0.991153597130201,0.999707630343451,1.00771863848097,1.01451724929020,1.01957971015749,1.02292890754400,1.02408734776336,1.02335939940512,1.02101448675558,1.01703412767700,1.01073978538003,1.00238201602046,0.991859778375628,0.980683771690154,0.972870044715305,0.971611739892830,0.969269605275424,0.965862830792782,0.961891542922626,0.952998931433828,0.948379405406072,0.984587124166634]'; @@ -463,12 +463,12 @@ h = model.h; load('Cons.mat') c = zeros(model.Ncon,1); % initialize the constraints - % c = a; % initialize the constraints + c = Cons; % initialize the constraints if model.nconpath == 2 -% c = [a;a(end)]; + c = [Cons;Cons(end)]; % c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = 0.8014; - c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; end par.Yankle = 0.5182; @@ -524,7 +524,7 @@ c(model.ncondyn + model.ncontaskper + 1) = L0 - model.task.Lmin; % difference between final and initial cable length c(model.Ncon-1) - % task constraint for the max cable length + % task constraint for the max cable length tmax = X(end-model.npar+1); i = find(min(diff(tmax > model.time)) == diff(tmax > model.time)); % find the index of Model.time which is just less than tmax: Huawei f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % @@ -535,57 +535,56 @@ Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes c(model.ncondyn + model.ncontaskper + model.ncontaskcbl) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length - - if model.nconpath>0 -% for i = 1:model.N -% for i = 1:model.nconpath - for i = 38 - - q1= X((model.nx+model.nu)*(i-1)+2); - q2= X((model.nx+model.nu)*(i-1)+3); - q3= X((model.nx+model.nu)*(i-1)+4); - q4= X((model.nx+model.nu)*(i-1)+5); - q5= X((model.nx+model.nu)*(i-1)+6); -% q = [q1,q2,q3,q4,q5]';%trasnpose -% % -% qddot = zeros(5,1); -% qdot = zeros(5,1); -% -% % F(:,i) = X((model.nx+model.nu)*(i-1)+13);%zero for this also -% F = 0; -% -% [~,~,~,~,~,~,~,~,stick] = rowerdynamics(q,qdot,qddot,F,model.parameters); -% wrist(i) = stick (6,2)';%keep the wrist higher than a constant value(so we dont need to use hip) - % wristXmine(i) = par.Yankle - par.ShankLen*sin(-q1(i)) +par.ThighLen*sin(q2(i)+q1(i))+... - % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i))- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i))+... - % par.ForearmLen*sin(+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); - % calculate the vertical cordinate of the wrist - c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = (par.Yankle + par.ShankLen*sin(pi-q1) -... - par.ThighLen*sin(q2-pi+q1)+... - par.TrunkLen*sin(-q2-q1-q3+2*pi)- par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... - par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; -% for j=model.N-35 - - - end + + if model.nconpath>0 + % for i = 1:model.N + % for i = 1:model.nconpath + i = 35; + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); + % q = [q1,q2,q3,q4,q5]';%trasnpose + % % + % qddot = zeros(5,1); + % qdot = zeros(5,1); + % + % % F(:,i) = X((model.nx+model.nu)*(i-1)+13);%zero for this also + % F = 0; + % + % [~,~,~,~,~,~,~,~,stick] = rowerdynamics(q,qdot,qddot,F,model.parameters); + % wrist(i) = stick (6,2)';%keep the wrist higher than a constant value(so we dont need to use hip) + % wristXmine(i) = par.Yankle - par.ShankLen*sin(-q1(i)) +par.ThighLen*sin(q2(i)+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i))- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i))+... + % par.ForearmLen*sin(+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); + % calculate the vertical cordinate of the wrist + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = (par.Yankle + par.ShankLen*sin(pi-q1) -... + par.ThighLen*sin(q2-pi+q1)+... + par.TrunkLen*sin(-q2-q1-q3+2*pi)-... + par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... + par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; + + if model.nconpath==2 + j = 36; + + q1= X((model.nx+model.nu)*(j-1)+2); + q2= X((model.nx+model.nu)*(j-1)+3); + q3= X((model.nx+model.nu)*(j-1)+4); + q4= X((model.nx+model.nu)*(j-1)+5); + q5= X((model.nx+model.nu)*(j-1)+6); + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = (par.Yankle + par.ShankLen*sin(pi-q1) -... + par.ThighLen*sin(q2-pi+q1)+... + par.TrunkLen*sin(-q2-q1-q3+2*pi)- ... + par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... + par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; - for i = 38 - - q1= X((model.nx+model.nu)*(i-1)+2); - q2= X((model.nx+model.nu)*(i-1)+3); - q3= X((model.nx+model.nu)*(i-1)+4); - q4= X((model.nx+model.nu)*(i-1)+5); - q5= X((model.nx+model.nu)*(i-1)+6); - c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = (par.Yankle + par.ShankLen*sin(pi-q1) -... - par.ThighLen*sin(q2-pi+q1)+... - par.TrunkLen*sin(-q2-q1-q3+2*pi)- par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... - par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; - end end end - Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes - c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length + % Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes + % c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length end % %task constraint for the flywheel position (in case of using both costraint for flywheel position model.ntask=4 @@ -594,11 +593,11 @@ % flywheel_pos2 = xi2(1); % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position - + model.c=c; + plot(model.c) end -% model.c=c; -% plot(model.c) + % a=c(917:model.Ncon); % plot(c,'r');hold on;plot(model.cl,'b');hold on;plot(model.cu,'g') @@ -609,7 +608,16 @@ global model h = model.h; +% c = zeros(model.Ncon,1); % initialize the constraints + load('Cons.mat') c = zeros(model.Ncon,1); % initialize the constraints + c = Cons; % initialize the constraints + + if model.nconpath == 2 + c = [Cons;Cons(end)]; +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = 0.8014; +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; + end par.Yankle = 0.5182; par.ForearmLen = 0.2355; par.ShankLen = 0.4252; @@ -674,8 +682,8 @@ % task constraint for the min cable length x0 = X(1:model.nx); [~,~,~,~,L0,dL0dq] = dynfun(x0,zeros(model.nx,1),zeros(model.nu,1)); % the cable length L only depends the body positions (q) - % c(end-model.ntask+1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data - J(model.Ncon-model.ntask+1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) + % c((model.ncondyn + model.ncontaskper + 1) = L0 - model.task.Lmin; % difference between initial cable length and the min cable length from the data + J(model.ncondyn + model.ncontaskper + 1 , 2:6 ) = dL0dq; % L0 is a function of qs (2-6) % task constraint for the max cable length tmax = X(end-model.npar+1); @@ -690,78 +698,85 @@ % Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes % c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length - J(model.Ncon-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = (1-f)* dLi1dt ; - J(model.Ncon-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = f*dLi2dt; + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, (model.nx+model.nu)*(i-1) + (2:6)) = (1-f)* dLi1dt ; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, (model.nx+model.nu)*i + (2:6)) = f*dLi2dt; dLtmaxdf = -Li1 + Li2; dfdtmax = 1/(model.time(i+1)-model.time(i)); - J(model.Ncon-model.ntask+2, end) = dLtmaxdf*dfdtmax; + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl, end) = dLtmaxdf*dfdtmax; if model.nconpath>0 - -% for i = 1:model.nconpath - for i = 38 - - q1= X((model.nx+model.nu)*(i-1)+2); - q2= X((model.nx+model.nu)*(i-1)+3); - q3= X((model.nx+model.nu)*(i-1)+4); - q4= X((model.nx+model.nu)*(i-1)+5); - q5= X((model.nx+model.nu)*(i-1)+6); - - % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... - % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... - % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... - par.ThighLen*cos(q2+q1-pi)-... - par.TrunkLen*cos(-q2-q1-q3)+... - par.UpparmLen*cos(-q2-q1-q3-q4) +... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... - par.TrunkLen*cos(-q2-q1-q3)+ par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... - par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - end + + % for i = 1:model.nconpath + i = 35; + + q1= X((model.nx+model.nu)*(i-1)+2); + q2= X((model.nx+model.nu)*(i-1)+3); + q3= X((model.nx+model.nu)*(i-1)+4); + q4= X((model.nx+model.nu)*(i-1)+5); + q5= X((model.nx+model.nu)*(i-1)+6); + + % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... + % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); + % c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = (par.Yankle + par.ShankLen*sin(pi-q1) -... + % par.ThighLen*sin(q2-pi+q1)+... + % par.TrunkLen*sin(-q2-q1-q3+2*pi)- par.UpparmLen*sin(-q2-q1-q3-q4+2*pi)+... + % par.ForearmLen*sin(-2*pi+q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... + par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4) +... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+ ... + par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1 , (model.nx+model.nu)*(i-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1, (model.nx+model.nu)*(i-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + if model.nconpath==2 - for i = 38 - - q1= X((model.nx+model.nu)*(i-1)+2); - q2= X((model.nx+model.nu)*(i-1)+3); - q3= X((model.nx+model.nu)*(i-1)+4); - q4= X((model.nx+model.nu)*(i-1)+5); - q5= X((model.nx+model.nu)*(i-1)+6); - - % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... - % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... - % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); -% model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:i) - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... - par.ThighLen*cos(q2+q1-pi)-... - par.TrunkLen*cos(-q2-q1-q3)+... - par.UpparmLen*cos(-q2-q1-q3-q4) +... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... - par.TrunkLen*cos(-q2-q1-q3)+ par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(i-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... - par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(i-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... - par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - - J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(i-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; - end + j = 36; + + q1= X((model.nx+model.nu)*(j-1)+2); + q2= X((model.nx+model.nu)*(j-1)+3); + q3= X((model.nx+model.nu)*(j-1)+4); + q4= X((model.nx+model.nu)*(j-1)+5); + q5= X((model.nx+model.nu)*(j-1)+6); + + % wristXmine(i) = par.Yankle + par.ShankLen*sin(pi-q1(i)) -par.ThighLen*sin(q2(i)-pi+q1(i))+... + % par.TrunkLen*sin(-q2(i)-q1(i)-q3(i)+2*pi)- par.UpparmLen*sin(-q2(i)-q1(i)-q3(i)-q4(i)+2*pi)+... + % par.ForearmLen*sin(-2*pi+q2(i)+q1(i)+q3(i)+q4(i)+q5(i)); + % model.ncondyn + model.ncontaskper + model.ncontaskcbl +( 1:i) + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(j-1) +2 ) = (-par.ShankLen*cos(pi-q1)-... + par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4) +... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(j-1) +3 ) = (-par.ThighLen*cos(q2+q1-pi)-... + par.TrunkLen*cos(-q2-q1-q3)+ par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2 , (model.nx+model.nu)*(j-1) +4 ) = (-par.TrunkLen*cos(-q2-q1-q3)+... + par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(j-1) +5 ) = (par.UpparmLen*cos(-q2-q1-q3-q4)+... + par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2, (model.nx+model.nu)*(j-1) +6 ) = (par.ForearmLen*cos(q2+q1+q3+q4+q5))*model.cgain; + end end end From c8da2df47dc9fceeec173aaeba8fc11081e737b1 Mon Sep 17 00:00:00 2001 From: Frohani Date: Sun, 20 May 2018 20:57:56 -0400 Subject: [PATCH 21/23] Updated 05202018 The problem is the optimization can not be solved using more than one node for path constraints. Please see "Setup.txt" for more information --- Setup.txt | 9 +++++++++ main/main.m | 6 +++--- main/rowingtest.mat | Bin 54898 -> 54756 bytes optimizer/optimize.m | 34 +++++++++++++++++++++++++++++----- 4 files changed, 41 insertions(+), 8 deletions(-) create mode 100644 Setup.txt diff --git a/Setup.txt b/Setup.txt new file mode 100644 index 0000000..16fb2fe --- /dev/null +++ b/Setup.txt @@ -0,0 +1,9 @@ +In order to perform the optimization code the "main.m" should be ran + +-"problem.nconpath" represent the number of path constraints (currently = 1). +-"optimize.m" is coded in a way that it can be increased to 2 also +-To start it is better to set problem.Wtrack =1 while problem.Weffort =0. + The reason is we are sure that the constaraints are satisfied in tracking + problem. In addition, when using only tracking, the optimization should + be solved within few iterations + -The rest can be the way they are. diff --git a/main/main.m b/main/main.m index 9709f3f..110e73a 100644 --- a/main/main.m +++ b/main/main.m @@ -22,7 +22,7 @@ problem.task.Lmin = 0.2077; % min and max of cable lenght from the data problem.task.Lmax = 1.1288; problem.cablecnst = 2; % number of constraints for task when doing predictive simulation (cable length) Lmin & Lmax - problem.nconpath = 2; % Zwrist constraint (depends on the number of nodes can be varies between 0 and model.N) + problem.nconpath = 1; % Zwrist constraint (depends on the number of nodes can be varies between 0 and model.N) else problem.ntask = 0; end @@ -31,8 +31,8 @@ problem.discretization = 'BE'; % Backward Euler(BE) or Midpoint Euler(ME) discretization problem.tracking = 3; % if 1 tracking the angles only else track all states (but flywheel velocity) % objective function gains (Wtrack=1 for the tracking and Weffort=1 for predictive simulation) - problem.Wtrack =1; - problem.Weffort =0; + problem.Wtrack =0; + problem.Weffort =1; result = optimize(problem); save 'rowingtest' result end diff --git a/main/rowingtest.mat b/main/rowingtest.mat index 795b7c3b67034fc8438a45d3eb2ee181ad03a7d4..7b9d8e9c65225b9273a9b44312a404154e6615e7 100644 GIT binary patch delta 41006 zcmV(_K-9nTtOMk$1CTTrQ*~}2O<{Q;GB6-AFgi3cIy5yPGB7bXkx?U&UzGk;f$QgzsS?5NV09Dkx4d*lV&K>*l8YU*=3ClQ{w|eF(5Iz z0x`Ta!eC=V)T;rTq-sRL^?_tTP*59D2x?)SjUt0lCu;y*0VyVGu@H;AL`2hj&OO)3 z?o4O$2YlZQ{N~<|`}=+8oZmh7!WcX~;Y>pfHPlc;4K>tILw^l5)KEhWHPlc;4Sxpu zi{H*5#(V_&F^TYa(>ULgF%Kqx;2AA`%7SRXtYHY|L5TqaG`?Fa-}e(XzW0z@9gqYXHq{e(O~{ z#M3Cz5oB-~vuhO3cQDpZ5BjTkpB*uybi0x9p~iqSR)5rSJpU>1@t~DOfYwE8vjFv7 zbt_5dBIWIhnZ2y@L_g~T@?o+qj|Jyt2|Q+Yo(^*HKW_S_Ha z9H;K?g}5r7y|4wwdGALK5?=+?=O*o&@#KRWqjlAtP(oeIXP?p zi8^~CkDw1cXB7aJoy`D0^IKE>`$*?pm`gmYg~nHv-<9tWJ8~8Y9dFN)^`P_k-sULO zu{$rF2ENdx!|3Z*6OLm%{69?vZh7kTl5wz#GdMO!M+u#xxQ6^Mjm-YkGv#)v 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z#oJD+jEJ%D>-Xx5rrS|$d|tMcb03&RCcfIvouKn;vZ{li59G{$+Hnc95xsnd-P2u9 z5zX_ZuRmin;lX*xXna%$p@;dB_cz`}x+uhGOUy~s-W^a9V-STGp13Uc-rx|v>mBRg z!iAW%VT$ie6TyPp#Uyc64aOJT>zhd##X27q$rf18hgCzx5`j%JY3SObqnfv46ki(q!8Dg0q2BPfyj(l zOxNv-hhj6stPD{LM(qxi+#3^t{L3!vlZS7lxVWHH^&oZQS5nnzx@g|{o4o1J2AH;Gi;iaEsZNM~N??gA4 zfFZI#vE;TxO?Y|hSJMqB%k@v3DUPF2j1@kfaO$N`IIj9s!m7`CT=nrmyX!UcV`dDJ z!(B3KIzA46ne^|fRrhyZ)22`;@2uptm8h?6#i*^_O8qgxLL+%xN^lG(Ff=HVr(nW30a5;;oJd6v3F30s m>dW~*-afCG+x3dMzy8JUKX4jr?-Xjk=vcx|`k%oAXo9z-R1seQ diff --git a/optimizer/optimize.m b/optimizer/optimize.m index fa9e708..6ccb4d6 100644 --- a/optimizer/optimize.m +++ b/optimizer/optimize.m @@ -84,8 +84,8 @@ % else % model.cablecnst = 0; % end -% model.umax = [ 6.11,6.00,6.071,1.3557,1.1164]'; - model.umax = [ 1,1,1,1,1]'; + model.umax = [ 6.11,6.00,6.071,1.3557,1.1164]'; +% model.umax = [ 1,1,1,1,1]'; @@ -119,7 +119,7 @@ if isfield(model,'task') - p_lb = 1; + p_lb = 0.5; p_ub = 1.4; % p_lb = 1; % p_ub = 1; @@ -463,7 +463,7 @@ h = model.h; load('Cons.mat') c = zeros(model.Ncon,1); % initialize the constraints - c = Cons; % initialize the constraints +% c = Cons; % initialize the constraints if model.nconpath == 2 c = [Cons;Cons(end)]; @@ -593,8 +593,21 @@ % flywheel_pos2 = xi2(1); % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position + + +% ivel = +% 7:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+7; +% %nvarpernode +% iF = 13:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+13; +% V_fw = X(ivel); +% F = X(iF); +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) / (model.N-1) - model.REQPOWER; + model.c=c; plot(model.c) + + + end @@ -781,7 +794,18 @@ end end - +% ivel = 7:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+7; +% iF = 13:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+13; +% V_fw = X(ivel); +% F = X(iF); +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) /(model.N-1) - model.REQPOWER; +% +% for i=1:model.N-1 +% +% J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, ivel(i)) = F(i)/(model.N-1); +% J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, iF(i)) = V_fw(i)/(model.N-1); +% end + end From c254bdd03cd3d11f1819b3fbdf1e8d9329786838 Mon Sep 17 00:00:00 2001 From: Frohani Date: Mon, 4 Jun 2018 09:41:52 -0400 Subject: [PATCH 22/23] Power constraint is added --- main/main.m | 7 +++-- main/rowingtest.mat | Bin 54756 -> 54655 bytes optimizer/optimize.m | 69 ++++++++++++++++++++++++------------------- 3 files changed, 42 insertions(+), 34 deletions(-) diff --git a/main/main.m b/main/main.m index 110e73a..84c02f6 100644 --- a/main/main.m +++ b/main/main.m @@ -18,6 +18,7 @@ problem.np =1; % on/off switch for constraints problem.N = 70; % number of collocation points % problem.N = 50; % used for derivetive checking + problem.Reqpower = 0.0976; if problem.np == 1 problem.task.Lmin = 0.2077; % min and max of cable lenght from the data problem.task.Lmax = 1.1288; @@ -27,12 +28,12 @@ problem.ntask = 0; end - problem.component = 'spring'; % choose if we want to use damper or spring + problem.component = 'damper'; % choose if we want to use damper or spring problem.discretization = 'BE'; % Backward Euler(BE) or Midpoint Euler(ME) discretization problem.tracking = 3; % if 1 tracking the angles only else track all states (but flywheel velocity) % objective function gains (Wtrack=1 for the tracking and Weffort=1 for predictive simulation) - problem.Wtrack =0; - problem.Weffort =1; + problem.Wtrack =1; + problem.Weffort =0; result = optimize(problem); save 'rowingtest' result end diff --git a/main/rowingtest.mat b/main/rowingtest.mat index 7b9d8e9c65225b9273a9b44312a404154e6615e7..2d8da2202838767e5ca085772e4d934cbec30c0f 100644 GIT binary patch literal 54655 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a/optimizer/optimize.m b/optimizer/optimize.m index 6ccb4d6..d3dba1d 100644 --- a/optimizer/optimize.m +++ b/optimizer/optimize.m @@ -21,6 +21,9 @@ model.tracking = problem.tracking; model.Wtrack = problem.Wtrack; model.Weffort = problem.Weffort; + if isfield(problem,'Reqpower') + model.Reqpower = problem.Reqpower; + end if isfield(problem,'task') model.task.Lmin = problem.task.Lmin; model.task.Lmax = problem.task.Lmax; @@ -88,8 +91,8 @@ % model.umax = [ 1,1,1,1,1]'; - - + +% % define the state variables x, controls u, and their bounds % x = [x_fw, q1 ...q5, v_fw, qd1...qd5, F(kn)] % u = [M1(knm)...M5]; @@ -183,6 +186,9 @@ model.ntask = model.ncontaskcbl + model.nconpath ; % sum of cable and path constraints model.Ncon = model.ncondyn + model.ncontaskper + model.ntask; % number of constrains (including state and control periodicity) + if isfield(problem,'Reqpower') + model.Ncon = model.ncondyn + model.ncontaskper + model.ntask + 1; + end if isfield(model,'task') model.ip = model.N*model.Nvarpernode + (1:model.npar); % since we only have 1 parameter, Npar = 1 else @@ -262,7 +268,8 @@ model.conjacstructure(end-1:end,:) = 1; % Check the derivations, if N=10 was specified - if N == 50 + if N == 4 + checkderiv; % compare gradient and Jacobian against finite difference approximations end @@ -594,15 +601,15 @@ % flywheel_pos = f*flywheel_pos1 + (1-f)*flywheel_pos2; % c(end-model.ntask+3) = flywheel_pos - model.task.Lmax; % difference between maximum cable length and flwyheel position - -% ivel = -% 7:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+7; -% %nvarpernode -% iF = 13:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+13; -% V_fw = X(ivel); -% F = X(iF); -% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) / (model.N-1) - model.REQPOWER; - + if model.Reqpower>0 + + ivel =7:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+7; + %nvarpernode + iF = 13:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+13; + V_fw = X(ivel); + F = X(iF); + c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) / (model.N-1) - model.Reqpower; + end model.c=c; plot(model.c) @@ -624,13 +631,13 @@ % c = zeros(model.Ncon,1); % initialize the constraints load('Cons.mat') c = zeros(model.Ncon,1); % initialize the constraints - c = Cons; % initialize the constraints +% c = Cons; % initialize the constraints - if model.nconpath == 2 - c = [Cons;Cons(end)]; -% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = 0.8014; -% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; - end +% if model.nconpath == 2 +% c = [Cons;Cons(end)]; +% % c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+1) = 0.8014; +% % c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+2) = 0.7866; +% end par.Yankle = 0.5182; par.ForearmLen = 0.2355; par.ShankLen = 0.4252; @@ -793,20 +800,20 @@ end end end - -% ivel = 7:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+7; -% iF = 13:model.nx+model.nu:(model.N-1)*(model.nx+model.nu)+13; -% V_fw = X(ivel); -% F = X(iF); -% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) /(model.N-1) - model.REQPOWER; -% -% for i=1:model.N-1 -% -% J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, ivel(i)) = F(i)/(model.N-1); -% J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, iF(i)) = V_fw(i)/(model.N-1); -% end - + if model.Reqpower>0 + ivel = 7:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+7; + iF = 13:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+13; + V_fw = X(ivel); + F = X(iF); +% c(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1) = sum(V_fw .* F) /(model.N) - model.Reqpower; + + for i=1:model.N-1 + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, ivel(i)) = F(i)/(model.N-1); + J(model.ncondyn + model.ncontaskper + model.ncontaskcbl+model.nconpath+1, iF(i)) = V_fw(i)/(model.N-1); + end + + end end %==================================================================== From 8367345c01a3d8c8e44ad93bfc9066bec991688c Mon Sep 17 00:00:00 2001 From: Frohani Date: Thu, 13 Sep 2018 13:47:44 -0400 Subject: [PATCH 23/23] Here is the final update for predictive simulation code It works for both tracking problem as well as the predictive simulation howver, in the case of predictive simulation the handle goes below the hip which is reality is not possible --- main/main.m | 20 +++++++++++----- main/rowingtest.mat | Bin 54655 -> 54757 bytes optimizer/optimize.m | 54 ++++++++++++++++++++++++++++++++++++++++--- 3 files changed, 65 insertions(+), 9 deletions(-) diff --git a/main/main.m b/main/main.m index 84c02f6..3248a03 100644 --- a/main/main.m +++ b/main/main.m @@ -17,23 +17,31 @@ problem.dyngain = 1; % scaling factor for non path constraint problem.np =1; % on/off switch for constraints problem.N = 70; % number of collocation points -% problem.N = 50; % used for derivetive checking - problem.Reqpower = 0.0976; +% problem.Reqpower = 0.0976; % we can define the woring power here + %( we can either use power or path constraint-so if using problem.Reqpower make sure that problem.nconpath = 0) if problem.np == 1 problem.task.Lmin = 0.2077; % min and max of cable lenght from the data problem.task.Lmax = 1.1288; + % task constraints---> when increased even by 1 either for cable for wrist position, the IPOPT cannot solve the + % problem anymore problem.cablecnst = 2; % number of constraints for task when doing predictive simulation (cable length) Lmin & Lmax - problem.nconpath = 1; % Zwrist constraint (depends on the number of nodes can be varies between 0 and model.N) + problem.nconpath = 1; % Zwrist constraint (depends on the number of nodes can be varies between 0 and 2 for now) + % when increasing the number of path constraint to 2 IPOPT connot + % solve it anymore! else problem.ntask = 0; end - problem.component = 'damper'; % choose if we want to use damper or spring + + problem.component = 'spring'; % choose if we want to use damper or spring problem.discretization = 'BE'; % Backward Euler(BE) or Midpoint Euler(ME) discretization problem.tracking = 3; % if 1 tracking the angles only else track all states (but flywheel velocity) % objective function gains (Wtrack=1 for the tracking and Weffort=1 for predictive simulation) - problem.Wtrack =1; - problem.Weffort =0; + problem.Wtrack =0; + problem.Weffort =1; + % tracking problem:when problem.Wtrack =1 and problem.Weffort =0 works perfectly; + % peredictive simulation problem: when problem.Wtrack =0 and problem.Weffort =1 works perfectly; + % for now we only use predictive simulation result = optimize(problem); save 'rowingtest' result end diff --git a/main/rowingtest.mat b/main/rowingtest.mat index 2d8da2202838767e5ca085772e4d934cbec30c0f..538120cf29ced7d34e8233166eae6d627d9c1fd2 100644 GIT binary patch literal 54757 zcmeFWWl&rJvn`4Q2oAyBEjR=l1_%-?1W#}YPJm%>cMA}lAc4U(Sdicv+(RJfV8Pwp 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zu}|&{K#u;YfO|xQ!Cj2n>ghXR(cXT*t6c{M_0P_KE*(NTA;d{*J*^F9>x|~k_B#La zjC2W&ETj=K!)5FI!_oeOo2w<~&Gu`xj*f`rbHxHFUz@qnLXkK&Tp$#S$gbFMo`5eD z&oGhU+~^2FxNs)#=8HtL@o&A)-Q{yWEN4aga2#zm&2X;&gEO3+U%y?p@sjP1b$0 + if isfield(model,'Reqpower') ivel =7:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+7; %nvarpernode @@ -800,7 +847,8 @@ end end end - if model.Reqpower>0 + if isfield(model,'Reqpower') + ivel = 7:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+7; iF = 13:model.nx+model.nu:(model.N-2)*(model.nx+model.nu)+13; V_fw = X(ivel);

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zj7A}bZO~}Mum>8I80J8u6T@L>lww#Mjn*v;Lr^*zwb%(S(dfnS1RBK{=0Kwv!{KOD zWB42z-59=wMmdIepwYgG!S$geH0-exlF{(T@B?%hz;Gct9ANkfIxJv#1|1$S+=>np v7-m6-3o3S`#{FvH*06z{upJ#fFzkd5BN#45hZ78^qQeS?FHnaUFpm5UkW~J% diff --git a/tools/bodyangles.m b/tools/bodyangles.m index 3933b1b..aa1409a 100644 --- a/tools/bodyangles.m +++ b/tools/bodyangles.m @@ -1,5 +1,6 @@ function [q,t2,p] = bodyangles % better fucntion name the part that produce p and q + global problem % load X2016_03_17_trial2_markers load('../data/Mdata2'); @@ -69,43 +70,50 @@ legend('q1','q2','q3','q4','q5'); set(gcf,'renderer','painters'); - % determine model parameters - p.ShankLen = mean(sqrt((kneeY-ankleY).^2+(kneeZ-ankleZ).^2)); - p.ThighLen = mean(sqrt((hipY-kneeY).^2+(hipZ-kneeZ).^2)); - p.TrunkLen = mean(sqrt((shoulderY-hipY).^2+(shoulderZ-hipZ).^2)); - p.UpparmLen = mean(sqrt((elbowY-shoulderY).^2+(elbowZ-shoulderZ).^2)); - p.ForearmLen = mean(sqrt((wristY-elbowY).^2+(wristZ-elbowZ).^2)); - % calculate the coordinate of ankle point, and assume it is fixed p.Xankle = mean(ankleZ); p.Yankle = mean(ankleY); - + % do the linear polyfit of hip motion track for the alpha angle coeff = polyfit(hipZ,hipY,1); p.a=coeff(1,1); p.b=coeff(1,2); %FIT A STAIGHT LINE THROUGH A LINEAR REGRETION - % define scale factor to convert kg to Mg and N to kN - scale = 0.001; - p.M = scale * 80; % body mass (kg) - % determins sprocket position based on the most forward position of the % wrist (IN FUTURE WORK WE NEED A MARKER) %i = find(max(wristZ)); [p.Xsprocket,i] = max(wristZ); p.Xsprocket = max(wristZ) + 0.1; p.Ysprocket = wristY(i); - - % These are model parameters + + % determine model parameters + p.ShankLen = mean(sqrt((kneeY-ankleY).^2+(kneeZ-ankleZ).^2)); + p.ThighLen = mean(sqrt((hipY-kneeY).^2+(hipZ-kneeZ).^2)); + p.TrunkLen = mean(sqrt((shoulderY-hipY).^2+(shoulderZ-hipZ).^2)); + p.UpparmLen = mean(sqrt((elbowY-shoulderY).^2+(elbowZ-shoulderZ).^2)); + p.ForearmLen = mean(sqrt((wristY-elbowY).^2+(wristZ-elbowZ).^2)); + + % define scale factor to convert kg to Mg and N to kN + scale = 0.001; + p.M = scale * 80; % body mass (kg) + + % These are model parameters p.g = 9.80665; % gravity(N/kg) - p.Kseat = scale * 10^5; % seat stiffness (kN/m) - p.Cseat = 2*sqrt(p.M*p.Kseat); % seat damping (kNs/m), close to critical damping + p.Kseat = 10^5; % seat stiffness (kN/m) + p.Cseat = 2*sqrt(p.M*p.Kseat); % seat damping (kNs/m), close to critical damping % rowing machine parameters from parameter identification p.C = scale * 89.68; % flywheel damping coefficient kN/(m/s)^2 - p.m = scale * 539.6; % flywheel equivalent mass - p.Kcrm = scale * 28386; % stiffness of ratchet mechanism (kN/m) - p.Bcrm = scale * 0; % damping of ratchet mechanism (kNs/m) + p.m = scale * 539.6; % flywheel equivalent mass + if strcmp(problem.component,'spring') + p.Kcrm = scale * 28386; % stiffness of cable and ratchet mechanism (kN/m) (CHECK VALUE IN PARAMETER IDENTIFICATION + p.Bcrm = scale * 0; + elseif strcmp(problem.component,'damper') + p.Bcrm = scale * 2700; % damping of ratchet mechanism (kNs/m) + p.Kcrm = scale * 0; + else + warning('Please especify the proper component (spring/damper)'); + end p.K = scale * 12.97 ; % shock cord stiffness (kN/m) p.L0 = 0.2; % the wrist-sprocket distance at which shock cord has no force @@ -124,7 +132,8 @@ p.ThighCM = (1-0.433)*p.ThighLen; p.TrunkCM = (1-0.500)*p.TrunkLen; p.UpparmCM = 0.436*p.UpparmLen; - p.ForearmCM = 0.430*p.ForearmLen; + p.ForearmCM = 0.430*p.ForearmLen; + %q = [q1,q2,q3,q4,q5]; % extract joint angle trajectories (states 1-5) %figure(9); %animate(q,p); From 65a7ea6bb339cd99e15371f781091e2e135bc68a Mon Sep 17 00:00:00 2001 From: Frohani Date: Mon, 19 Mar 2018 16:16:54 -0400 Subject: [PATCH 16/23] The most updated code by 03192018 --- main/main.m | 20 ++++++++++++++++---- main/rowingtest.mat | Bin 0 -> 50464 bytes optimizer/optimize.m | 19 ++++++++++++------- tools/bodyangles.m | 18 ++++++++++++++---- 4 files changed, 42 insertions(+), 15 deletions(-) create mode 100644 main/rowingtest.mat diff --git a/main/main.m b/main/main.m index eeaa7ec..35bcf21 100644 --- a/main/main.m +++ b/main/main.m @@ -12,17 +12,29 @@ addpath(genpath('tools')) addpath(genpath('data')) - problem.initialguess = 'midpoint'; + problem.initialguess = 'sim'; + %wt=1 we=1 + %using sim:3.0867449e-002 + %using midpoint:3.0867449e-002 + %using random: 5.7851888e-002 + %using zero: IPOPT did not solve + + %wt=1 we=10 + %using sim:6.9785323e-002 + %using midpoint:6.9785323e-002 + %using random: 1.2850537e-001 + %using zero: IPOPT did not solve + problem.N = 70; % number of collocation points - % problem.N = 4; % used for derivetive checking +% problem.N = 4; % used for derivetive checking problem.np = 1; problem.task.Lmin = 0.2077; % min and max of cable lenght from the data problem.task.Lmax = 1.1288; problem.component = 'damper'; % choose if we want to use damper or spring problem.discretization = 'BE'; % Backward Euler(BE) or Midpoint Euler(ME) discretization problem.tracking = 3; % if 1 tracking the angles only else track all states (but flywheel velocity) - problem.Wtrack = 0; - problem.Weffort = 1; + problem.Wtrack = 1; + problem.Weffort = 0; result = optimize(problem); save 'rowingtest' result end diff --git a/main/rowingtest.mat b/main/rowingtest.mat new file mode 100644 index 0000000000000000000000000000000000000000..62f2c7d869e46b6aba5f89c46655aff4f281f789 GIT binary patch literal 50464 zcmeFZRZv`g^evbK3m!bUySqCCcXzkYK=9xRF2S9~-DxDa1$Pb5cyNc%SbzpD@cr+d znwpn+ny2YQ6^ANn)!u9E-`;C;PN5{OsVFW%#?8V;rX;S(Y;6ayVj@!on7LUyxi|=r zsY>d|Df4hKkx9B(nYme6k~ujFkSRGik|~+Fkg@ZVv2zM=^9itVka4iF^O60({Ji#EQ(@pU{Ce8a?P z3<=eF5ml>`MO?s)=>3xbi=;Y+Yu=9;J&}UhV z*f$eh-8WNMDsKfHCHn029>xdF%0>m@aLQ{09oh>;hjUs~$%|B6kzT$@J`q|8`}>&p z*g1wCEy_ho>3I_rq-S|5QG0Qnceix=Pn{V4&Wt|d(o+-#YxzM#bSP?&5#rOxV<;HG zdKXP8_f(#f)L%)%(U{xZc6#3#Bp9|CS49ts5!MEa$)c3IWXLWWq#914TR z&6Caxi-5GEcz#Wy`G*Xu{>Kxl|7V?v^N_x~KduGb zyMwYM0gblA+eYHoFhaLSFR*$55vn89%2E10;UKP;Lp}|9-mq}`wdx?^v|L*h3DcF1*s7`r(fuVh40w!Ut!nv=IM73Wy 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index of Model.time which is just less than tmax: Huawei + i = find( -1 == diff(tmax > model.time) ); % find the index of Model.time which is just less than tmax: Huawei + f = (tmax-model.time(i))/(model.time(i+1)-model.time(i)); % xi1 = X( (model.nx+model.nu)*(i-1) + (1:model.nx) ) ; % the state x at node i [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point diff --git a/tools/bodyangles.m b/tools/bodyangles.m index aa1409a..c4ce5e2 100644 --- a/tools/bodyangles.m +++ b/tools/bodyangles.m @@ -103,18 +103,28 @@ p.Cseat = 2*sqrt(p.M*p.Kseat); % seat damping (kNs/m), close to critical damping % rowing machine parameters from parameter identification - p.C = scale * 89.68; % flywheel damping coefficient kN/(m/s)^2 - p.m = scale * 539.6; % flywheel equivalent mass + p.C = scale * 92.7427; % flywheel damping coefficient kN/(m/s)^2 + p.m = scale * 557.6094; % flywheel equivalent mass if strcmp(problem.component,'spring') p.Kcrm = scale * 28386; % stiffness of cable and ratchet mechanism (kN/m) (CHECK VALUE IN PARAMETER IDENTIFICATION p.Bcrm = scale * 0; elseif strcmp(problem.component,'damper') - p.Bcrm = scale * 2700; % damping of ratchet mechanism (kNs/m) + p.Bcrm = scale * 3111.8023; % damping of ratchet mechanism (kNs/m) p.Kcrm = scale * 0; else warning('Please especify the proper component (spring/damper)'); end - p.K = scale * 12.97 ; % shock cord stiffness (kN/m) + +% Estimated model parameters: +% b1 = 0.0000 Ns/m +% c1 = 92.7427 Ns^2/m^2 +% m1 = 557.6094 kg +% k = 0.0000 N/m +% b2 = 3111.8023 Ns/m +% m2 = 0.0000 kg +% k2 = 14.0700 N/m +% epsilon = 0.0001 + p.K = scale * 14.07 ; % shock cord stiffness (kN/m) p.L0 = 0.2; % the wrist-sprocket distance at which shock cord has no force % body segment parameters calculated using the tables from Winter's book From e109c3f2d5672b4b3050c1e1f35ca9f7162632ec Mon Sep 17 00:00:00 2001 From: Ton van den Bogert Date: Tue, 20 Mar 2018 17:15:43 -0400 Subject: [PATCH 17/23] corrected an error in the Lmax linear interpolation --- optimizer/optimize.m | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/optimizer/optimize.m b/optimizer/optimize.m index 96fa3df..2b2a06f 100644 --- a/optimizer/optimize.m +++ b/optimizer/optimize.m @@ -419,7 +419,7 @@ [~,~,~,~,Li1] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes + Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes c(end-model.ntask+2) = Ltmax - model.task.Lmax; % difference between maximum cable length from the previous simulation results and maximum cable length end @@ -509,7 +509,7 @@ [~,~,~,~,Li1,dLi1dt] = dynfun(xi1,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length first point xi2 = X( (model.nx+model.nu)*i + (1:model.nx)) ; % the state x at node i+1 [~,~,~,~,Li2,dLi2dt] = dynfun(xi2,zeros(model.nx,1),zeros(model.nu,1)); % find the max cable length second point - Ltmax = f*Li1 + (1-f)*Li2 ; % linear interpolation of two above nodes + Ltmax = (1-f)*Li1 + f*Li2 ; % linear interpolation of two above nodes J(end-model.ntask+2 , (model.nx+model.nu)*(i-1) + (2:6)) = f* dLi1dt ; J(end-model.ntask+2 , (model.nx+model.nu)*i + (2:6)) = (1-f)*dLi2dt; dLtmaxdf = Li1 - Li2; From a6fd8f1e9ec28531e8f84a07a84464a211cf95a1 Mon Sep 17 00:00:00 2001 From: Frohani Date: Fri, 11 May 2018 11:58:20 -0400 Subject: [PATCH 18/23] 05112018 Included path constraint --- main/Cons.mat | Bin 0 -> 3994 bytes main/main.m | 41 +++-- main/rowingtest.mat | Bin 50464 -> 54841 bytes model/animate.m | 6 +- model/dynfun.m | 3 +- optimizer/makeplots.m | 242 ++++++++++++++++++++------ optimizer/optimize.m | 385 +++++++++++++++++++++++++++++++++--------- 7 files changed, 517 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