Cyclist-leg

Cyclist-leg - % Cyclist leg % 2 DOF closed-loop leg model...

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Sheet1 Page 1 % Cyclist leg % 2 DOF closed-loop leg model use to demonstrate % a) Forward dynamics, % b) Inverse dynamics, and % c) Mixed dynamics % with geometric (i.e., holonomic) constraints % N1> is to the right, N2> is upward, and N3> = N1> x N2> % Set up problem OVERWRITE ON FRAMES N,B BODIES T,S,F,C POINTS H,K,A,P,O CONSTANTS LT,LS,LF,LC,LB,G,QB MASS T=MT,S=MS,F=MF,C=MC INERTIA T,0,0,MASS(T)*LT^2/2 INERTIA S,0,0,MASS(S)*LS^2/2 INERTIA F,0,0,MASS(F)*LF^2/2 INERTIA C,0,0,MASS(C)*LC^2/2 VARIABLES QT',QS',QF'',QC'',F1,F2,TH,TK,TA AUTOZ ON ZEE_NOT=[QF'',QC'',F1,F2,TH,TK,TA] % Rotation matrices SIMPROT(N,T,3,QT) SIMPROT(N,S,-3,QS) SIMPROT(N,F,3,QF) SIMPROT(N,C,-3,QC) SIMPROT(N,B,3,QB) % Loop equations for kinematic constraints % Solve for QT' and QS' as functions of QF' and QC' % Anywhere QT'' or QS'' would appear in the future, we will % have combinations of QF'' and QC'' instead LOOP>=-LT*T2>-LS*S2>-LF*F2>-LC*C2>+LB*B2> LOOP=DOT(LOOP>,[N1> LOOPDOT=DT(LOOP) SOLVE(LOOPDOT,QT',QS') % Rotational kinematics W_T_N>=QT'*N3> W_S_N>=-QS'*N3> W_F_N>=QF'*N3> W_C_N>=-QC'*N3> ALF_T_N>=DT(W_T_N>,N) ALF_S_N>=DT(W_S_N>,N) ALF_F_N>=DT(W_F_N>,N) ALF_C_N>=DT(W_C_N>,N) % Translational kinematics V_H_N>=0> P_H_TO>=-0.5*LT*T2>

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Sheet1 Page 2 V2PTS(N,T,H,TO) % V_TO_N> P_H_K>=-LT*T2> V2PTS(N,T,H,K) % V_K_N> P_K_SO>=-0.5*LS*S2> V2PTS(N,S,K,SO) % V_SO_N> P_K_A>=-LS*S2> V2PTS(N,S,K,A) % V_A_N> P_A_FO>=-0.5*LF*F2> V2PTS(N,F,A,FO) % V_FO_N> V_O_N>=0> P_O_CO>=0.5*LC*C2> V2PTS(N,C,O,CO) % V_CO_N> A_H_N>=0> A2PTS(N,T,H,TO) % A_TO_N> A2PTS(N,T,H,K) % A_K_N> A2PTS(N,S,K,SO) % A_SO_N> A2PTS(N,S,K,A) % A_A_N> A2PTS(N,F,A,FO) % A_FO_N> A_O_N>=0> A2PTS(N,C,O,CO) % A_CO_N>
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Cyclist-leg - % Cyclist leg % 2 DOF closed-loop leg model...

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