Lagrangian Formulation Space Biomedical Engineerin Life Support Compute the velocity and angular velocity of an individual link i ( think of the link as an end effector with coord sys at the link c. m) Ja,+.,+J q1 0=h+…+J=Jq (2-2) where Ju? and JU are the j-th column vectors of the 3xn Jacobian matrices J and Jw for the linear and angular velocities of link i, e J….J0….0 J000 (2-3) Note: Since the motion of link i depends on only joints 1 through i, the column vectors are set to zero for i>Lagrangian Formulation • Compute the velocity and angular velocity of an individual link i (think of the link as an end effector with coord sys a t the link c.m.) ω J J J q v J J J q D l D D D l D D ( ) ( ) 1 ( ) 1 ( ) ( ) 1 ( ) 1 i i A i Ai i ci A i i L i Li i ci L q q q q = + + = = + + = where j-th column vectors of the 3xn Jacobian matrices link i, i.e., (i ) Lj J (i ) Aj J (i ) J L (i ) J A [ ] [ ] ( ) ( ) 1 ( ) ( ) ( ) 1 ( ) J J J 0 0 J J J 0 0 h h h h i Ai i A i A i Li i L i L = = Note: tion of link i depends on only joints 1 through i, the column vectors are set to zero for j ≥ (2-2) (2-3) and are the and for the linear and angular velocities of Since the mo i