Lagrangian Formulation Space Biomedical Engineerin Life Support Each column vector is given by G-b, xri-lci (revolute jt) Position vector of centroid of link i wrt inboard link (prismatic jt) coordinate frame b (revolute jt) bi-1= 3x1 unit vector along joint (prismatic jt) axIs T=∑(mvva+0o)(25) Where m=mass of link i I. =3x 3 inertia tensor at the centroid wrt base coord frame Note: I. varies with the orientation of the link wrt the base coord frameLagrangian Formulation • Each column vector is given by:    =    × = − − − − 0 b J b b r J ( ) 1 1 1 1, ( ) i j Aj j j j ci i Lj (revolute jt) (prismatic jt) (revolute jt) (prismatic jt) rj −1,ci = Position vector of centroid of link i wrt inboard link coordinate frame b j −1 = 3x1 unit vector along joint axis j-1 (2-4) ∑ ( = = + n i i i T ci i T m i ci 1 2 1 2 T 1 v v ω I ω (2-5) where inertia tensor at the centroid, wrt base coord frame mass of link = 3 × 3 = i i m i I Note: wrt the base coord frame i I ) varies with the orientation of the link