8.2 Inverse dynamics - analytically, Round II

Using our preliminary data from Problem 8.1 above, we were able to land a small grant and have used the money to purchase a force plate. With our improved experimental set-up we can now measure the horizontal (fore-aft) and vertical ground reaction forces during the sit-to-stand motion. Also, our video system remains operational, and we shall continue to record the time history of the angular displacements of the shank, thigh, and trunk.

On the basis of the three segment, planar model shown below, use the kinematic and force-plate data now available to:
(a) Derive complete analytical expressions for the net joint torques exerted at the ankle (), knee (), and hip () during the sit-to-stand motion. Again, assume that the foot remains flat on the floor.

(b) By comparing the terms in your equations for , , and  derived in part (a) to those derived in Problem 8.1(a), discuss the advantages to being able to accurately estimate the ground reaction forces and relevant kinematic parameters when calculating joint torques. 

Figure 1. Planar 3 segment model