Development of a set of equations describing joint trajectories during para-sagittal lifting

Given a lifting task with predetermined starting and ending positions, the angular trajectories are usually very consistent with a distinctive pattern. This paper derives a set of equations that can describe the joint trajectories during a para-sagittal lifting task. Three optimal motion patterns were also expressed by the polynomials: minimal hand jerk, minimal center of gravity (CG) jerk, and minimal muscle utilization rate (MUR). The variability of the joint movements were synthesized by overlapping the optimal patterns.