Jerk (time derivative of acceleration) of the endpoint of a multi-joint kinematic chain can be represented as the sum of terms related to jerks, accelerations, and velocities in individual joints. We investigated the relative contribution of these terms during simulations of planar movement of a 3-segment kinematic chain and also during unconstrained movements at different velocities, over different amplitudes, and with different intentionally changed curvature. Our results demonstrate that the term related to individual joint jerks dominates in the total endpoint jerk. This domination was particularly strong during voluntary movements and was not as striking during the simulations based on 5th-order polynomial functions for individual joint trajectories. Thus, the minimum-jerk criterion for multi-joint movements can be well approximated by minimization of the jerk-related terms for individual joints. The decomposition of endpoint jerk into its terms shows potential limitations of the commonly used 5th-order polynomial modeling for describing voluntary multi-joint movements.
J. Laczko and J. Tihanyi are with the Hungarian University for Physical Education, Budapest H-1125, Hungary. S. Jaric is with the Center for Musculo-skeletal Research at the National Institute for Working Life, Umeo, Sweden. V.M. Zatsiorsky and M.L. Latash are with the Department of Kinesiology at the Pennsylvania State University, University Park, PA 16802.