Kinematic models and human elbow flexion movements: quantitative analysis.

The smoothness with which movements are customarily performed has led Hogan (1984) to formulate a model for trajectory planning by the central nervous system in which the goal is to maximize smoothness, one measure of which is the integrated mean squared magnitude of jerk (jerk cost). We tested the applicability of this minimum-jerk model to one-joint goal directed movements performed by human subjects at different speeds and amplitudes, by comparing kinematic parameters and the jerk cost predicted by the mathematical model with values calculated from experimental data. We also tested a higher order, minimum-snap kinematic model. Normal subjects performed elbow flexions of 5 to 50 degrees "as rapidly and accurately as possible" and also at slower speeds. The boundary conditions of both models were adjusted to account for the failure of subjects to produce movements which reached equilibrium precisely at the target (so that acceleration and velocity reached zero together). Typically, fast movements (less than 300 ms duration) were fairly symmetric in that the durations and amplitudes of acceleration and deceleration were approximately equal; slower movements (greater than 300 ms) were asymmetric with strong, brief acceleration peaks and broad, slow deceleration peaks. In fast movements, the calculated jerk cost was consistently higher than predicted by the minimum-jerk model; a good fit to all kinematic parameters was provided by the minimum-snap model (a seventh-order polynomial). Neither model consistently predicted the trajectories of slower movements. We conclude that muscle/limb dynamics can account for the success of the minimum-snap model with fast movements, and that there is no evidence of planning for maximal smoothness in slower movements.