Asymmetric velocity and acceleration profiles of human arm movements.

Displacement, velocity, acceleration and jerk (change of acceleration with time) were analyzed for arm flexion movement over a wide range of movement amplitudes and speeds. Relative time to peak velocity or relative duration of acceleration, k, was approximately 0.5 for the movements with intermediate speed (about 0.5 s in movement time), i.e., symmetric velocity and acceleration profiles. For the slow and ballistic movements, k shifted towards values below and above 0.5, respectively creating asymmetric profiles. Consistent k-dependence of movement time, peak velocity, maximum acceleration and maximum deceleration were observed. "Jerk cost", the square of the magnitude of jerk integrated over the entire movement, was calculated for each movement. A dynamic optimization technique to minimize jerk cost under the constraint on jerk input was applied to interpret the results, assuming that a major goal of skilled movements was to produce optimally smooth movements. The constrained minimum-jerk model explained speed-dependent asymmetry of the velocity and acceleration profiles. Jerk cost consumed by the movements with intermediate speed approximately satisfied minimum-cost criterion predicted by the model but was higher than the criterion for slow and ballistic movements. The results suggested that optimality criteria other than jerk cost also should be considered to predict movement profiles over the entire range of speeds.