Invariant characteristics of horizontal-plane minimum-torque-change movements with one mechanical degree of freedom

Abstract

Uno et al. (1989) suggested that movements are organized such that the squared change of torque is minimized over time. Although influential, this theory has attracted much less attention from experimental researchers than the competing minimum-jerk model (Flash and Hogan 1985). One reason for this relative neglect has been the lack of general quantitative predictions, which results from the belief that minimum-torque-change trajectories have to be computed numerically for individual movements and arm-dynamical parameters. In the present paper, we show that for an important special case, that of planar horizontal movements with one mechanical degree of freedom (DOF), it is actually possible to find an analytic expression for the predicted minimum-torque-change trajectories. Based on this mathematical result, we derive a set of properties which are characteristic of these trajectories and compare them to experimental data which have not previously been related to the minimum-torque-change model. Certain discrepancies between these experimental data and minimum-torque-change model predictions are revealed.