Theoretical Analysis of the Force and Position Synergies in Two-Joint Movements

Abstract

A theoretical approach is proposed to define the force and position singular points (FSPs and PSPs) in the circular, ellipsoidal, and linear planar two-joint movements produced under steady loadings directed along the movement traces. The FSPs coincide with changes in the direction of the force moments acting around the joints; the PSPs show the locations of the extrema at the joint angle trajectories. The force synergy (defined by the location of FSPs) provides a strong influence on the activation synergy; the latter is largely described by correlations between the activities recorded from the muscles participating in the movement. The position synergy (defined by the location of PSPs) is responsible for a hysteresis-related modulation of the activation synergy. Geometrical procedures are proposed to define positions of the FSPs and PSPs along various movement traces; this can provide a general description of the force and position synergies for the movements. The force synergies in the circular movements cover four sectors with diverse loading combinations of the flexor and extensor muscles belonging to different joints. The variability of the synergy effects for changes in the size and position of the circular trajectories is analyzed; the synergy patterns are also considered for ellipsoidal and linear movement traces. A Force Feedback Control Hypothesis is proposed; it allows one to explain the decrease in the number of controlled variables during real multi-joint movements.