SELF-ORGANIZATION OF TRAJECTORY FORMATION .2. THEORETICAL-MODEL

Most studies of movement coordination deal with temporal patterns of s ynchronization between components, often without regard to the actual amplitudes the components make. When such a system is required to prod uce a composite action that is spatially constrained, coordination per sists, but its stability is modulated by spatial requirements effected , we hypothesize, through the component amplitudes. As shown experimen tally in part I, when a redundant three-joint system (wrist, elbow, an d shoulder) is required to trace a specified are in space, the joint a ngles may be frequency- and phased-locked even as the curvature of the trajectory is manipulated. Transitions between joint coordination pat terns occur at a critical curvature, accompanied by a significant redu ction in wrist amplitude. Such amplitude reduction is viewed as destab ilizing the existing coordinative pattern under current task constrain ts, thereby forcing the joints into a more stable phase relationship. This paper presents a theoretical analysis of these multijoint pattern s and proposes an amplitude mechanism for the transition process. Our model uses three linearly coupled, nonlinear oscillators for the joint angles and reproduces both the observed interjoint coordination and c omponent amplitude effects as well as the resulting trajectories of th e end effector.