SELF-ORGANIZATION OF TRAJECTORY FORMATION .1. EXPERIMENTAL-EVIDENCE

Most studies examining the stability and change of patterns in biologi cal coordination have focused on identifying generic bifurcation mecha nisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescen t degrees of freedom (df) are spontaneously recruited and active df su ppressed. To examine such behavior, in part I we study a single limb s ystem composed of three joints (wrist, elbow, and shoulder) performing the kinematically redundant task of tracing a sequence of two-dimensi onal arcs of monotonically varying curvature, kappa. Arcs were display ed on a computer screen in a decreasing and increasing kappa sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted t o flexion-extension of the wrist, elbow, and shoulder. Only a few coor dinative patterns among the three joints were stably produced, e.g., i n-phase (flexion-extension of one joint coordinated with flexion-exten sion of another joint) and antiphase (flexion-extension coordinated wi th extension-flexion). As kappa was systematically increased and decre ased, switching between relative phase patterns was observed around cr itical curvature values, kappa(c). A serendipitous finding was a stron g 2:1 frequency ratio between the shoulder and elbow that occurred acr oss all curvature values for some subjects, regardless of the wrist-el bow relative phase pattern. Transitions from 1:1 to 2:1 frequency entr ainment and vice versa were also observed. The results indicate that b oth amplitude modulation and relative phase change are utilized to sta bilize the end-effector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators,in which the relativ e phases (phi) between the components and the relative-joint amplitude s (rho) are treated as collective Variables with are curvature as a co ntrol parameter.