ORIGINS OF THE POWER-LAW RELATION BETWEEN MOVEMENT VELOCITY AND CURVATURE - MODELING THE EFFECTS OF MUSCLE MECHANICS AND LIMB DYNAMICS

1. When subjects trace patterns such as ellipses, the instantaneous ve locity of movements is related to the instantaneous curvature of the t rajectories according to a power law-movements tend to slow down when curvature is high and speed up when curvature is low. It has been prop osed that this relationship is centrally planned. 2. The arm's muscle properties and dynamics can significantly affect kinematics. Even unde r isometric conditions, muscle mechanical properties can affect the de velopment of muscle forces and torques. Without a model that accounts for these effects, it is difficult to distinguish between kinematic pa tterns that are attributable to central control and patterns that aris e because of dynamics and muscle properties and are not represented in the underlying control signals. 3. In this paper we address the natur e of the control signals that underlie movements that obey the power l aw. We use a numerical simulation of arm movement control based on the lambda version of the equilibrium point hypothesis. We demonstrate th at simulated elliptical and circular movements, and elliptical force t rajectories generated under isometric conditions, obey the power law e ven though there was no relation between curvature and speed in the mo deled control signals. 4. We suggest that limb dynamics and muscle mec hanics-specifically, the springlike properties of muscles-can contribu te significantly to the emergence of the power law relationship in kin ematics. Thus, without a model that accounts for these effects, care m ust be taken when making inferences about the nature of neural control .