Trajectory determines movement dynamics

Abstract

The relation between figurai and kimematic aspects of movement was studied in handwriting and drawing. It was found that, throughout the movement, the tangential velocity V is proportional to the radius of curvature r of the trajectory: V = kr, or, equivalently, that the angular velocity is constant: dα(t)/dt = k. However, the constant k generally takes several distinct values during the movement, the changes being abrupt. These changes suggest a clear segmentation of the movement into units of action which overlap but do not coincide with the figurai units as defined by the discontinuities of the movement (cuspids, points of inflection). This organisational principle holds even when movements are mechanically constrained or are executed under strict visuo-motor guidance. Moreover, the segmentation of a given trajectory is invariant with respect to the total duration of the movement. A tentative interpretation of the principle is proposed which results from the assumption that the actual movement is produced as a continuous approximation to an intended movement, and that the well known relationship between movement speed and extent in rectilinear trajectories (Fitts' law) also applies to such continuous approximation.