Musculoskeletal, Neural, and Ocular Physiology Commons^™

Three-Dimensional Arm Movements At Constant Equi-Affine Speed, Frank E. Pollick, Uri Maoz, Amir A. Handzel, Peter J. Giblin, Guillermo Sapiro, Tamar Flash

Psychology Faculty Articles and Research

It has long been acknowledged that planar hand drawing movements conform to a relationship between movement speed and shape, such that movement speed is inversely proportional to the curvature to the power of one-third. Previous literature has detailed potential explanations for the power-law’s existence as well as systematic deviations from it. However, the case of speed-shape relations for three-dimensional (3D) drawing movements has remained largely unstudied. In this paper we first derive a generalization of the planar power law to 3D movements, which is based on the principle that this power law implies motion at constant equi-affine speed. This generalization …