Modeling time invariance in human arm motion coordination

This paper proposes that two-degree-of-freedom Curvature Theory provides a mathematical representation of the kinematics of planar human arm motion coordination. Arguing that an internal inverse, time-invariant kinematic model is fundamental to human motor coordination, Curvature Theory provides a concise, efficient mapping of a desired output trajectory geometry to the joint angles' instantaneous speed ratios. If the speed ratios for a motion are learned through experience, one can subsequently execute the motion at different speeds. This formulation is consistent with a structure for the internal model that the central nervous system may use as a feed-forward element for planning motions. A simple example is presented to illustrate how the model works.