The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements

Curvature and tangential velocity of voluntary hand movements are constrained by an empirical relation known as the Two-Thirds Power Law. It has been argued that the law reflects the working of central control mechanisms, but it is not known whether these mechanisms are specific to the hand or shared also by other types of movement. Three experiments tested whether the power law applies to the smooth pursuit movements of the eye, which are controlled by distinct neural motor structures and a peculiar set of muscles. The first experiment showed that smooth pursuit of elliptic targets with various curvature–velocity relationships was most accurate when targets were compatible with the Two-Thirds Power Law. Tracking errors in all other cases reflected the fact that, irrespective of target kinematics, eye movements tended to comply with the law. Using only compatible targets, the second experiment demonstrated that kinematics per se cannot account for the pattern of pursuit errors. The third experiment showed that two-dimensional performance cannot be fully predicted on the basis of the performance observed when the horizontal and vertical components of the targets used in the first condition were tracked separately. We conclude that the Two-Thirds Power Law, in its various manifestations, reflects neural mechanisms common to otherwise distinct control modules.