Can the relationship between tangential velocity and radius of curvature explain motor constancy?

To address contributions of speed, efficiency, radius of curvature and joint complexity to the strength of the lawful relationship between tangential velocity and radius of curvature (power law), an experiment considered the strength of the power law when participants were instructed to perform circling movements using the elbow, finger, shoulder, or wrist. Five participants performed circling motions in a vertical plane upon a Smartboard that sampled finger tip position at 200Hz. Page's L tested whether the strength of the power law could be predicted by: (1) speed; (2) submovements; (3) joint complexity; (4) radius of curvature. A second experiment considered the strength of the power law when six participants were instructed to perform circling movements of different sizes (large, medium, and small) using their shoulders. Movement speed or efficiency could not explain the strength of the power law, instead the power law was stronger for movements with a smaller radius of curvature or fewer joints. The strength of the power law varied with effector, questioning the role of the power law in motor constancy.