Relation between velocity and curvature in movement: equivalence and divergence between a power law and a minimum-jerk model.
Unconstrained hand movements typically display a decrease in hand speed around highly curved sections of a trajectory. It has been suggested that this relation between tangential velocity and radius of curvature conforms to a one-third power law. We demonstrate that a one-third power law can be explained by models taking account of trajectory costs such as a minimum-jerk model. Data were analyzed from 6 subjects performing elliptical drawing movements of varying eccentricities. Conformity to the one-third power law in the average was obtained but is shown to be artifactual. It is demonstrated that asymmetric velocity profiles may result in consistent departures from a one-third power law but that such differences may be masked by inappropriate analysis procedures. We introduce a modification to the original minimum-jerk model by replacing the assumption of a Newtonian point-mass with a visco-elastic body. Simulations with the modified model identify a basis for asymmetry of velocity profiles and thereby predict departures from a one-third law commensurate with the empirical findings.
Wann
J
J
Medical Research Council Applied Psychology Unit, Cambridge, England.
Nimmo-Smith
I
I
Wing
A M
AM
D000328:Adult; D001132:Arm / Q000502:physiology; D005260:Female; D006801:Humans; D008297:Male; D008960:Models, Psychological; D015233:Models, Statistical; D009038:Motion; D009068:Movement; D011597:Psychomotor Performance / Q000502:physiology