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Relation between velocity and curvature in movement: Equivalence and divergence between a power law and a minimum-jerk model.
Wann, J.P., Nimmo-Smith, I. & Wing, A.M.
Journal of Experimental Psychology: Human Perception and Performance, 14, 622-637.
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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 analysed from six 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.