Abstract
The speed-curvature power law is an intriguing constraint between the geometry and the kinematics of a movement trajectory. It dictates, for instance, how much slower the hand should move in curves. The empirical phenomenon has led to various interesting theoretical proposals for its origin and possible generating processes. Its formulation based on tangential speed (V∼Cβ) is considered equivalent to its angular speed counterpart (A∼Cβ+1), with the corresponding change in the exponent. In the case of drawing ellipses, these relationships are respectively known as the “one-third power law” or the “two-thirds power law”, after the values of the exponents. Here we show that using angular speed instead of tangential speed tends to result in much stronger data correlations, impacting on the interpretation of the strength of relationship, the putative value of the exponents, and even the very existence of the power law. We explain how and why this is the case, using both empirical and synthetic data. We conclude that angular speed should be avoided when expressing the speed-curvature power law.
Competing Interest Statement
The authors have declared no competing interest.
