Speed–curvature relations for speech-related articulatory movement

Abstract During speech production, oral articulator points exhibit spatially complex trajectories. This spatial complexity is partially reflected in the trajectory's curvature history (where curvature is defined as the rate of change of direction, parameterized for arc length). Informal observation of articulatory movement reveals that an increase in the degree of trajectory curvature is often associated with a slowing of the articulator. Such a relation between the speed and curvature of movement has been quantified for a variety of behaviors within the limb and oculomotor systems. This relation has been called the 1/3 power law. Such an association has not been quantified for speech movements. If speech movements adhere to the 1/3 power law, it would imply a specific constraint on the variability in spatial complexity (as reflected by curvature) and the time course of speech-related movements. This study empirically evaluated the relationship between articulator speed and trajectory curvature for speech-related mid-sagittal planar movements of the tongue, lower lip and mandible in a group of healthy speakers. Results revealed that movement speed and trajectory curvature are related by a power function whose exponent is near, but not exactly 1/3. Articulators exhibited systematic variations in the strength of association, and value of the exponent. These results suggest that speed and curvature of speech movement covary in ways similar to other motor systems.