Why does Fitts’ law fit various human behavioural data well even though it is not a model based on human physical dynamics? To clarify this, we derived the relationships among the factors applied in Fitts’ law—movement duration and spatial endpoint error—based on a multi-joint forward- and inverse-dynamics models in the presence of signal-dependent noise. As a result, the relationship between them was modelled as an inverse proportion. To validate whether the endpoint error calculated by the model can represent the endpoint error of actual movements, we conducted a behavioural experiment in which centre-out reaching movements were performed under temporal constraints in four directions using the shoulder and elbow joints. The result showed that the distributions of model endpoint error closely expressed the observed endpoint error distributions. Furthermore, the model was found to be nearly consistent with Fitts’ law. Further analysis revealed that the coefficients of Fitts’ law could be expressed by arm dynamics and signal-dependent noise parameters. Consequently, our answer to the question above is: Fitts’ law for reaching movements can be expressed based on human arm dynamics; thus, Fitts’ law closely fits human’s behavioural data under various conditions.

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Previous studies on human motor control reported a phenomenon called isochrony, which is the compensatory increase of movement speed with increasing movement distance. On the other hand, in complex via-points trajectory formation, a possible computational model that can estimate via-point time has been proposed. This model is optimized on the condition that the Duration average of the Commanded Torque Change (DCTC) between each via-point is equal. In this paper, we consider the possibility that human isochrony can be explained by the computational theory and investigate the human drawing movement of a set of figure eight and double elliptical patterns. Results show that isochrony was observed in both duration and DCTC and that relative variance with an increasing movement perimeter ratio of DCTC was significantly less than duration. The possibility is suggested that human isochrony is a phenomenon observed as a result of movement time planning to equalize DCTC.

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