Investigation of isochrony phenomenon based on the computational theory of human arm trajectory planning

The isochrony principle is a well-known phenomenon whereby the speed of human arm movement is regulated to increase as its trajectory distance increases. However, the relationship between the trajectory planning and the isochrony phenomenon has never been sufficiently explained. One computational study derived the algorithm for estimating the optimal movement segmentation and its duration based on the framework of the minimum commanded torque change criterion. By extending this finding, we can consider the hypothesis that the human arm trajectory is generated based on the minimum commanded torque change criterion to ensure that the duration average of the commanded torque changes (DCTCs) are equivalent between certain movement segmentations, rather than to satisfy the isochrony phenomenon. To test this hypothesis, we measured the behavioral performance of hand movement tasks in which subjects write eight-shaped and double-elliptical-shaped trajectories including two similar shaped arcs of different sizes (hereafter called large and small loops). Our results indicate that the human arm movement is planned in such a manner that the DCTCs for the large and small loops are equivalent during writing of the double-elliptical-shaped trajectories regardless of the arc size. A similar tendency was also observed for the data during the eight-shaped movements, although the ratio of the DCTCs slightly changed depending on the arc size conditions. Thus, our study provides experimental evidence that the isochrony phenomenon is ensured through the computational process of trajectory planning.