The relation between linear extent and velocity in drawing movements.

The speed of execution of complex movements depends on both the local, differential properties of the trajectory and on some of its more global metric parameters. The effects of these global factors were studied in free, writing-like movements with either piece-wise constant, or regularly changing curvature. It is demonstrated that the tangential velocity of the pen's tip is tightly correlated, through a power function, with the total linear extent of the trajectory (perimeter). Thus, a strong tendency exists to keep the execution time of these complex trajectories independent of the movement size (isochrony). Furthermore, it is shown that the average tangential velocity over identifiable segments of the trajectory also depends on the corresponding average curvature. The implications of these results vis-à-vis the central representation and planning of movements are discussed.