Kinematics invariance in multi-directional complex movements in free space: effect of changing initial direction

We investigated in normal human subjects the effect of changing the initial direction on the kinematic properties of figure '8' movement performed as fast as possible by the right arm extended in free space. To this end, the motion of the index finger was monitored by the ELITE system. The figure '8' movement was characterized by a complex tangential velocity profile (Vt) presenting 5 bell-shaped components. It was found that the temporal segmentation following Vt was not significantly different, whatever the initial direction of the movement. The decomposition of Vt into different velocity profiles with respect to vertical (3 phases, Iy-IIIy) and horizontal (5 phases, Iz-Vz) directions showed a significant relationship between the amplitude and the maximal velocity for all the different phases (except the IIy phase), which demonstrated a good conservation of the Isochrony Principle. However, we showed that the transition between the clockwise and counter-clockwise loop (inflection point) induced greater variability in the vertical velocity profile than in the horizontal one. Moreover, some parameters such as the maximal velocity of Iy and the movement amplitude of the last phases (IIIy and Vz) showed significant changes depending on the initial direction. A highly significant positive correlation was observed between the instantaneous curvature and angular velocity. This was expressed by a power law similar to that previously describe for other types of movement. Furthermore, it was found that this covariation between geometrical and kinematic properties of the trajectory is not dependent on the initial direction of movement. In conclusion, these results support the idea that the fast execution in different directions of a figure '8' movement is mainly controlled by two types of invariant commands. The first one is reflected in the 2/3 power law between angular velocity and curvature and the second one is represented by a segmented tangential velocity profile.