Trajectory formation of the center-of-mass of the arm during reaching movements.

We attempted to identify the invariant kinematic properties of multijoint arm reaching movements in the horizontal plane to explore the planning variable(s) involved in their coordination. Different targets were placed near the perimeter of the workspace boundary, thereby causing variation of size and orientation of the hand stroke. We have a special interest in the trajectory characteristics of the most massive point within the arm system, the center-of-mass of the entire arm system, in addition to those of the hand or joints. The motion of the individual segments (the forearm plus hand and the upper arm) or joints (shoulder and elbow) was modulated in a different way depending on the tasks; thus, there was no invariance in the relationships between paired variables (displacement or velocity) for segment or joint motions. For relatively short hand strokes, the trajectory of the hand and the center-of-mass of the entire arm system were characterized by a nearly straight path, and a smooth, bell-shaped velocity curve along the path, symmetrical about the mid-portion of the movement, starting from nearly zero, growing to a single peak and declining again to nearly zero. However, in large hand strokes the hand path was highly curved and the velocity curve was asymmetric. Although the path of the center-of-mass of the entire arm system also tended to be curved with the increase of the hand stroke, a bell-shaped velocity curve along the path and its typical symmetry were preserved over a wide range of stroke sizes and orientations, and its peak was scaled in proportion to movement distance and movement time. Our findings indicate that it is not valid to postulate solely the joint- or hand-based planning strategies which have been proposed previously. Rather, the planning of the spatial aspects of the motion is largely dependent on the interaction of multiple variables, including those not analysed in this study. The bell-shaped pattern of the center-of-mass velocity profile represents a certain efficiency of movement, since it corresponds to a single accelerative and a decelerative phase of a mass over the movement, with no intermediate force reversals. The simple structure of the center-of-mass velocity profiles may reflect a fundamental organization principle underlying the temporal aspects of movement planning.