Segmentation of endpoint trajectories does not imply segmented control.

While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in three-dimensional human drawing movements are reexamined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the two-thirds power law changes discontinuously with each new "stroke," and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of three-dimensional drawing movements. In two experiments human subjects performed a set of elliptical and figure eight patterns of different sizes and orientations using their whole arm in three dimensions. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features to those reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom (DOF) anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.