Is a virtual trajectory necessary in reaching movements?

The mass-spring model of limb control was extended to two-joint arm movements in the horizontal plane and tested against kinematic data from human subjects. Two versions of the model were compared in order to test the idea that the equilibrium position of the hand moves along a "virtual" trajectory as demonstrated in single-joint arm movements (Bizzi et al. 1982, 1984; Latash and Gottlieb 1991). In the peripheral version, the equilibrium position was shifted abruptly, while the torques generated at the joints are gated by rise-time functions. In the central version, the equilibrium position was updated gradually according to a predefined trajectory. The paths and tangential velocity profiles of the hand generated by these two versions were compared to Morasso's (1981) experimental data. The central version generally performed better throughout the workspace except in certain special directions. Moreover, its paths exhibited more stability as the movement speed was varied.