Effect of position- and velocity-dependent forces on reaching movements at different speeds

The speed of voluntary movements is determined by the conflicting needs of maximizing accuracy and minimizing mechanical effort. Dynamic perturbations, e.g., force fields, may be used to manipulate movements in order to investigate these mechanisms. Here, we focus on how the presence of position- and velocity-dependent force fields affects the relation between speed and accuracy during hand reaching movements. Participants were instructed to perform reaching movements under visual control in two directions, corresponding to either low or high arm inertia. The subjects were required to maintain four different movement durations (very slow, slow, fast, very fast). The experimental protocol included three phases: (i) familiarization—the robot generated no force; (ii) force field—the robot generated a force; and (iii) after-effect—again, no force. Participants were randomly assigned to four groups, depending on the type of force that was applied during the “force field” phase. The robot was programmed to generate position-dependent forces—with positive (K+) or negative stiffness (K−)—or velocity-dependent forces, with either positive (B+) or negative viscosity (B−). We focused on path curvature, smoothness, and endpoint error; in the latter we distinguished between bias and variability components. Movements in the high-inertia direction are smoother and less curved; smoothness also increases with movement speed. Endpoint bias and variability are greater in, respectively, the high and low inertia directions. A robust dependence on movement speed was only observed in the longitudinal components of both bias and variability. The strongest and more consistent effects of perturbation were observed with negative viscosity (B−), which resulted in increased variability during force field adaptation and in a reduction of the endpoint bias, which was retained in the subsequent after-effect phase. These findings confirm that training with negative viscosity produces lasting effects in movement accuracy at all speeds.