End points of planar reaching movements are disrupted by small force pulses: An evaluation of the hypothesis of equifinality

A single force pulse was applied unexpectedly to the arms of five normal human subjects during nonvisually guided planar reaching movements of 10-cm amplitude. The pulse was applied by a powered manipulandum in a direction perpendicular to the motion of the hand, which gripped the manipulandum via a handle at the beginning, at the middle, or toward the end the movement. It was small and brief (10 N, 10 ms), so that it was barely perceptible. We found that the end points of the perturbed motions were systematically different from those of the unperturbed movements. This difference, dubbed "terminal error," averaged 14.4 +/- 9.8% (mean +/- SD) of the movement distance. The terminal error was not necessarily in the direction of the perturbation, although it was affected by it, and it did not decrease significantly with practice. For example, while perturbations involving elbow extension resulted in a statistically significant shift in mean end-point and target-acquisition frequency, the flexion perturbations were not clearly affected. We argue that this error distribution is inconsistent with the "equilibrium point hypothesis" (EPH), which predicts minimal terminal error is determined primarily by the variance in the command signal itself, a property referred to as "equifinality." This property reputedly derives from the "spring-like" properties of muscle and is enhanced by reflexes. To ensure that terminal errors were not due to mid-course voluntary corrections, we only accepted trials in which the final position was already established before such a voluntary response to the perturbation could have begun, that is, in a time interval shorter than the minimum reaction time (RT) for that subject. This RT was estimated for each subject in supplementary experiments in which the subject was instructed to move to a new target if perturbed and to the old target if no perturbation was detected. These RT movements were found to either stop or slow greatly at the original target, then re-accelerate to the new one. The average latency of this second motion was used to estimate the voluntary RT for each subject (316 ms mean). Additionally, we found that the hand neither exerted target-oriented force against the handle nor drifted toward the desired end point just before coming to rest, making it unlikely that the mechanical properties of the manipulandum prevented the hand from reaching its intended target.