HALVING AND DOUBLING ISOMETRIC FORCE - EVIDENCE FOR A DECELERATING PSYCHOPHYSICAL FUNCTION CONSISTENT WITH AN EQUILIBRIUM-POINT MODEL OF MOTOR CONTROL

Several previous investigations have measured accelerating psychophysi cal functions for perceived force with exponents of about 1.7. Two hal ving and doubling experiments presented here imply a psychophysical fu nction for perceived force with an exponent between 0.6 and 0.8. That is, more than a doubling of force was needed to double the sensation, and similarly for halving. In the first experiment, subjects squeezed rigid instrumented cylinders between the thumb and first two fingers o f each hand. They generated and released a reference force with one ha nd, and then squeezed the opposite hand to produce a sensation magnitu de equal to, twice that, or half that of the reference. An analysis us ing a model that accounted for compression bias yielded average psycho physical functions with exponents of 0.58 and 0.59 (nondominant and do minant hands, respectively). The second experiment was an attempt to r eplicate earlier results and to reconcile them with the first experime nt by using a paradigm duplicated from a previous study. Subjects in t he second experiment made unilateral halving and doubling judgments of handgrip while squeezing a hand dynamometer. Again, the halving and d oubling judgments yielded decelerating functions with exponents of 0.7 5 and 0.80 (nondominant and dominant hands, respectively). Even though the results of the first two experiments contradict earlier investiga tions, they can be explained by an equilibrium model of motor control assuming that subjects halve and double the central motor command rath er than the sensation of force. The force is simply the result of the mechanical equilibrium established between the load and the compliant effector (the hand). The predicted relationship between the motor comm and judgments, the compliance of the hand, and the resultant forces wa s confirmed in a third experiment in which the mechanical compliance o f the three-finger pinch was measured by using a pneumatic manipulandu m to apply force perturbations in a ''do-not-intervene'' paradigm. The measured compliance characteristic was accelerating, just as predicte d by the model, in order to produce a decelerating psychophysical func tion for ''perceived force.'' In this experiment, then, judgments of p erceived force appear to be judgments of the central motor command.