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 psychophysical functions for perceived force with exponents of about 1.7. Two halving and doubling experiments presented here imply a psychophysical function 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 of each hand. They generated and released a reference force with one hand, and then squeezed the opposite hand to produce a sensation magnitude equal to, twice that, or half that of the reference. An analysis using a model that accounted for compression bias yielded average psychophysical functions with exponents of 0.58 and 0.59 (nondominant and dominant hands, respectively). The second experiment was an attempt to replicate earlier results and to reconcile them with the first experiment by using a paradigm duplicated from a previous study. Subjects in the second experiment made unilateral halving and doubling judgments of handgrip while squeezing a hand dynamometer. Again, the halving and doubling judgments yielded decelerating functions with exponents of 0.75 and 0.80 (nondominant and dominant hands, respectively). Even though the results of the first two experiments contradict earlier investigations, they can be explained by an equilibrium model of motor control assuming that subjects halve and double the central motor command rather 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 command judgments, the compliance of the hand, and the resultant forces was confirmed in a third experiment in which the mechanical compliance of the three-finger pinch was measured by using a pneumatic manipulandum to apply force perturbations in a "do-not-intervene" paradigm. The measured compliance characteristic was accelerating, just as predicted by the model, in order to produce a decelerating psychophysical function for "perceived force." In this experiment, then, judgments of perceived force appear to be judgments of the central motor command.