Maintaining rotational equilibrium during object manipulation: Linear behavior of a highly non-linear system

We address issues of simultaneous control of the grasping force and the total moment of forces applied to a handheld object during its manipulation. Six young healthy male subjects grasped an instrumented handle and performed its cyclic motion in the vertical direction. The handle allowed for setting different clockwise (negative) or counterclockwise torques. Three movement frequencies: 1, 1.5 and 2 Hz, and five different torques: -1/3, -1/6, 0, 1/6 and 1/3 Nm, were used. The rotational equilibrium was maintained by two means: (1) Concerted changes of the moments produced by the normal and tangential forces, specifically antiphase changes of the moments during the tasks with zero external torque and in-phase changes during the non-zero-torque tasks, and (2) Redistribution of the normal forces among individual fingers such that the agonist fingers - the fingers that resist external torque - increased the force in phase with the acceleration, while the forces of the antagonist fingers - those that assist the external torque - especially, the fingers with the large moment arms, the index and little fingers, stayed unchanged. The observed effects agree with the principle of superposition - according to which some complex actions, for example, prehension, can be decomposed into elemental actions controlled independently - and the mechanical advantage hypothesis according to which in moment production the fingers are activated in proportion to their moment arms with respect to the axis of rotation. We would like to emphasize the linearity of the observed relations, which was not prescribed by the task mechanics and seems to be produced by specific neural control mechanisms.