Internal forces during object manipulation.

Internal force is a set of contact forces that does not disturb object equilibrium. The elements of the internal force vector cancel each other and, hence, do not contribute to the resultant (manipulation) force acting on the object. The mathematical independence of the internal and manipulation forces allows for their independent (decoupled) control realized in robotic manipulators. To examine whether in humans internal force is coupled with the manipulation force and what grasping strategy the performers utilize, the subjects (n=6) were instructed to make cyclic arm movements with a customized handle. Six combinations of handle orientation and movement direction were tested. These involved: parallel manipulations (1) VV task (vertical orientation and vertical movement) and (2) HH task (horizontal orientation and horizontal movement); orthogonal manipulations (3) VH task (vertical orientation and horizontal movement) and (4) HV task (horizontal orientation and vertical movement); and diagonal manipulations (5) DV task (diagonal orientation and vertical movement) and (6) DH task (diagonal orientation and horizontal movement). Handle weight (from 3.8 to 13.8 N), and movement frequency (from 1 to 3 Hz) were systematically changed. The analysis was performed at the thumb-virtual finger level (VF, an imaginary finger that produces a wrench equal to the sum of wrenches produced by all the fingers). At this level, the forces of interest could be reduced to the internal force and internal moment. During the parallel manipulations, the internal (grip) force was coupled with the manipulation force (producing object acceleration) and the thumb-VF forces increased or decreased in phase: the thumb and VF worked in synchrony to grasp the object more strongly or more weakly. During the orthogonal manipulations, the thumb-VF forces changed out of phase: the plots of the internal force vs. object acceleration resembled an inverted letter V. The HV task was the only task where the relative phase (coupling) between the normal forces of the thumb and VF depended on oscillation frequency. During the diagonal manipulations, the coupling was different in the DV and DH tasks. A novel observation of substantial internal moments is described: the moments produced by the normal finger forces were counterbalanced by the moments produced by the tangential forces such that the resultant moments were close to zero. Implications of the findings for the notion of grasping synergies are discussed.