On the equivalence of internal and interaction forces in multifingered grasping

This paper deals with the problem of the equivalence of internal and interaction forces in multifingered grasping. The dimensions of these two force spaces are analyzed. It is shown that the internal force space can be more generally expressed as the direct sum of the interaction and parallel force spaces. Under certain conditions, the parallel force space disappears and the internal and interaction force spaces become coincident. In this sense, the internal force can be equivalently characterized by the interaction force or pairs of equal and opposite collinear forces. The necessary and sufficient conditions for this equivalent characterization, which depends upon the number of contacts and the distribution of their locations, are derived. The algebraic structure of the parallel force spaces is given. Some illustrative examples are also presented