Multi-arm/finger grasping: One view to the stability problem

The paper deals with the rotational stability of a rigid body under the constant internal forces. For this problem, first, the stiffness tensor is constructed and its basic properties are analyzed. The internal force parameterization is done with the use of the virtual linkage/spring model. Within this parameterization, necessary and sufficient conditions of stability are obtained in the analytical form. In the space of the internal forces they form a region given by intersection of a plane and a singular quadric. Since the stability conditions guarantee only positive definiteness of the stiffness tensor, the contact friction is taken into account separately. In this paper analysis of the unilateral constraints is done under a study case, where achieving stable grasp of a convex object, with the stretching internal forces created by friction, is studied in an analytical example.