Internal forces and stability in multi-finger grasps

Abstract This paper deals with the rotational stability of a rigid body under the constant contact forces. For this problem, first, the stiffness tensor is constructed and its basic properties are analyzed. Stability due to the gravitational and the internal forces is considered separately. For the gravity-induced stiffness only one necessary condition of stability, formulated in terms of geometric and gravity centers, is obtained. The internal force parameterization is done with the use of a virtual linkage/spring model. Within this parameterization, necessary and sufficient conditions of stability under internal force loading 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. These conditions can be incorporated into the grasping force planner