Rigid body analysis of power grasps: bounds of the indeterminate grasp force

The equilibrium equation of a power grasp cannot determine the grasp force uniquely in general. This paper proves that the indeterminate grasp force is, within a bounded hyper-polyhedron, not necessarily convex by considering the compatibility with rigid body motion. The maximum fraction angle is found at its vertex. Thus, if all forces at the vertices are within the friction cone, then all forces in the hyper-polyhedron are within the friction cone. Based on this analysis, we present an algorithm for computing the joint torques that can balance a given set of external disturbances.