Abstract
This paper analyzes the indeterminate grasp force in power grasps or enveloping grasps and shows that its region is a bounded hyper-polyhedron. In power grasps a hand grasps an object at multiple points on the surface of the hand. If the hand and the object are modeled as rigid bodies, then it is known that the grasp force is in general not determined uniquely even if joint torques are given. We have already shown that the sliding directions of the contact points are restricted in power grasps to be consistent with rigid body motion. Static friction force acts only in the opposite direction of sliding. This characteristic of friction leads to our previous conclusion that the grasp force is also restricted. This paper shows that the region of the indeterminate grasp force is a bounded hyper-polyhedron that is not necessarily convex. The force that requires maximum friction exists at the vertices of the polyhedron. We present a simple algorithm for computing the vertices of the hyper-polyhedron. It can efficiently compute the coefficient of friction sufficient to maintain static equilibrium given an external disturbance and joint torques taking the indeterminacy of the grasp force into account.
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