Seven fingers allow force-torque closure grasps on any convex polyhedron.

We prove that a robot hand whose fingers make frictionless contact with a convex polyhedral object will be able to find a grasp where the hand can exert any desired force-torque on the object provided the hand has seven fingers. We present an algorithm for grasping any convex polyhedron and we prove rigorously that it works for any convex polyhedron. The algorithm requires O( n√log n) steps (in the worst case) where n is the number of vertices. [ABSTRACT FROM AUTHOR]