On characterizing and computing three- and four-finger force-closure grasps of polyhedral objects

The problem of characterizing the force-closure grasps of a three-dimensional object by a hand equipped with three or four hard fingers is addressed. Several necessary and several sufficient conditions for force-closure are proved. For polyhedral objects, sufficient conditions that are linear in the unknown parameters are proved. This reduces the problem of computing force-closure grasps of polyhedral objects to the problem of projecting a polytope onto some linear subspace. An efficient, output-sensitive algorithm is presented for computing the projection, together with an algorithm using linear programming for computing maximal grasp regions.>