ON COMPUTING 3-FINGER FORCE-CLOSURE GRASPS OF POLYGONAL OBJECTS

This paper addresses the problem of computing stable grasps of 2-D pol ygonal objects. We consider the case of a hand equipped with three har d fingers and assume point contact with friction. We prove new suffici ent conditions for equilibrium and force closure that are linear in th e unknown grasp parameters. This reduces computing the stable grasp re gions in configuration space to constructing the three-dimensional pro jection of a five-dimensional polytope. We present an efficient projec tion algorithm based on linear programming and variable elimination am ong linear constraints. Maximal object segments where fingers can be p ositioned independently while ensuring force closure are found by line ar optimization within the grasp regions. The approach has been implem ented and several examples are presented.