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This paper addresses the problem of computing stable grasps of 2-D polygonal objects. We consider the case of a hand equipped with three hard fingers and assume point contact with friction. We prove new sufficient conditions for equilibrium and force closure that are linear in the unknown grasp parameters. This reduces computing the stable grasp regions in configuration space to constructing the three-dimensional projection of a five-dimensional polytope. We present an efficient projection algorithm based on linear programming and variable elimination among linear constraints. Maximal object segments where fingers can be positioned independently while ensuring force closure are found by linear optimization within the grasp regions. The approach has been implemented and several examples are presented.
Ponce et al. (Sun,) studied this question.