The synthesis of 3D form-closure grasps

Presents a formulation of the synthesis of 3D frictional form-closure grasps of n robot fingers. First, using a recursive reduction technique, we transform the problem in 6D wrench space to one in three dimensions. Then we rewrite the sufficient and necessary condition for form-closure grasps in the equivalent form of the inconsistency of each of the two sets of linear inequalities. Then we propose three conditions to check the inconsistency of the inequality system, which geometrically indicates whether the convex region formed by the inequality system is empty. We have implemented the algorithms and confirmed their real-time efficiency for the synthesis of 3D form-closure grasps