Finger design automation for industrial robot grippers: A review <s> Unlimited Contact Methods for Polyhedral Objects <s> This paper formalizes qualitative test of 3D frictional form-closure grasps of n robotic fingers as a problem of linear programming (LP). It is well-known that a sufficient and necessary condition for form-closure grasps is that the origin of the wrench space lies inside the convex hull of primitive contact wrenches. We demonstrate that the problem of querying whether the origin is contained by the convex hull is equivalent to a ray-shooting problem, which is dual to a LP problem based on the duality between convex hulls and convex polytopes. Furthermore, this paper addresses a problem of minimizing the L/sub 1/ norm of the grasp force balancing an external wrench, which can be also transformed to a ray-shooting problem. We have implemented the algorithms and confirmed their real-time efficiency. <s> BIB001 </s> Finger design automation for industrial robot grippers: A review <s> Unlimited Contact Methods for Polyhedral Objects <s> We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are calledpositive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip. <s> BIB002
By considering the fact that a necessary and sufficient condition for force closure grasps is that the origin of the wrench space lies precisely inside the convex hull of the primitive contact wrenches resulted by the contact forces at the fingers  BIB002 ,  present a qualitative test based on linear matrix inequalities that deal efficiently with frictional constraints to avoid the linearization of the friction cones. Another method is proposed by BIB001 that tests the force closure condition by using a ray-shooting problem and solves as a linear programing problem. Based on the force-closure tests presented in BIB001  , 3D grasp synthesizer algorithms for unlimited number of contacts are proposed. Liu (2000) propose a grasp synthesis method for contacts when − 1 contacts have fixed positions and the grasp with the − 1 contacts is not force-closure. Utilizing the linear parametrization of a point on a facet, the algorithm searches locations on that face for the th contact that secures force-closure. Pros: These methods are applicable to any number of contacts. Cons: The approaches suffer from an exhaustive search procedure.