Finger design automation for industrial robot grippers: A review <s> Analytical Approaches <s> This paper presents fast and simple algorithms for directly constructing force-closure grasps based on the shape of the grasped object. The synthesis of force-closure grasps constructs independent regions of contact for the fingertips, such that the motion of the grasped object is totally constrained. A force-closure grasp implies equilibrium grasps exist. In the reverse direction, we prove that non-marginal equilibrium grasps with at least two soft-finger contacts, or three hard-finger contacts with friction are also force-closure grasps. <s> BIB001 </s> Finger design automation for industrial robot grippers: A review <s> Analytical Approaches <s> Modular fixturing kits are sets of components used for flexible, rapid construction of fixtures. A modular vise is a parallel-jaw vise, each jaw of which is a modular fixture plate with a regular grid of precisely positioned holes. To fixture a part, one places pins in some of the holes so that when the vise is closed, the part is reliably located and completely constrained. The modular vise concept can be adapted easily to the design of modular parallel-jaw grippers for robots. By attaching a grid-plate to each jaw of a parallel-jaw gripper we gain the ability to easily construct high-quality grasps for a wide variety of parts from a standard set of hardware. Wallack and Canny (1994) developed an algorithm for planning planar grasp configurations for the modular vise. We expand this work to produce a 3D fixture/gripper design tool. We describe several analyses we have added to the planar algorithm, including a 3D grasp quality metric based on force information, 3D geometric loading analysis, and inter-gripper interference analysis. Finally, we describe two applications of our code. One of these is an internal application at Sandia, while the other shows a potential use of our code for designing part of an agile assembly line. <s> BIB002 </s> Finger design automation for industrial robot grippers: A review <s> Analytical Approaches <s> In this paper, we survey the field of robotic grasping and the work that has been done in this area over the last two decades, with a slight bias toward the development of the theoretical framework and analytical results in this area. <s> BIB003 </s> Finger design automation for industrial robot grippers: A review <s> Analytical Approaches <s> An algorithm for automatically generating a common jaw design and planning grasps for a given set of polyhedral objects is presented. The algorithm is suitable for a parallel-jaw gripper equipped with three cylindrical fingers. The common jaw design eliminates the need for custom made grippers and tool changing. The proposed jaw configuration and planning approach reduces the search associated with locating the finger contacts from six degrees-of-freedom to one degree-of-freedom. Closed-form algorithms for checking force closure and for predicting jamming are developed. Three quality metrics are introduced to improve the quality of the planned grasps. The first is a measure of the sensitivity of the grasp to errors between the actual and planned finger locations. The second is a measure of the efficiency of the grasp in terms of the contact forces. The third is a measure of the dependence of force closure on friction. These quality metrics are not restricted to cylindrical fingers and can be applied to n finger grasps. Running on a standard PC, the algorithm generated a solution in less than five minutes for a set of five objects with a total of 456 triangular facets. © 2003 Wiley Periodicals, Inc. <s> BIB004 </s> Finger design automation for industrial robot grippers: A review <s> Analytical Approaches <s> In this paper, we present a novel algorithm for computing three-finger force-closure grasps of 2D and 3D objects. In the case of a robot hand with three hard fingers and point contact with friction, new necessary and sufficient conditions for 2D and 3D equilibrium and force-closure grasps have been deduced, and a corresponding algorithm for computing force-closure grasps has been developed. Based on geometrical analysis, the algorithm is simple and only needs a few algebraic calculations. Finally, the algorithm has been implemented and its effectivity has been demonstrated by two examples. <s> BIB005
Analytical approaches consist of methods that use geometric, kinematic and dynamic formulations in order to verify a grasp. BIB003 have properly reviewed these analytical formulations. BIB001 proves that non-marginal equilibrium grasps are forceclosure grasps if each grasp has at least two soft-finger contacts or three hard-finger contacts in 3D. He proves that a grasp with 2 soft-finger contacts is force-closure if and only if the contact points connection line is located in the contacts friction cones. Also a grasp with at least three distinct hard-finger contacts is force-closure if it is in equilibrium, with contact forces pointing strictly within the friction cones at the respective points of contact. Nguyen also presents that at least 7 contact points are required to achieve from-closure with frictionless contacts (see Fig. 5 ). BIB002 propose a method that imports the disturbance wrenches to be applied to the object and tests grasps for force-closure. While their method has the benefit of computing the minimum required jaw closing force using linear programming, it would be difficult for the user to know all of the disturbance wrenches. BIB004 proposed a closed-form algorithm for testing non-marginal equilibrium grasps BIB001 . In comparison to BIB002 , this method has the advantage that the closed-form solution has a much lower computational complexity. Still it has the disadvantage that the assumptions employed are conservative, which means it may reject some valid force closure grasps. BIB005 propose a method for grasp synthesizing three-finger grippers with hard-finger contacts. Their algorithm computes the force-closure grasp of 3D workpieces based on the intersection of the three contact point's triangle area and each contact's friction cone. Pros: The searching method in these approaches enables global contact sets to be found. Cons: These methods are applicable to grasps with a very limited number of contact points. Thus, more general methods are required for synthesizing grasps regardless of number of contact points.