Modular fixturing kits are sets of components used for flexible, rapid construction of fixtures. A modular vise is a parallel-jaw vise, with a regular grid of precisely positioned holes on each jaw. Parts are held by placing pins in 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, 1996) developed an algorithm for planning planar grasp configurations for the modular vise. In this paper, 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.

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.

This paper presents an implemented algorithm that automatically designs fixtures and assembly pallets to hold three-dimensional parts. The designed fixtures rigidly constrain and locate the part, obey task constraints, are robust to part shape variations, are easy to load, and are economical to produce. The algorithm is guaranteed to find the global optimum solution that satisfies these and other pragmatic conditions. We present the results of the algorithm applied to several practical manufacturing problems. For these complex problems the algorithm typically returns initial high-quality fixture designs in less than two minutes, and identifies the global optimum design in just over an hour.

We present an implemented algorithm that accepts a polygonal description of a part's silhouette, and efficiently constructs the set of all feasible fixture designs that kinematically constrain the part in the plane. Each fixture is composed of three locators rigidly attached to the lattice and one sliding clamp, and constrains the part without relying on friction. The algorithm is based on an efficient enumeration of admissible designs that exploits part geometry and graphical force analysis. The algorithm run time is linear in the number of designs found, which is bounded by a polynomial in the number of part edges and the part's maximal diameter in lattice units. Our review of the literature suggests that this is the first fixturing algorithm that is complete in the sense that it is guaranteed to find all admissible fixture designs for an arbitrary polygonal silhouette and to identify the optimal fixture relative to an arbitrary quality metric. The algorithm does not consider out-of-plane forces or motions; however, we view this planar result as an essential component of a larger algorithm that solves the 3D fixture design problem by treating the planar and out-of-plane constraint problems separately. This approach is analogous to the widely used 3-2-1 fixture design heuristic.

Commercially-available modular fixturing systems typically include a square lattice of tapped and bushed holes with precise spacing and an assortment of precision locating and clamping elements that can be rigidly attached to the lattice using dowel pins or expanding mandrels. Currently, human expertise is required to synthesize a suitable arrangement of these elements to hold a given part. Besides being time consuming, if the set of alternatives is not systematically explored, the designer may fail to find an acceptable fixture or may settle upon a suboptimal fixture. The authors consider a class of modular fixtures that prevent a part from translating or rotating in the plane using four point contacts on the part's boundary. These fixtures are based on three round locators, each centered on a lattice point, and one translating clamp. The authors present an algorithm that accepts a polygonal part shape as input and synthesizes the set of all fixture designs that achieve form closure for the given part. The algorithm also allows the user to specify geometric access constraints on fixtures. If the part has n edges and its maximal diameter is d lattice units, the asymptotic running time of the algorithm is O(n/sup 5/d/sup 5/). The authors have implemented the algorithm and present example fixtures that it has synthesized. This implementation includes a metric to rank fixtures based on their ability to resist applied forces. The authors believe this is the first fixture synthesis algorithm that is complete in the sense that it is guaranteed to find an admissible fixture if one exists. Furthermore, the algorithm is guaranteed to find the optimal fixture, relative to any well-defined quality metric.>

The author presents two algorithms that construct a set of initial configurations from which a given action will reliably accomplish a planar manipulation task. The first algorithm applies energy arguments to construct a conservative set of successful initial configurations, while the second algorithm performs numerical integration to construct a set that is much less conservative. The algorithms may be applied to a variety of tasks, including pushing, placing-by-dropping, and force-controlled assembly tasks. Both algorithms consider the task geometry and mechanics, and allow uncertainty in every task parameter except for the object shapes. Experimental results which demonstrate the validity of the algorithms output for two example manipulation tasks are presented.>

The author describes an algorithm that takes two polygons as input, and computes a representation of their corresponding configuration-space obstacle, including contact information. The algorithm's output includes a full metric and topological description of the obstacle surface, as well as the set of polygon features that are in contact for each point of the surface. The representation is exact, up to the limits of floating-point arithmetic. The algorithm has been implemented and test-run on over 40 input pairs; run times varied between 12 and 135 s.>

This paper presents a method for automatic planning of robot grasping motions that are insensitive to bounded uncertainties in the object's location. The method exploits the physics of friction to generate all grasp plans that utilize either a squeez-grasp, offset-grasp, or push-grasp motion. All plans that are found will succeed even if the worst-case error occurs. From this space of plans, a plan can be chosen and executed without sensing or feedback. Moreover, executing the motion removes two degrees of uncertainty from the object's position. For simplicity, planar motion of the object during grasping is assumed. The planner has been implemented, and the resulting program has been tested on an industrial manipulator.