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Computer-Aided Design Components of a modular fixture.fixtures are typically supported on tooling plates with grid which the fixture is planning and configuration is a largely experience driven activity that focuses on determining precise location to a part can include tooling and expected tool paths, clamps to specified locations, part deformation under forces, availability of fixture elements, tolerances etc. In focus constraints and choose components from an avail- able catalog of fixture elements to determine the automatic and realistic solutions for modular . 1.1. Related work Many approaches for computer assisted fixture planning have been developed over the last two decades to address different types of process constraints; comprehensive reviews can be found in relevance to this paper are methods to determine accessible and collision free locations of fixture points that ensure part immobility under the application of external forces and moments, and we do not address problems such as deformation anal-tolerance analysis, and so on.Most automated solutions for modular fixture synthesis are restricted to planar shapes where it is assumed that three locators and a clamp are sufficient to immobilize the shape, for example The assumption is valid for two dimensional fixture syn-thesis because it has been shown that four fixture locations are necessary and sufficient to guarantee complete part immobility for planar degrees of freedom (see Section 3 for detailed explanations). Stability analysis to restrict planar motions relies on reasoning about a three dimensional configuration space of forces and moments. For three dimensional motions (i.e. six degrees of freedom) the problem requires stability analysis in six dimensional space which is substantially more challenging.Due to the similarity between fixture planning and 3d robotic grasp planning [3], algorithms for grasp planning are sometimes directly used in fixture planning [8–10], and often propose criteria to generate optimal stable fixtures that resist three dimensional forces and torques.We argue that such solutions are partial at best even for purely geometric analysis for two reasons: – the analysis typically stops at generating fixture locations and does not connect to a realistic modular fixture system, which is key to providing practical solutions. A notable exception to this is in [5] where modular fixtures for two dimensional parts are generated by exhaustively searching the space of stable grasps, but it is clear that the approach will be computationally prohibitive upon extension to three dimensions.Furthermore, realistic solutions require post-processing the generated locations to check for collision avoidance and repeating fixture synthesis if necessary; – for the purposes of process planning we argue that providing qualitatively distinct solutions is more critical than providing a single optimized solution, which is more appropriate and necessary for compliant robot grasping. Optimizing a single grasp in the six dimensional configuration space of forces and moments is an iterative process, and furthermore optimal grasps may fail to pass other process constraints such as accessibility and collision avoidance.In three dimensional fixture synthesis, six locators and at least one clamp are required for a grasp or fixture. Contact locations are typically chosen by sampling the surface of the part to be fix . A fixture is found when a combination of seven contacts capable of balancing any external force or moment; the part is then said to be in form closure [11–14]. Determining form closure in immediately creates a for candidate samples there are combinations of fixture locations and therefore exhaustive searches quickly become impractical,suggesting the need to formulate fixture planning and synthesis as a constrained optimization problem.The quality of a particular grasp is typically identified with the of the forces and moments or wrenches resisted by the combination of contacts, and is quantified by a grasp metric convex spans correspond to lower reaction forces required to be applied on the part to resist external wrenches. Usually, an initial configuration of wrenches is converged to a form closure configuration that locally maximizes the grasp metric [17,9,18,10], where the iterations in the optimization algorithm tend to push the initial configuration towards the convex hull of all candidate wrenches.Instead of using an iterative procedure that will converge slowly with a large sampled set of wrenches, we will adopt a strategy that generates fixture locations by sampling near the convex hull of all candidate wrenches to construct form closure grasps. At first sight it may appear that such a computation is quite expensive since a d > 3 dimensional convex hull of n locations may have) time complexity, and even if the six dimensional hull with is computed, there is still the problem of choosing a form closure configuration from the wrench combinations. However,we demonstrate a novel approach to dramatically reduce the search space of candidate fixture locations without explicitly computing the convex hull, and rapidly generate form closure configurations that are locally optimal and can be fixture by physical clamps. 1.2. Novelty and contributions In this paper we first demonstrate a divide and conquer scheme that hashes samples in the six dimensional space of wrenches to rapidly generate fixture locations that resist large forces and moments, are qualitatively distinct, and provide guaranteed stability through form closure. The hashing relies on an indexing scheme that identifies sub to unique force–moment combinations and uses properties of the indexing system to provide form closure configurations while dramatically reducing the search space of candidate solutions.We then use the generated locations to select available clamps in a catalog of modular fixtures by constructing clearance volumes at each location to fit the collision free clamps that are capable of reaching the given locations. Collision analysis is performed for the chosen clamps until a valid, non-colliding set of clamps that match Computer-Aided Design Contents lists available at Science Direct Computer-Aided Design journal homepage Automated fixture configuration for rapid manufacturing planning ?Christian Fritz Alto Research Center, 3333 Coyote Hill Road, Alto, CA - 94304, United States ? Automatic rapid modular fixture configuration. ? Fast hashing algorithms to generate form/force closure grasps. ? Automatic selection & assembly of modular elements from user specified library. ? Includes accessibility & collision constraints for machining/inspection. ? Results for complex parts in realistic process plans. The wide adoption of agile manufacturing systems has necessitated the design and use of fixtures work holding devices that have in-built flexibility to rapidly respond to part design changes. Despite the availability of recon fig fixtures, practical fixture configuration largely remains an experience driven manual activity to enable customization for varying work piece geometry, and most automated solutions do not scale well to accommodate such variation. In this paper, we address the problem of rapidly synthesizing a realistic fixture that will guarantee stability and immobility of a specified polyhedral work-part.We propose that the problem of automated fixture layout may be approached in two distinct stages. First, we determine the spatial locations of clamping points on the work piece boundary using the principles of force and form closure, to ensure immobility of the fix part under external perturbation.In particular, we show that the candidate restraints mapped to the six dimensional vector space of wrenches (force–moment pairs) may be hashed in a straightforward manner to efficiently generate force closure configurations that restrain part movement against large external wrenches. When clamps are allowed to exert arbitrarily high reaction forces on the part, the spatial arrangement of the clamping locations ensures the part is in form closure. On generating force/form closure configurations, the chosen locations are matched against a user-specified library of recon lamps to synthesize a valid fixture layout comprising clamps that are accessible and collision free with each other and the part.Additionally, in the case of determining machining setups the clamps are chosen to avoid collisions with the moving cutting tool. We demonstrate fast algorithms to perform both location selection and fixture matching, and show several results that underscore the practical application of our solution in automated manufacturing process planning. 1. Introduction Fixtures are work-holding devices used to locate and clamp a part surface to support manufacturing operations such as machining, inspection, and assembly. Typical part manufacturing requires planning several fixture setups to immobilize the work part while it is operated on in various orientations. Given a library of fixtures that may be used in a manufacturing process, a key challenge in automate ability analysis is the synthesis ? Corresponding author. E-mail address: nelaturi@parc.com).of a fixture configuration that may be used to effectively clamp a specified work part during a manufacturing operation, and is the problem addressed in this paper.The design and fabrication of fixtures can take up to 20% of the total manufacturing cost, and using flexible or recon able fixtures can lead to as much as 80% reduction in the fixture cost [1].Modular fixtures represent the most widely used class of flexible fixtures and are adaptable to a large class of parts. They are often used for moderate or small lot sizes, especially when the cost of dedicated fixtures and the time required to produce them maybe difficult to justify. Complex work pieces are located through fixtures produced quickly from standard components and can then be disassembled when a production run is complete. Modular see front matter Ltd. All rights reserved.the generated locations are found. The proposed methods are intended for integration into a larger automated process planning system, and therefore we provide checks to ensure that fixtures are not generated at locations that will interfere with the tool motion during machining or inspection. The output of the system is an automatically configured fixture layout that reflects shop capability and guarantees part stability. If no such configuration is possible the part is classified as non able.Automatic fixture configuration setups for re parts and process planning with clamps from a vendor supplied catalog has not been effectively addressed. We have developed novel algorithms that solve several sub-problems required in automatic fixture configuration for process planning. Determining of the part as dictated by process specific constraints such as tool movement and accessibility. – Rapidly determining locating points on the surface of the solid model at locations by partitioning six dimensional wrench space sampled at coordinates of candidate fixture locations, and picking optimal configurations. – Identifying physical clamps from a vendor supplied catalog amounts to performing fast collision checks that determine parameters for usable clamps at each location. 1.3. Outline We propose that the problem of automated fixture selection and layout may be solved in two stages using a generate and test strategy—we will first generate locating clamping points that guarantee part immobility, and subsequently test these points against a library of fixtures to determine if the points are accessible and without collisions by any configuration of the available clamps. If such a configuration exists, it is identified as a valid fixture.Locating clamping points: in Section 3, we determine the spatial locations of clamping points on the work part that ensure immobility of the clamped part under the application of any external force.The theories of force and form closure used in robotic grasping provide the mathematical foundation for identifying such clamping lo-cations which are inherent to the geometry of the work part and independent of the part’s spatial position and orientation. In particular, we will use the properties that seven points are necessary and sufficient for grasping, and four points for grasping a polyhedral part with frictional contact [12,11]. The novel algorithm to determine locating points relies on a partitioning of six dimensional wrench space sampled at coordinates derived from candidate fixture locations. This partitioning scheme facilitates rapid identification of a form closure configuration. In particular, form closure is guaranteed by the requirement that the convex hull of the chosen vectors contains the origin of the wrench space [13].Fixture selection: given a set of form closure clamping locations on a work part, we solve the problem of selecting candidate clamps from a given library of parts. The fixtures are assumed to be modular, which would maximize their ability to satisfy clamping conditions, with minimal disruption to the existing tooling. The input set of locating points is vetted against the library to generate parameters for clamps that are accessible and pass collision tests with the part and surrounding tooling. The parameters are matched against the catalog to retrieve a set of clamps, if they exist, and assemble a fixture configuration to guarantee stability. If there is no such solution, the algorithm is repeated until all form closure configurations of clamps in the catalog are exhausted. 2. Process solid models to identify fix able locations 2.1. Machining process planning Typically all locations on the boundary of a part will not be available for In machining operations, material in a removal volume is removed from a larger shape which could be raw stock or an intermediate staging model in a manufacturing process plan. One constraint in the problem is to locate the part without interfering with the tool’s ability to remove the material as planned. Given the staging model and removal volume,we first identify locations on the part boundary that will not be approached by a moving tool while removing material from the staging model. These are the surfaces exposed after the machining process is complete in a process step.To discard the exposed surfaces, we first construct binary space partitioning trees, or BSP trees [19], of the staging model and removal volume. BSP trees are optimized for ray intersection calculations and allow fast evaluation of whether a ray shot from a location on the part boundary along the part normal will intersect(a triangle on) the removal volume or another location on the staging model. This computation coarsely approximates whether the location on the part boundary is approachable by a clamp without collision with the volume to be removed by a translating cut- ting tool, and avoids placing clamps in undesirable locations such as pockets and holes. Locations from which an emanating ray along the part surface normal intersects triangles on the removal volume are discarded before performing form closure configuration.To discard reachable locations in a form closure grasp where the clamp will interfere with the tool, we perform an intersection test between a clamp model contacting the location and a sweep of the removal volume in the direction of the tool approach, or along the tool path.