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1、AUTOMATIC FIXTURE SYNTHESIS IN 3DKamen PenevProgrammable Automation LaboratoryComputer Science Department and Institute for Robotics and Intelligent SystemsUniversity of Southern CaliforniaLos Angeles, CA 90089-0781 Aristides A. G. RequichaLos Angeles, CA 90089-0781AbstractA fixture is an arrangemen

2、t of fixturing modules that locate and hold a workpart during a manufacturing operation. In this work we. consider fixtures with frictionless point contacts and present a method for placement of contact points on a non-prismatic 3D workpart. It is a non-deterministic, potential field algorithm for c

3、ontact point placement. The method provides a basic framework for the integration of heterogeneous high-level fixturing agents through an interface based on zones of attraction and repulsion on the workpart boundary. The algorithm may produce redundant fixtures, and can augment partial solutions to

4、complete form closure fixtures.1. IntroductionA fixture is an arrangement of fixturing modules that locate and hold a workpart during a manufacturing operation, such as machining, assembly and inspection. Fixturing is of essential importance to industrial manufacturing and constitutes a significant

5、part of all manufacturing costs. Therefore, fixture design automation is very important. Fixture design involves a great variety of considerations, such as restraint, deterministic location, loadability, and tool accessibility. Efficient algorithms that address the whole range of fixturing issues fo

6、r a comprehensive domain of workparts do not yet exist. Recently, Brost and Peters published an algorithm Brost & Peters 1996 that extends the earlier classic work of Brost and Goldberg Brost & Goldberg, 1994 to the 3D domain. This algorithm, however, requires vertical and horizontal planar surfaces

7、 to constitute a substantial part of the workpart boundary. It generates all possible fixtures and then rates them accordingly to certain metrics. This is computationally expensive. Wagner et al presented an algorithm that uses seven modular struts mounted in a box to fixture polyhedra Wagner et al

8、1995. This algorithm is not complete in the sense that it cannot effectively handle certain cases, such as a cube with faces parallel to the box. It also suffers from high computational complexity. Wallack and Canny suggested another method with an “enumerate-and-rate” flavor Wallack & Canny 1996. I

9、t can fixture prismatic workparts with planar and cylindrical vertical surfaces. Ponce proposed an algorithm that utilizes curvature effects to compute fixtures with four fingers for polyhedral parts Ponce 96. The reduced number of contacts should provide for better complexity of this algorithm, but

10、 the quality of the produced fixtures seems to be inferior to the ones that utilize more contacts and provide classical form closure.In this paper we present a new potential-field algorithm that efficiently produces quality fixture designs. Our algorithm works for arbitrary workparts and provides co

11、nvenient universal means for representing various fixturing requirements. This algorithm is a direct generalization of the 2D potential field fixturing algorithm of Penev and Requicha Penev & Requicha 1996. We consider fixtures with frictionless point contacts. It has been proven that seven contacts

12、 are necessary. Somoff, 1900 and sufficient Markenscoff et al, 1990 to immobilize any workpart in 3DFollowing a least-commitment strategy, the process of fixture synthesis may be separated into three stages fixturing task analysis, contact point placement, and fixture layout design. In the fixturing

13、 task analysis phase the workpart geometry and manufacturing process are analyzed to identify various parameters of the fixturing problem, such as cutting forces, inaccessible or forbidden areas, and also to find features that may be useful for applying fixturing devices, such as machined flat surfa

14、ces, horizontal and vertical surfaces, pairs of parallel surfaces, pairs of perpendicular surfaces, etc.Figure 1: Contact point placementIn the contact point placement phase a number of contact points are placed on the workpart boundary （Figure 1）, so that the resulting configuration of contacts sat

15、isfies the constraints identified in the analysis phase as well as certain kinematic requirements that must be satisfied by any fixture, such as total restraint.Figure 2: From contact point configuration to fixture layout designIn the layout design phase “towers” of fixturing components are built an

16、d placed around the workpart so as to contact the part at the point locations computed in the contact point placement phase. For example, a contact point on a horizontal workpart surface （Figure 2a） may lead to the instantiation of an overhead clamp that contacts the workpart at that particular poin

17、t （Figure 2b）. This is a design-for-function problem constrained by the set of available fixturing modules and their parameters. The set of contact points are the functional specification and the fixture layout is a configuration of components that achieves it.In this research we focus on contact po

18、int placement and its integration with part and task analysis. An arrangement of contact points must satisfy certain kinematic conditions in order to be a basis for a good fixture. In particular, it must provide form closure, deterministic location, clamping stability, detachability and loadability

19、Asada & By. The algorithm uses a discretization of the workpart boundary, similar to the meshes used in FEA. However, unlike FEA, our attention is on the mesh nodes, rather than on the mesh elements. Discretization was chosen for the following reasons: First, we can handle workparts with arbitrary g

20、eometry, as long as the parts boundary is a collection of smooth surfaces which we know how to mesh. This requirement is satisfied by all surfaces used in modern CAD systems. Second, discretization is necessary in order to avoid an expensive computation of geodesic curves. Third, discretization shou

21、ld not significantly affect the results, as long as the number of discrete candidate locations on the boundary is much larger than the number of surfaces. In our implementation the discretized boundary consists of several hundred points only. Experimental evidence indicates that this is sufficient f

22、or realistic workparts.We introduce a potential field on the workpart boundary defined by zones of attraction and repulsion, which we call P-zones. The contacts are modeled as charged particles that move on the boundary driven by this potential field. The contacts are also subject to mutual repulsio

23、n based on the distance between each two contacts in the wrench vector space. The algorithm executes a series of simulation epochs. Each epoch starts with a random configuration, proceeds through a certain number of steps toward lower potential energy and ends with a test for kinematic conditions （f

24、orm closure）. The algorithm terminates when an epoch produces satisfactory configuration. To spread the contact points on the boundary we simulate repulsion between each pair of them. The intensity of repulsion between two contact points depends on the distance between their corresponding wrenches i

25、n the wrench vector space. Our simulation proceeds in a limited number of steps or until equilibrium is reached. The resulting placement should have a good chance of leading to a good fixture. Such a randomized method assumes that the set of n-tuples of contact points （for n greater than three） that

26、 satisfy the kinematic requirements has measure greater than zero and is relatively large. That is, the solution space is large. Although we have not been able to prove this hypothesis mathematically, our experiments have confirmed it. Moreover, the measure increases with the number of contact point

27、s, e.g. it is easier to find a form closure arrangement with eight points than with seven. The notion of repulsion is essential in our method as it allows other considerations to be accommodated easily. We can put additional repulsion spots on the workpart boundary to represent forbidden regions. We

28、 can also introduce centers of attraction. These correspond to areas that were recommended by the analysis phase as desirable for placing contact points, e.g. datum surfaces. Thus, we propose a potential field for uniformly representing heterogeneous fixturing information. Regions of repulsion corre

29、spond to areas with positive potential. Negative potential is associated with attraction. Zero potential corresponds to neutral areas. The initial randomly selected contact points are regarded as particles that are being attracted or repelled by a potential field that includes a pairwise repulsion.

30、The goal of the system of contact points is to minimize its total potential energy. 2 The InputThe input to our algorithm consists of CAD models of the workpart boundary and a set of solid P-zones. Each P-zone defines a potential-field influencing region with non-zero charge. 3 Discretizing the Work

31、part BoundaryThe first step in our method is to discretize the boundary of the workpart, thus creating the candidate contact point locations which we call nodes. Discretization is done by invoking a standard faceter embedded in the geometric modeler we use. The discretization is stored in an oriente

32、d graph data structure. Each node of the graph corresponds to a node on the mesh. The edges of the graph correspond to edges of the mesh connecting neighboring nodes. At each node the screw representing the point contact is computed and stored. A screw is a concise and convenient representation of the surface normal and the location of the node. It is used in all kinematic tests based on screw theory.4 Computing the Po