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A Complete Algorithm for Designing Planar Modular Using Fixtures Components



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IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION VOL 12 NO 1 FEBRUARY 1996 31 A Complete Algorithm for Designing Planar Fixtures Using Modular Components Randy C Brost Member IEEE and Kenneth Y Goldberg Member IEEE Abstruct Commercially available modular fixturing systems typically include a lattice of holes with precise spacing and an assortment of precision locating and clamping modules that can be rigidly attached to the lattice Currently machinists manually design a suitable arrangement of these modules to hold a given part This requires expertise and can delay production Futhermore a machinist may in many cases settle upon an arrangement that is not optimal for a given machining operation In this paper we present an implemented algorithm that accepts a polygonal description of the part silhouette and efficiently constructs the set of all feasible fixture designs that kinematically constrain the part in the plane Each fixture is comprised 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 a 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 part silhouette and to identify the optimal fixture relative to an arbitrary quality metric The algorithm does not consider out ofplane forces or motions however we view this planar result as an essential component of a larger algorithm that solves the 3 D 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 and appears to be applicable to a broad class of man made parts to reduce the number of alternatives is to limit consideration to a small set of components that must be located on a regular lattice structure Such modular fixturing systems also have the advantage of allowing rapid set up and changeover for new parts precision locating on a tightly toleranced lattice and a reduced fixture inventory comprised of re usable components VI The concept of modular fixturing using a family of interchangeable components was originally developed in England during World War 11 and has resulted in a variety of commercially available modular fixturing systems 4 These systems typically include a square lattice of tapped and doweled holes with spacing toleranced to zt0 0002 in and an assortment of precision locating and clamping elements that can be rigidly attached to the lattice using dowel pins or expanding mandrels Although the lattice and set of modules greatly reduce the number of alternatives designing a suitable fixture currently requires human intuition and trial and error Designing a new fixture can be time consuming Furthermore if the set of alternatives is not systematically explored the designer may settle upon a suboptimal design or fail to find any acceptable design In this paper we present an algorithm for automatically designing a class of modular fixtures These fixtures constrain all motion of a part in the support plane Constraint is provided by four point contacts and does not rely on friction Each I INTRODUCTION fixture in this class uses three round locators each centered on OST automated manufacturing assembly and inspec a lattice point and one translating clamp that must be attached tion operations require fixtures to locate and hold parts to the lattice via a pair of unit spaced holes thus allowing Given part shape and desired position and orientation fixtures contact at a variable distance along the principle axes of the are usually custom designed by manufacturing engineers and lattice We use the temfiel fixture element to refer to either machinists Although there are a few general guidelines and a locator or a clamp and the temfiture to refer to a geometric a number of studies systematic algorithms for automatically arrangement of three locators and one clamp on the lattice designing fixtures based on CAD part models are still lacking An acceptable fixture design must satisfy several require ll P I ments First it must fully constrain the part to prevent its This is partly due to the uncountable set of alternative fixture motion We require fixtures to provide form closure which designs that must be considered in the general case One way is a kinematic constraint condition that prevents all motion 5 In addition to constraining the part the fixture must not Manuscriptreceived January 15 1994 revised December 9 1994 The work of R C Brost was supported by the U S DOE under Contract DE ACO4 interfere with certain geometric regions of the part perhaps 94AL85000 The work of K Y Goldberg was supported by the NSF under due to cosmetic surfaces or the need to retain clearance for Award DDM 9215362 and Award IRI 9123747 the NYI under Award IRI9457523 and by equipment grants from Adept Technology Inc and Qu CO grasping machining assembly or other operations Thus we Inc define geometric access constraints which define regions of R C Brost is with Sandia National Laboratories Albuquerque NM 87185 points that must remain free of fixture components With these USA K Y Goldberg was with the University of Southem California Los requirements in mind we say that a fixture is admissible Angeles CA 90089 USA He is now with the Department of Industrial if it provides form closure and obeys the geometric access Engineering and Operations Research University of California Berkeley CA constraints In this paper we further restrict our attention to 94720 USA fixtures where each fixe1 makes point contact with only one Publisher Item Identifier S 1042 296X 96 01060 3 M 1042 296W96 05 00 0 1996 IEEE 32 P LEEE TRANS ACTIONS ON ROBOTICS AND AUTOMATION VOL 12 NO 1 FEBRUARY 199 linear edge of the part Given a part as input the algorithm efficiently enumerates all admissible fixtures and ranks them according to a user definable scalar quality metric The algorithm begins with a geometric transformation that expands the part edges by the radius of the locators this allows us to treat the locators as points on the transformed edges


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