A complete algorithm for synthesizing modular fixtures for polygonal parts

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(n⁵d⁵). 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