A complete algorithm for designing planar fixtures using modular components

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-of-plane 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.