Topological Fixture Synthesis Using Semide nite Programming
1. Abstract Topological xture synthesis is an important issue to consider for most manufacturing operations performed on solid and sheet metal workpieces. Recent work on optimal xture design has focused on determining the positions of locators and clamps to minimize workpiece deformation. These approaches restrict the locators and clamps to three mutually perpendicular planes selected according to the \3-2-1" or the \N-2-1" locating principle. In this article, mixed-integer quadratic programming is used to identify the optimal distribution and position (i.e., topology) of locators in order to minimize the mean compliance of the workpiece. We present a semide nite programming (SDP) relaxation method to solve the underlying combinatorial problem. Illustrative examples (with symmetric and asymmetric loads) validate the formulation and solution approach.