Optimized Synthesis of Snapping Fixtures

Fixtures for constraining the movement of parts have been extensively investigated in robotics, since they are essential using robots automated manufacturing. This paper deals with design and optimized synthesis a special type fixtures, which we call snapping fixtures. Given polyhedral workpiece P n vertices constant genus, need to hold, fixture is semi-rigid polyhedron G, made palm several fingers, such that when G well separated, can push toward slightly bending fingers on way (exploiting its mild flexibility), obtain configuration, where back original shape inseparable as rigid bodies. We prove minimal closure conditions under fixtures hold parts, Helly’s theorem. then introduce an algorithm running \(O(n^3)\) time produces fixture, minimizing number optimizing additional objectives, if exists. also provide efficient robust implementation simpler version algorithm, model be 3D printed runs \(O(n^4)\) time. describe two applications different optimization criteria: add-ons drones, aim make lightweight possible, small-scale precious stones jewelry, maximize exposure stones, namely minimize obscuring by fixture.