Mechanical Parts Orienting: The Case of a Polyhedron on a Table

Abstract

The positioning and orienting of parts is a standard problem in manufacturing. Orienting parts is often a prelude to the assembly of parts at tight tolerances. This paper considers the problem of orienting a part resting on a table, by tilting the table. The initial orientation of the part is assumed to be completely unknown. The objective is to tilt the table in a manner that reduces the uncertainty in the part's orientation. This paper focuses on three-dimentional polyhedral parts, with infinite friction between the parts and the table, and for which all transitions between difference face-table contacts may be regarded as rotations across edges. The paper proposes a planner that determines a sequence of tilting operations designed to minimize the uncertainty in the part's orientation. The planner runs in time on O(n^3), where n is the number of faces of the polyhedron. The planner produces a sequence of O(n) distinct tilting operations. Each tilting operation wobbles the table until the part is in steady state.