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

Michael Erdmann, Matthew T. Mason, and George Vanecek
Algorithmica, Vol. 10, No. 2/3/4, August, 1993


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.

Keywords
Parts orienting, Part sorters, Manipulation, Material handling

Notes

Text Reference
Michael Erdmann, Matthew T. Mason, and George Vanecek, "Mechanical Parts Orienting: The Case of a Polyhedron on a Table," Algorithmica, Vol. 10, No. 2/3/4, August, 1993

BibTeX Reference
@article{Erdmann_1993_3841,
   author = "Michael Erdmann and Matthew T. Mason and George Vanecek",
   title = "Mechanical Parts Orienting: The Case of a Polyhedron on a Table",
   journal = "Algorithmica",
   month = "August",
   year = "1993",
   volume = "10",
   number = "2/3/4",
}