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Algorithmica

, Volume 13, Issue 6, pp 539–552 | Cite as

Assembly sequences for polyhedra

  • A. Schweikard
  • R. H. Wilson
Article

Abstract

The problem of finding sequences of motions for the assembly of a given object consisting of polyhedral parts arises in assembly planning. We describe an algorithm to compute the set of all translations separating two polyhedra withn vertices inO(n4) steps and show that this is optimal. Given an assembly ofk polyhedra with a total ofn vertices, an extension of this algorithm identifies a valid translation and removable subassembly inO(k2n4) steps if one exists. Based on the second algorithm, a polynomial-time method for finding a complete assembly sequence consisting of single translations is derived. An implementation incorporates several changes to achieve better average-case performance; experimental results obtained for simple assemblies are described.

Key words

Assembly planning Arrangement computation in the plane Separating polyhedra 

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Copyright information

© Springer-Verlag New York Inc 1995

Authors and Affiliations

  • A. Schweikard
    • 1
  • R. H. Wilson
    • 1
  1. 1.Robotics Laboratory, Department of Computer ScienceStanford UniversityStanfordUSA

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