Algorithmica

, Volume 26, Issue 3–4, pp 577–601 | Cite as

A General Framework for Assembly Planning: The Motion Space Approach

  • D. Halperin
  • J.-C.  Latombe
  • R. H. Wilson

Abstract.

Assembly planning is the problem of finding a sequence of motions to assemble a product from its parts. We present a general framework for finding assembly motions based on the concept of motion space . Assembly motions are parameterized such that each point in motion space represents a mating motion that is independent of the moving part set. For each motion we derive blocking relations that explicitly state which parts collide with other parts; each subassembly (rigid subset of parts) that does not collide with the rest of the assembly can easily be derived from the blocking relations. Motion space is partitioned into an arrangement of cells such that the blocking relations are fixed within each cell. We apply the approach to assembly motions of several useful types, including one-step translations, multistep translations, and infinitesimal rigid motions. Several efficiency improvements are described, as well as methods to include additional assembly constraints into the framework. The resulting algorithms have been implemented and tested extensively on complex assemblies. We conclude by describing some remaining open problems.

Key words. Assembly planning, Assembly sequencing, Motion space, Nondirectional blocking graph, Manufacturing. 

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Copyright information

© 2000 Springer-Verlag New York Inc.

Authors and Affiliations

  • D. Halperin
    • 1
  • J.-C.  Latombe
    • 2
  • R. H. Wilson
    • 3
  1. 1.Department of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. halperin@math.tau.ac.il.IL
  2. 2.Department of Computer Science, Stanford University, Stanford, CA 94305, USA. latombe@cs.stanford.edu.US
  3. 3.Eastman Kodak Company, Albuquerque, NM 87112-1881, USA. rwilson@kodak.com.US

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