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

Assembly sequences for polyhedra

  • A. Schweikard
  • R. H. Wilson


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman,Data Structures and Algorithms, Addison-Wesley, Reading, MA, 1983.Google Scholar
  2. [2]
    E. M. Arkin, R. Connelly, and J. S. B. Mitchell. On monotone paths among obstacles, with applications to planning assemblies.Proc. ACM Symp. on Computational Geometry, 1989, pp. 334–343.Google Scholar
  3. [3]
    B. Chazelle, L. J. Guibas, and D. T. Lee. The power of geometric duality.BIT, 25: 76–90, 1985.Google Scholar
  4. [4]
    R. J. Dawson. On removing a ball without disturbing the others.Mathematics Magazine, 57(1): 27–30, 1984.Google Scholar
  5. [5]
    H. Edelsbrunner.Algorithms in Combinatorial Geometry. Springer-Verlag, Heidelberg, 1987.Google Scholar
  6. [6]
    L. S. Homem de Mello and A. C. Sanderson. Automatic generation of mechanical assembly sequences. Technical Report CMU-RI-TR-88-19, Robotics Institute, Carnegie-Mellon University, 1988.Google Scholar
  7. [7]
    S. S. Krishnan and A. C. Sanderson. Path planning algorithms for assembly sequence planning.Proc. Internat. Conf. on Intelligent Robotics, 1991, pp. 428–439.Google Scholar
  8. [8]
    J.-C. Latombe.Robot Motion Planning. Kluwer, Boston, 1991.Google Scholar
  9. [9]
    T. Lozano-Pérez. Spatial planning: A configuration space approach.IEEE Transactions on Computers, 32(2): 108–120, 1983.Google Scholar
  10. [10]
    J. S. B. Mitchell. Personal Communication, December 1990.Google Scholar
  11. [11]
    B. K. Natarajan. On planning assemblies.Proc. ACM Symp. on Computational Geometry, 1988, pp. 299–308.Google Scholar
  12. [12]
    R. Pollack, M. Sharir, and S. Sifrony. Separating two simple polygons by a sequence of translations.Discrete & Computational Geometŕy, 3: 123–136, 1988.Google Scholar
  13. [13]
    F. P. Preparata and M. I. Shamos.Computational Geometry: An Introduction. Springer-Verlag, New York, 1985.Google Scholar
  14. [14]
    J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands.Discrete & Computational Geometry, 12: 367–384, 1994.Google Scholar
  15. [15]
    G. T. Toussaint. Movable separability of sets. In G. T. Toussaint, editor,Computational Geometry. Elsevier, North-Holland, Amsterdam, 1985.Google Scholar
  16. [16]
    G. T. Toussaint. On separating two simple polygons by a single translation.Discrete & Computational Geometry, 1989 4: 265–278.Google Scholar

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

Personalised recommendations