Skip to main content
SpringerLink
Log in

Representations for assemblies

  • Chapter
Computer-Aided Mechanical Assembly Planning

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 148))

Abstract

Mechanical, electrical and electronic products typically are assemblies of many component solid parts. The components of a product may be joined so as to form either (1) a rigid assembly, (2) an articulated collection of rigid bodies that may move relative to one another (often called a mechanism), or (3) a flexible, non—rigid assembly. No solid is perfectly rigid, and sometimes non—rigidity must be acknowledged explicitly, for example when two parts are press—fitted, or when one of the components is a spring.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. A. P. Ambler and R. J. Popplestone, “Inferring the positions of bodies from specified spatial relationships”, Artificial Intelligence, Vol. 6, No. 2, pp. 157–174, Summer 1975.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ø. Bjorke, Computer-Aided Tolerancing. New York: ASME Press, 2nd ed., 1989.

    Google Scholar 

  3. A. Borning, “ThingLab — A constraint-oriented simulation laboratory”, Ph.D. Dissertation, Dept. of Computer Science, Stanford University, July 1979.

    Google Scholar 

  4. M. Boyer and N. F. Stewart, “Modelling spaces for toleranced objects”, Départment d’informatique et de recherche opérationnelle, Université de Montréal, July 1990.

    Google Scholar 

  5. M. Boyer and N. F. Stewart, “Modelling spaces for toleranced objects: 32-classes suitable for practical use”, Départment d’informatique et de recherche opérationnelle, Université de Montréal, November 1990.

    Google Scholar 

  6. C. M. Brown, “PADL-2: A technical summary”, IEEE Computer Graphics and Applications, Vol. 2, No. 2, pp. 69–84, March 1982.

    Article  Google Scholar 

  7. S. A. Cameron, “Modelling solids in motion”, Ph.D. Dissertation, University of Edinburgh, 1984.

    Google Scholar 

  8. K. W. Chase and W. H. Greenwood, “Design issues in mechanical tolerance analysis”, Manufacturing Review, Vol. 1, No. 1, pp. 50–59, March 1988.

    Google Scholar 

  9. F. Etesami, “Tolerance verification through manufactured part modeling”, Journal of Manufacturing Systems,Vol. 7, No. 3, pp. 223–232, September 1988.

    Article  Google Scholar 

  10. A. Fleming, “Analysis of uncertainties in a structure of parts”, Proc. 9th Intl. Joint Conf. on Artificial Intelligence, Los Angeles, CA, pp. 1113–1115, August 18–23, 1985.

    Google Scholar 

  11. A. D. Fleming, “Analysis of uncertainties and geometric tolerances in assemblies of parts”, Ph.D. Dissertation, Dept. of Artificial Intelligence, University of Edinburgh, 1987.

    Google Scholar 

  12. A. Fleming, “Geometric relationships between toleranced features”, Artificial Intelligence, Vol. 37, No. 1–3, pp. 403–412, December 1988.

    Article  Google Scholar 

  13. D. C. Gossard, R. P. Zuffante and H. Sakurai, “Representing dimensions, tolerances, and features in MCAE systems”, IEEE Computer Graphics e4 Applications, Vol. 8, No. 2, pp. 51–59, March 1988.

    Article  Google Scholar 

  14. D. D. Grossman, “Monte Carlo simulation of tolerancing in discrete parts manufacturing and assembly”, Computer Science Report Number STANCS-76–555, Stanford University, May 1976.

    Google Scholar 

  15. P. Hoffman, “Analysis of tolerances and process inaccuracies in discrete part manufacturing”, Computer-Aided Design, Vol. 14, No. 2, pp. 83–88, March 1982.

    Article  Google Scholar 

  16. C. M. Hoffmann, Geometric and Solid Modeling. San Mateo, CA: Morgan Kaufmann Publishers, 1989.

    Google Scholar 

  17. R. Jayaraman and V. Srinivasan, “ Geometric tolerancing: I. Virtual boundary requirements”, IBM Journal of Research and Development, Vol. 33, No. 2, pp. 90–104, March 1989.

    Article  MathSciNet  MATH  Google Scholar 

  18. H. Ko, “Empirical assembly planning: A learning approach”, Ph.D. Dissertation, Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1989.

    Google Scholar 

  19. G.A. Kramer, “Solving geometric constraint systems”, Proc. 8th National Conf. on Artificial Intelligence, Boston, MA, pp. 708–714, July 29-August 3, 1990.

    Google Scholar 

  20. G.A. Kramer, “Geometric reasoning in the kinematic analysis of mechanisms”, Ph.D. Dissertation (draft), University of Sussex, October 1990.

    Google Scholar 

  21. K. Lee and G. Andrews, “Inference of the positions of components in an assembly: Part 2”, Computer Aided Design, Vol. 17, No. 1, pp. 20–24, January/February 1985.

    Article  Google Scholar 

  22. K. Lee and D.C. Gossard, “A hierarchical data structure for representing assemblies: Part 1”, Computer Aided Design, Vol. 17, No. 1, pp. 15–19, January/February 1985.

    Article  Google Scholar 

  23. W.-J. Lee and T. C. Woo, “Tolerances: Their analysis and synthesis”, Journal of Engineering for Industry, Vol. 112, No. 2, pp. 113–121, May 1990.

    Article  MathSciNet  Google Scholar 

  24. E. C. Libardi, J. R. Dixon and M.K. Simmons, “Computer environments for the design of mechanical assemblies: A research review”, Engineering with Computers, Vol. 3, No. 3, pp. 121–136, Winter 1988.

    Article  Google Scholar 

  25. R. A. Light and D.C. Gossard, “Modification of geometric models through variational geometry”, Computer-Aided Design, Vol. 14, No. 4, pp. 209–214, July 1982.

    Article  Google Scholar 

  26. Y. Liu and R. J. Popplestone, “Assembly feature-mating inference from solid models using symmetry groups”, COINS Tech. Report 90–34, Computer and Information Science Dept., University of Massachusetts at Amherst, 1990.

    Google Scholar 

  27. G. H. Morris and L. S. Haynes, “Robotic assembly by constraints”, Proc. 1987 IEEE Intl. Conf. on Robotics and Automation, Raleigh, NC, pp. 1481–1486, March 31-April 3, 1987.

    Google Scholar 

  28. G. Mullineaux, “Optimization scheme for assembling components”, Computer-Aided Design, Vol. 19, No. 1, pp. 35–40, January/February 1987.

    Article  Google Scholar 

  29. R. J. Popplestone, A. P. Ambler and I. M. Bellos, “An interpreter for a language for describing assemblies”, Artificial Intelligence, Vol. 14, No. 1, pp. 79–107, August 1980.

    Article  Google Scholar 

  30. R. J. Popplestone, Y. Liu and R. Weiss, “A group theoretic approach to assembly planning”, AI Magazine, Vol. 11, No. 1, pp. 82–97, Spring 1990.

    Google Scholar 

  31. A. A. G. Requicha, “Mathematical models of rigid solid objects”, Tech. Memo. No. 28, Production Automation Project, Univ. of Rochester, November 1977.

    Google Scholar 

  32. A. A. G. Requicha, “Representations for rigid solids: Theory, methods, and systems”, ACM Computing Surveys, Vol. 12, No. 4, pp. 437–464, December 1980.

    Article  Google Scholar 

  33. A. A. G. Requicha, “Toward a theory of geometric tolerancing”, Intl. Journal of Robotics Research, Vol. 2, No. 4, pp. 45–60, Winter 1983.

    Article  Google Scholar 

  34. A. A. G. Requicha, “Representation of tolerances in solid modeling: Issues and alternative approaches”, in M. S. Pickett and J. W. Boyse, Eds., Solid Modeling by Computers. New York: Plenum Press, 1984, pp. 3–22.

    Google Scholar 

  35. A. A. G. Requicha, “Solid modeling and its applications: Progress in tolerancing, inspection, and feature recognition”, IRIS Tech. Report No. 259, Institute for Robotics and Intelligent Systems, University of Southern California, November 1989.

    Google Scholar 

  36. A. A. G. Requicha and S. C. Chan, “Representation of geometric features, tolerances, and attributes in solid modelers based on constructive geometry”, IEEE Journal of Robotics and Automation, Vol. RA-2, No. 3, pp. 156–186, September 1986.

    Article  Google Scholar 

  37. D. N. Rocheleau and K. Lee, “System for interactive assembly modelling”, Computer-Aided Design, Vol. 19, No. 2, pp. 65–72, March 1987.

    Article  Google Scholar 

  38. J. R. Rossignac, “Constraints in constructive solid geometry”, Proc. 1986 Workshop on Interactive 3D Graphics, Chapel Hill, NC, pp. 93–110, October 23–24, 1986.

    Google Scholar 

  39. J. R. Rossignac and A. A. G. Requicha, “Offsetting operations in solid modelling”, Computer-Aided Geometric Design, Vol. 3, No. 2, pp. 129–148, August 1986.

    Article  Google Scholar 

  40. V. Srinivasan and R. Jayaraman, “Geometric tolerancing: II. Conditional tolerances”, IBM Journal of Research and Development, Vol. 33, No. 2, pp. 105–124, March 1989.

    Article  MathSciNet  MATH  Google Scholar 

  41. I. E. Sutherland, “Sketchpad: A man-machine graphical communication system”, Ph.D. Dissertation, Dept. of Electrical Engineering, Massachusetts Institute of Technology, January 1963.

    Google Scholar 

  42. R. H. Taylor, “A synthesis of manipulation control programs from task level specifications”, Ph. D. Dissertation, Dept. of Computer Science, Stanford University, July 1976.

    Google Scholar 

  43. F. Thomas and C. Torras, “A group theoretic approach to the computation of symbolic part relations”, IEEE Journal of Robotics and Automation,Vol. 4, No. 6, pp. 622–634, December 1988.

    Article  Google Scholar 

  44. R. B. Tilove, “Extending solid modeling systems for mechanism design and kinematic simulation”, IEEE Computer Graphics and Applications, Vol. 3, No. 3., pp. 9–19, May/June 1983.

    Article  Google Scholar 

  45. J. U. Turner, “Tolerances in computer-aided geometric design”, Ph.D. Dissertation, Dept. of Computer and System Engineering, Rensselaer Polytechnic Institute, May 1987.

    Google Scholar 

  46. J. U. Turner, “Relative Positioning of parts in assemblies using mathematical programming”, Tech. Report TR-89046, Rensselaer Polytechnic Institute, 1989.

    Google Scholar 

  47. H. B. Voelcker, A. A. G. Requicha, E. E. Hartquist, W. B. Fisher, J. Metzger, R. B. Tilove, N. K. Birrell, W. A. Hunt, G. T. Armstrong, T. F. Check, R. Moote and J. McSweeney, “The PADL-1.0/2 system for defining and displaying solid objects”, Computer Graphics (Proc. Sig graph ‘87), Vol. 12, No. 3, pp. 257–263, August 1978.

    Article  Google Scholar 

Download references

Authors
  1. Aristides A. G. Requicha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Timothy W. Whalen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology, USA

    Luiz S. Homem de Mello  & Sukhan Lee  & 

  2. Department of Electrical Engineering Systems, University of Southern California, USA

    Sukhan Lee

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Requicha, A.A.G., Whalen, T.W. (1991). Representations for assemblies. In: Homem de Mello, L.S., Lee, S. (eds) Computer-Aided Mechanical Assembly Planning. The Springer International Series in Engineering and Computer Science, vol 148. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4038-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-4038-0_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6806-9

  • Online ISBN: 978-1-4615-4038-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation