Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A geometric constraint solver for 3-D assembly modeling

  • Original Article
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this paper, we propose a geometric constraint solver for 3-D assembly applications. First, we give a new geometry and constraint expression based on Euler parameters, which can avoid singular points during the solving process and simplify constraint types. Then we present a directed graph based constructive method to geometric constraint system solving that can handle well-, over- and under-constrained systems efficiently. The basic idea of this method is that it first simplifies the constraint graph by pruning those vertices which have only in-arcs from the graph and then reduces the size of strongly connected components (SCCs) left in the graph by DOF-based analysis. The method can solve all kinds of configurations including closed-loops. After that, we apply a hybrid numerical method of Newton–Raphson and Homotopy to solve under-constrained systems. The hybrid method makes use of the high efficiency of the Newton–Raphson method as well as the outstanding convergence of the Homotopy method. Finally, we give a practical example and conclusion.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kim J, Kim K, Choi K, Lee JY (2000) Solving 3D geometric constraints for assembly modeling. Int J Adv Manuf Technol 16:843–849

    Article  Google Scholar 

  2. Light R, Gossard D (1982) Modification of geometric models through variational geometry. Comput Aided Des 14(3):209–214

    Article  Google Scholar 

  3. Sutherland I (1963) Sketchpad, a man-machine graphical communication system. Proc Spring Joint Comp Conference, North Holland, pp 329–345

  4. Gao XS, Zhou SC (1998) Solving geometric constraint systems II. A symbolic approach and decision of rc-constructibility. Comput Aided Des 30(2):115–22

    Article  Google Scholar 

  5. Kondo K (1992) Algebraic method for manipulation of dimensional relationships in geometric models. Comput Aided Des 24(3):141–7

    Article  MATH  Google Scholar 

  6. Aldefeld B (1988) Variation of geometries based on a geometric-reasoning method. Comput Aided Des 20(3):117–126

    Article  MATH  Google Scholar 

  7. Roller D (1990) A System for Interactive Variation Design. In: Wozny MJ, Turner JU, Preiss K (eds) Geometric Modeling for Product Engineering. Elsevier Science Publishers B.V. (North Holland), pp 207–210

  8. Verroust A, Schonek F, Roller D (1992) Rule-oriented method for parameterized computer-aided design. Comput Aided Des 24(3):531–540

    Article  MATH  Google Scholar 

  9. Sunde G (1987) A CAD system with declarative specification of shape. Eurographics workshop on intelligent CAD systems. Noorwijkerhout, The Netherlands, pp 90–104

  10. Kramer G (1992) Solving geometric constraint system: A case study in kinematics. MIT Press, Cambridge, MA

    Google Scholar 

  11. Owen J C (1991) Algebraic solution for geometry from dimensional constraints. Proc ACM Symp Found of Solid Modeling, Austin, TX, pp 397–407

  12. Bouma W, Fudos I, Hoffmann C, Cai J, Paige R (1995) Geometric constraint solver. CAD 27(5):487–501

    MATH  Google Scholar 

  13. Hoffmann CM, Vermeer P (1995) Geometric constraint solving in R2 and R3. In: Computing in Euclidean geometry. World Scientific Publishing, , pp 170–195

  14. Lee JY, Kim K (1998) A 2-D geometric constraint solver using DOF-based graph reduction. Comput Aided Des 30(9):883–896

    Article  MATH  Google Scholar 

  15. Li YT, Hu SM, Sun JG (2002) A constructive approach to solving 3-D geometric constraint systems using dependence analysis. Comput Aided Des 30:97–108

    Article  Google Scholar 

  16. Peng XB, Chen LP, Zhou FL, Zhou J (2002) Singularity analysis of geometric constraint system. J Comput Sci Technol 17(3):314–323

    Article  MATH  Google Scholar 

  17. Hoffmann CM, Lomonosov A, Sitharam M (1998) Geometric constraint decomposition. In: Geometric constraint solving and applications. Springer, Berlin Heidelberg New York, pp 170–195

  18. Ge J-X, Chou S-C, Gao X-S (1999) Geometric constraint satisfaction using optimization methods. Comput Aided Des 31:867–879

    Article  MATH  Google Scholar 

  19. Kang YS (1996) Principles and methods of variational assembly design. Dissertation, Huazhong Univ Sci & Tech

  20. Lamure H, Michelucci D (1996) Solving geometric constraints by homotopy. IEEE Trans Visual Comput Graph 2(1):28–34.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Design & Production Engineering, Seoul National University, Seoul, South Korea

    Xiaobo Peng & Kunwoo Lee

  2. School of Mechanical Science & Engineering, Huazhong University of Science & Technology, Wuhan, China

    Liping Chen

Authors
  1. Xiaobo Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kunwoo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liping Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaobo Peng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, X., Lee, K. & Chen, L. A geometric constraint solver for 3-D assembly modeling. Int J Adv Manuf Technol 28, 561–570 (2006). https://doi.org/10.1007/s00170-004-2391-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-004-2391-1

Keywords

Search

Navigation