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A geometric constraint solver for 3-D assembly modeling

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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.

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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
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  2. Kunwoo Lee
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  3. Liping Chen
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Correspondence to Xiaobo Peng.

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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

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

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