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3D geometric constraint solving using the method of kinematic analysis

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Abstract

In this paper, an approach based on kinematic method for solving 3D geometric assembly constraints is presented. The relative generalized coordinates and generalized recursive formulations used in kinematic analysis are utilized to reduce the size of constraint equations. Based on the cut-constraint method, this approach can be used to solve all kinds of configurations. In the case of an open-loop constraint system, the geometric constraints can be satisfied by sequentially determining the values of relative generalized coordinates. With respect to a closed-loop constraint system, the proposed approach converts it to a spanning tree structure by cutting constraints and introducing cut-constraint equations. Furthermore, a topological analysis method is also developed to obtain the spanning tree with the minimal number of cut-constraint equations, and the analytical Jacobian matrix of cut-constraint equations is derived to enhance computational efficiency. In the end, the proposed approach is demonstrated and validated using two examples of closed-loop geometric constraint system.

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Authors and Affiliations

  1. CAD Center, School of Mechanical Science & Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China

    Hongjian Xia, Boxing Wang, Liping Chen & Zhengdong Huang

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  1. Hongjian Xia
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  2. Boxing Wang
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  3. Liping Chen
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  4. Zhengdong Huang
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Correspondence to Hongjian Xia.

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Xia, H., Wang, B., Chen, L. et al. 3D geometric constraint solving using the method of kinematic analysis. Int J Adv Manuf Technol 35, 711–722 (2008). https://doi.org/10.1007/s00170-006-0748-3

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  • DOI: https://doi.org/10.1007/s00170-006-0748-3

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