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Received: 2001-01-28

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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.1 P.24-29

http://doi.org/10.1631/jzus.2002.0024


A mathematical model of symmetry based on mathematical definition


Author(s):  LIU Yusheng, YANG Jiangxin, WU Zhaotong, Gao Shuming

Affiliation(s):  State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s): 

Key Words:  mathematical definition, symmetry tolerance, mathematical model, CAD/CAM, production engineering


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LIU Yusheng, YANG Jiangxin, WU Zhaotong, Gao Shuming. A mathematical model of symmetry based on mathematical definition[J]. Journal of Zhejiang University Science A, 2002, 3(1): 24-29.

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Abstract: 
Tolerance is imperative for seamless integration of CAD/CAM (Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[4] Liu,Y.S., Yang,J.X., Wu,Z.T., 1999. A CAD Model for Geometric Tolerance. In: The 6th International Conference of CAD/CG, Shanghai, p.35-42.

[5] Liu,Y.S., 2000. Study on Tolerance Modeling and Representation of Plane Based on Mathematic Definition. Ph.D. thesis, Zhejiang University,(in Chinese).

[6] Newsroom of International Dynamic Standard, 1983. User Guide for Geometric Tolerance Labeling. Science Document Press, Beijing (in Chinese).

[7] Ngoi,B.K.A., Ong,C.T., 1998. Product and Process Dimensioning and Tolerancing Techniques. A State-of-the-Art Review. International Journal of Advanced Manufacturing Technology, 14(8):910-917.

[8] Roy,U., 1998. Representation and interpretaiton of geometric tolerances for polyhedral objects: I. Form tolerances. CAD, 30(2):151-161.

[9] Wu,Z.T., Yang,J.X., 1999. Computer Aided Optimal Design of Tolerance. Zhejiang University Press. Zhejiang(in Chinese).

[10] Xu,Z.J., 1982. Monte Carlo Method. Shanghai Science and Technology Press, Shanghai,(in Chinese).

[11] Yang,J.X., Liu,Y.S., Tan,J.R., et al., 2000. A CAD Model for Concurrent Tolerance. Journal of Mechnical Engineering( English Edition), 13(2):96-101

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