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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2002, Vol. 3 Issue (1): 24-29    DOI: 10.1631/jzus.2002.0024
Computer & Industrial Engineering     
A mathematical model of symmetry based on mathematical definition
LIU Yusheng, YANG Jiangxin, WU Zhaotong, Gao Shuming
State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China; Institute of Production Engineering, Zhejiang University, Hangzhou 310027, China
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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.

Key words： mathematical definition      symmetry tolerance      mathematical model      CAD/CAM      production engineering     
Received: 28 January 2001     
CLC:  TP391.72  
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LIU Yusheng
YANG Jiangxin
WU Zhaotong
Gao Shuming
Cite this article:

LIU Yusheng, YANG Jiangxin, WU Zhaotong, Gao Shuming. A mathematical model of symmetry based on mathematical definition. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2002, 3(1): 24-29.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2002.0024     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2002/V3/I1/24

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