【转帖】A Mathematical Model of Symmetry

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A Mathematical Model of Symmetry

Based on Mathematical Definition*

LIU Yusheng1 YANG Jiangxin2 WU Zhaotong2 Gao Shuming1

(1 State Key Lab. of CAD&CG, Zhejiang University, Hangzhou, 310027)

(2 Production Engineering Institute of Zhejiang University, Hangzhou, 310027 )

Reference

1． 吴昭同，杨将新. 计算机辅助公差优化设计. 浙江大学出版社，1999.

2． ASME Dimensioning and Tolerancing Principles. ANSI Standard Y14.5.1M, ASME,1994

3． 刘玉生. 基于数学定义的平面尺寸和形位公差建模与表示技术的研究. 浙江大学博士学位论文. 2000.9.

4． 《国外标准化动态》编辑部. 形位公差注法使用指南. 科学技术文献出版社.

5． 徐钟济编著. 蒙特卡罗方法. 上海科学技术出版社

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1. Introduction
    The seamless integration of CAD and CAM is not easily accessible because there is not enough useful information such as tolerance in CAD systems. How to interpret the semantics of tolerance, i.e. the modeling and representation of tolerance is becoming more and more important for the integration of tolerance in CAD/CAM. The research on tolerance has been carried out for many years[1], but the emphasis is on tolerance synthesis, tolerance analysis and optimal design of tolerance, not on tolerance modeling. Tolerance is defined with expressive mathematical expression exactly and unambiguously in ANSI Y14.5.1.M[2], which eliminate the unambiguity of literal definition and interpret tolerance definitely. So the mathematical definition is very suitable for tolerance modeling and representation, whereas how to embody the semantics of tolerance and how to realize the application of mathematical definition in tolerance analysis should be researched deeply. Herein a mathematical model is needed which should express the semantics of tolerance with an appropriate way.
In this paper, taking the variations of DOF(Degree Of Freedom) as model variables, a mathematical model of symmetry is researched systematically based on mathematical definition of tolerance and its application in tolerance analysis is also discussed.

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comment：
公差的数学定义在不断添新，specification系列标准不统一，各国公差标准的不统一和还不完善是影响集成的关键因素。相对而言，美国公差标准成熟点。