Full Text:   <1791>

CLC number: TP391.72

On-line Access: 

Received: 2001-01-28

Revision Accepted: 2001-06-29

Crosschecked: 0000-00-00

Cited: 0

Clicked: 4204

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

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


Share this article to: More

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.

@article{title="A mathematical model of symmetry based on mathematical definition",
author="LIU Yusheng, YANG Jiangxin, WU Zhaotong, Gao Shuming",
journal="Journal of Zhejiang University Science A",
volume="3",
number="1",
pages="24-29",
year="2002",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0024"
}

%0 Journal Article
%T A mathematical model of symmetry based on mathematical definition
%A LIU Yusheng
%A YANG Jiangxin
%A WU Zhaotong
%A Gao Shuming
%J Journal of Zhejiang University SCIENCE A
%V 3
%N 1
%P 24-29
%@ 1869-1951
%D 2002
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2002.0024

TY - JOUR
T1 - A mathematical model of symmetry based on mathematical definition
A1 - LIU Yusheng
A1 - YANG Jiangxin
A1 - WU Zhaotong
A1 - Gao Shuming
J0 - Journal of Zhejiang University Science A
VL - 3
IS - 1
SP - 24
EP - 29
%@ 1869-1951
Y1 - 2002
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2002.0024


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

[1] ASME, 1994. Dimensioning and Tolerancing Principles. ANSI Standard Y14.5.1M, ASME.

[2] Bjorke,O., 1989. Computer Aided Tolerancing. 2nd edition. New York.

[3] Lee,Y.C., 1998. Process Capability-Based Tolerance Design to Minimise Manufacturing Loss. International Journal of Advanced Manufacturing Technology,14(1):33-37.

[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

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE