huangyhg

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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