A mathematical model of symmetry based on mathematical definition

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 clarfy: (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.