Abstract: Tolerance is essential for integration of CAD and CAM and how to interpret its semantics is becoming a focus. Mathematical representation of planar surface is given based on variation of DOF at first. Second, the planar surface is classified according to the number of DOFs which are decided implicitly. Different dimension constraint modes are detailed. Third, a generic mathematical model of size tolerance is deduced based on mathematical definition systematically which can interpret the semantics of size tolerance exactly and completely. Last, an example is given to illustrate the application of the model in tolerance analysis.

Key words: DOF, Mathematical definition, Mathematical model, Plane, Size tolerance