Tolerance is an almost ubiquitous concern during the whole product life cycle, and its management is imperative for seamless integration of CAD and CAM. In this paper, how to interpret tolerance semantics based on a mathematical definition of tolerance is presented. First, the tolerance zone is divided into three types according to four basic attributes: size, form, position, and orientation. The key to representing tolerance semantics exactly is to determine the position and orientation of the tolerance zone. Then, based on variations in degrees of freedom (DOF), the algebraic constraint equations for the tolerance zone boundary and variational features are deduced systematically, leading to an exact and complete interpretation of the tolerance semantics. Finally, an example is given to illustrate the rationality of the proposed method.
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