Mathematical model for linear symmetry based on tolerancing principle

Tolerance is defined by graphic example and text description in the national standard and is not adaptable for expressing, processing and transferring in computers. It is essential for the integration of CAD and CAM and how to interpret its semantics is becoming a focus. Research on tolerance of mathematical model has been the topic of active research in recent years. But the models seldom consider the tolerancing principle. Thus an improved mathematical model based on independence principle (IP) and maximum material requirement (MMR) was proposed for linear symmetry tolerance. Small displacement torsor (SDT) was introduced in tolerance modeling. The constraint conditions of linear symmetry tolerance were developed systematically under IP and MMR. The corresponding mathematical models of linear symmetry of surface feature and central feature were deduced. The models can interpret the semantics of symmetry tolerance exactly and completely and can be used with the following processing. It´s very important applications for seamless integration of CAD and CAM