Manufacturing error and assembly error should be taken into consideration during evaluation and analysis of accurate product performance in the design phase. Traditional tolerance analysis methods establish error propagation model based on dimension chains with tolerance values being regarded as error boundaries, and obtain the limit of target feature error through optimization methods or conducting statistical analysis with the tolerance domain being the boundary. As deviations of the tolerance feature (TF) on degrees of freedom (DOF) have coupling relations, accurate deviations on all DOF may not be obtained, even though these deviations constitute the basis for product performance analysis. Therefore, taking the widely used shaft-hole fit as an example, a pose decoupling model of the axis TF was proposed based on an area coordinate system. This model realized decoupling analysis of any pose of the axis TF within the tolerance domain. As proposed by the authors, by combining a tolerance analysis model based on tracking local coordinate systems, ultimate pose analysis of the closed-loop system, namely the target feature, as well as statistical analysis could be further implemented. This method contributed to analysis of true product performance with arbitrary error in the product design phase from the angle of tolerance, therefore, shortening the product research and development cycle. This method is demonstrated through applying it to a real-life example.

Tolerance analysis refers to the process of establishing mapping relations between tolerance features and the target feature along the dimension chain. Traditional models for tolerance analysis are all based on rigid body kinematics, and they adopt the Homogeneous Transformation Matrix to describe feature variation and accumulation. However, those models can hardly reveal the nature of feature variations. This paper proposes a new tolerance analysis method based on the screw and the Lie Algebra of Lie Group, which describes feature variation as the screw motion, and completely maps the twist, an element of the Lie Algebra, to the Lie Group that represents the feature configuration space. Thus, the analysis can be conducted in a more succinct and direct way. In the end, the method is applied in an example and proven to be robust and effective.