基于李群的特征和变动几何约束理论基础研究

Study on the Theoretical Basis of Feature and Variational Geometric Variation Based on Lie Group Theory

建立了计算机辅助公差设计的数学基础。首先 ,基于特征几何变动的对称李子群 ,将对称特征划分为 7类 ;然后 ,基于对称特征 ,划分了自参考、互参考和配合变动几何约束 ;最后 ,给出了完全约束的互参考变动几何约束分解规则。

This paper establishes the mathematic basis of computer aided tolerancing. Firstly, based on the symmetrical Lie subgroups of geometric variation of feature, symmetrical features are classified into seven classes. Secondly, variational geometric constraints (VGCs) are classified into three categories: self referenced VGC, cross referenced VGC and mating VGC. Finally, well constrained decomposition rule of cross referenced VGC is presented. The theoretical basis in this paper can be used to synthetically design dimensional and geometric tolerance for 3D CAD system.