中文摘要：

为更加全面地考察零件的对称性与其可装配性之间的关系，在国内外首先把图像对称群的概念引入机械零件结构对称性及其应用的研究，探讨机械零件的点对称群及其判定方法。总对称角是零件在装配时相应两个旋转对称角的总和，表征零件的对称性，影响零件装配的定向难度，分析零件点群与其总对称角的关系，发现零件点群的总对称角取决于其纯转动子群，且以特定的离散值呈现区间分布。总结面向可装配性的零件对称性设计取向，提出零件结构的点对称群的概念体系及其判定方法，通过分析零件点群的总对称角分布区间图，提出面向可装配性的零件点群结构优化方法。

英文摘要：

In order to study the symmetry of the assembling parts more systematically, the concept of the image symmetry groups is first introduced into the study of the structural symmetry and its application to mechanical parts. The point symmetry groups of mechanical parts and their determination methods are discussed. Every part has two kinds of rotation angles when it is assembled. The sum of these two angles is the total rotation angle which affects the directional difficulty of the part. It is found that the total rotation angle of the point group of a part depends on its pure rotation subgroup and appears to be interval distribution. The orientation of symmetry design for assembling parts is summarized. The conceptual system of the part point symmetry groups and the corresponding determination method are put forward. By analyzing the graphs of the total rotation angle distribution interval of the part point group, the optimization of the structure of the part point group is proposed to improve the assembly of parts.