Abstract: Based on the Geometrical Product Specification (GPS) of new generation and verification standards,the relationship between the features of assembly parts and assembly positions was investigated.To express assembly-tolerances-relative features and their relations clearly and visually,Assembly Geometry Graph (AGG) by using Assembly Oriented Graph (AOG) was developed.Homogeneous Transformation Matrix (HTM) and 3-dimenstional vector were also used to express the mathematical model of assembly tolerance of main and auxiliary APJ between the joint parts.An example was given to illustrate the application of the proposed model.

Key words: homogeneous transformation matrix, statistic assembly tolerance, assembly positioning, assembly oriented graph, tolerance analysis

摘要： 基于新一代产品几何规范与认证体系,研究了基于齐次坐标变换的统计装配公差建模方法。将装配有向图改进为装配体几何关系图,图象化地表达与装配公差有关的关键特征及特征间的关系。用三维向量和齐次坐标转换矩阵来建立能够表达主要装配定位连接和辅助装配定位连接信息的装配公差传递模型。以实际零件为随机自变量,以该装配公差传递模型为映射函数,建立了统计装配公差分析模型。给出了该方法在公差分析中的应用实例。

关键词: 齐次坐标转换矩阵, 统计装配公差, 装配定位约束, 装配有向图, 公差分析