Assembly Model Representation for Variation Analysis

Assembly modeling is a very important activity for computerized analysis of product assembly, and it has been a subject of intense research over the past years. However, most of the assembly models focus on the assembly connective relationships between parts rather than assembly spatial relationships. Variation analysis is becoming a critical issue when specifying and verifying the geometric and dimensional requirements of assembly. In order to support dimensional variation analysis, a mathematical assembly model representation considering assembly spatial relationships is proposed in this paper. Four types of coordinate systems are defined. The nominal and variational spatial relationships among assembly elements are represented as homogeneous transformation matrix among different coordinate systems. The variations of assembly elements, mating interface and locating interface are represented as variation transformation matrix among corresponding coordinate systems. The variation of the final assembly is modeled as stack up of the differential motion vectors of coordinate systems of all the parts with respect to global coordinate system, and it can be calculated by homogeneous transformation and variation transformation. The different situations for two types of assemblies are distinguished in this novel assembly model representation.