Assemblability based on maximum likelihood configuration of tolerances

An assembly is defined by a configuration of parts of known geometries subj ect to tolerances in the pose, dimensions, and mating relations among part features. Using a tolerance model based on matrix transforms and Gaussian m odels of geometric variations [1], the pose and dimensional tolerance model s are considered as a priori models of the assembly with nominal and variat ional components for both position and orientation. The mating relations ar e regarded as linear relational constraints, also with nominal and variatio nal components. With this formulation, estimation of the configuration of p arts may be posed as a maximum Likelihood problem and solved by a Kalman fi lter algorithm. The resulting maximum likelihood configuration of the assem bly may be used to evaluate the required deviation from nominal and the ass emblability as defined by the maximum likelihood clearance from constraints . In addition. application of the technique to intermediate subassemblies m ay be used to evaluate assemblability of specific steps and discriminate am ong alternative assembly sequence plans.