Assemblability based on maximum likelihood configuration of tolerances

An assembly is defined by a configuration of parts of known geometries subject to tolerances in the pose, dimensions, and mating relations among part features. Using a tolerance model based on matrix transforms and Gaussian models of geometric variations, the pose and dimensional tolerance models are considered as a priori models of the assembly with nominal and variational components for both position and orientation. The mating relations are regarded as linear relational constraints, also with nominal and variational components. With this formulation, estimation of the configuration of parts may be posed as a maximum likelihood problem and solved by a Kalman filter algorithm. The resulting maximum likelihood configuration of the assembly may be used to evaluate the required deviation from nominal and the assemblability as defined by the maximum likelihood clearance from constraints. In addition, application of the technique to intermediate subassemblies may be used to evaluate assemblability of specific steps and discriminate among alternative assembly sequence plans.