Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies

The authors report on efforts to develop a tolerance representation for assemblies compatible with tolerance analysis based on a closed form algorithm used in robotic applications. A methodology to represent standard Y14.5M-1982 tolerances using homogeneous matrix transforms is described. Transforms represent both the nominal relations between parts and the variations caused by geometric deviations allowed by the tolerances. The analysis calculates a statistical estimate of the location of the Nth part in an assembly starting from the first part or a fixture. Except for form tolerances, most types of tolerance specifications are compatible with the proposed representation. This approach is well suited for integration with CAD systems and feature-based design