A Geometrical Product Specification Language Based on a Classification of Symmetry Groups

A relatively old and deeply entrenched engineering "language" universally used by draughtsmen for specifying product geometry is undergoing renovation for the modern information age. Part of the renovation process is to find a set of firm mathematical principles that can support much of the edifice that has served industry well thus far. This search has turned up a set of surprisingly powerful results based on an elegant classification of continuous subgroups of rigid motion. Among them is a compact classification of surface features and lower order kinematic pairs, their reduction to simpler geometric elements that preserve the classification and serve as datums, and a rationale for parameterizing the relative positioning of geometric objects. These results are now being enthusiastically embraced by the International Organization for Standardization (ISO) as part of the basic principles to define the next generation of a product geometry specification language. The paper tells this story.