A class of forms from function: the case of parts moving in contact

We consider the general problem of designing mechanical parts moving in contact under the influence of externally applied loads. Geometrically, the problem may be characterized in terms of a conjugate triplet which is formed by the two shapes moving in contact and their relative motion. We show that every such triplet belongs to one or more classes of functionally equivalent designs that may be represented uniquely by maximal triplets, corresponding respectively to the two largest contact shapes that are guaranteed to contain all other possible solutions to the contact design problem. In practical terms, the proposed characterization of the contact problem enables the systematic exploration of the design space using fully defined representatives of the functionally equivalent class of parts. Furthermore, such exploration may be performed using standard tools from geometric modeling, and without assuming any particular parametrization that necessarily restrict both the design space and possible computational techniques for exploring feasible designs. Because it supports generation of an essentially unlimited space of design solutions for a given contact problem, the proposed approach is particularly effective at the conceptual design stage.