On the synthesis of functionally equivalent mechanical designs

Conventional mechanical design focuses on a single com-pletely specified nominal shape that is later toleranced to al-low for variations in form. The corresponding design pro-cesses usually involve arbitrary decisions affecting the geom-etry and do not support systematic generation of alternative shapes satisfying identical or altered functionalities. This places a serious handicap on the design cycle of a product, since most new designs are obtained by modifying existing products to comply with new functional specifications. Since the functionality of a part does not usually define all of its geometry, a more coherent approach would be to de-sign classes of equivalent mechanical parts that satisfy a given functionality. We show here that, by replacing the completely specified geometry of the traditional approaches with par-tial geometry and functional specification, we can generate classes of mechanical parts that are equivalent, in the sense that all members of the class satisfy the same functional spec-ifications. Ability to define, compute, and represent classes of func-tionally equivalent parts will allow one to generate, compare and modify functionally equivalent designs, perhaps having dissimilar geometries. We identify three such equivalence classes for artifacts with parts moving in contact, which pre-sume, at the very least, contact between parts, spatial contain-ment during their relative motion, and external loads applied on the moving parts. We show that these classes of function-ally equivalent parts are computable and may be represented unambiguously by maximal elements of each class