Equivalence Classes for Shape Synthesis of Moving Mechanical Parts

Abstract

Moving parts in contact have been traditionally synthesized through specialized techniques that focus on completely specified nominal shapes. Given that the functionality does not completely constrain the geometry of any given part, the design process leads to arbitrarily specified portions of geometry, without providing support for systematic generation of alternative shapes satisfying identical or altered functionalities. Hence the design cycle of a product is forced to go into numerous and often redundant iterative stages that directly impact its effectiveness. We argue that the shape synthesis of mechanical parts is more efficient and less error prone if it is based on techniques that identify the functional surfaces of the part without imposing arbitrary restrictions on its geometry. We demonstrate that such techniques can be formally defined for parts moving in contact through equivalence classes of mechanical parts that satisfy a given functionality. We show here that by replacing the completely specified geometry of the traditional approaches with partial geometry and functional specification, we can formally define classes of mechanical parts that are equivalent, in the sense that all members of the class satisfy the same functional specifications. Moreover, these classes of functionally equivalent parts are computable, may be represented unambiguously by maximal elements in each class, and contain all other functional designs that perform the same function.