A topological model of limitations in design for manufacturing

Design for manufacturing (DFM) is a methodology that requires the use of specific manufacturing information at all stages of design. The method relies on a collection of informal and often controversial principles that seem to have eluded the benefits of formal analysis. The transition from design to manufacturing can be modeled as a mathematical mapping, and it has been previously shown how the discontinuity of this mapping formally captures the folklore that small design changes can lead to significantly increased manufacturing cost. We study the properties of the transition map in the presence of design and manufacturing variations, and show that its continuity is closely related to the structure of design and manufacturing topological spaces. The main result of this paper establishes conditions on these spaces under which design for manufacturing cannot be described by any continuous transition map. In practical terms, our study reveals the limitations of many DFM systems and approaches in their ability to relate design and manufacturing knowledge, and explains these limitations in terms of a basic incompatibility between the underlying design and manufacturing representations. We discuss how our model applies to DFM relative to traditional manufacturing methods (such as casting and stamping) and we speculate what changes might occur for alternative manufacturing technologies (such as electrical discharge machining (EDM), stereolithography, laser machining, and particle deposition).