Geometric and Computational Aspects of Manufacturing Processes

Two of the fundamental questions that arise in the manufacturing industry concerning every type of manufacturing process are: 1) Given an object, can it be built using a particular process? 2) Given that an object can be built using a particular process, what is the best way to construct the object? The latter question gives rise to many different problems depending on how best is qualified. We address these problems for two complimentary categories of manufacturing processes: rapid prototyping systems and casting processes. The method we use to address these problems is to first define a geometric model of the process in question and then answer the questions on that model. In the category of rapid prototyping systems, we concentrate on stereolithography, which is emerging as one of the most popular rapid prototyping systems. We model stereolithography geometrically and then study the class of objects that admit a construction in this model. For the objects that admit a construction, we find the orientations that allow a construction of the object. In the category of casting processes, we concentrate on gravity casting and injection molding. We first model the process and its components geometrically. We then characterize and recognize the objects that can be formed using a re-usable two-part cast. Given that a cast of an object can be formed, we determine a suitable location for the pin gate, the point from which liquid is poured or injected into a mold. Finally, we compute an orientation of a mold that ensures a complete fill and minimizes the number of venting holes for molds used in gravity casting processes.