Geometric Reasoning About Mechanical Assembly

Abstract In which order can a product be assembled or disassembled? How many hands are required? How many degrees of freedom? What parts should be withdrawn to allow the removal of a specified subassembly? To answer such questions automatically, important theoretical issues in geometric reasoning must be addressed. This paper investigates the planning of assembly algorithms specifying (dis) assembly operations on the components of a product and the ordering of these operations. It also presents measures to evaluate the complexity of these algorithms and techniques to estimate the inherent complexity of a product. The central concept underlying these planning and complexity evaluation techniques is that of a “non-directional blocking graph”, a qualitative representation of the internal structure of an assembly product. This representation describes the combinatorial set of parts interactions in polynomial space. It is obtained by identifying physical criticalities where geometric interferences among parts change. It is generated from an input geometric description of the product. The main application considered in the paper is the creation of smart environments to help designers create products that are easier to manufacture and service. Other possible applications include planning for rapid prototyping and autonomous robots.

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