A graph-based geometric problem-solving system for mechanical design and manufacturing

Most mechanical design and manufacturing problems involve manipulation and reasoning about geometry. Though diverse, there is an underlying similarity in these problems. The research presented here attempts to establish a fundamental set of geometric problem types, which can be used as a basis to describe all geometric problems in design and manufacturing. The problem representation structure divides problems into three elements: entities, constraints (active, passive, solution selectors) and generic tasks. Active constraints directly control the part's shape by controlling the degrees-of-freedom of geometric entities. Passive constraints, on the other hand, provide limits and other conditions for which the part is valid, but do not reduce the part's degrees-of-freedom. Solution selectors provide a mechanism for choosing the required solution from the multiple solutions arising from the active constraints. Types of entities, constraints and tasks are categorized by level of abstraction: arithmetical, geometrical and topological. Using a new concept, the "Geometry Exemplar," geometric aspects of a design and manufacturing task can be mapped to the core problem. Geometry Exemplars represent application-specific geometric characteristics as constraint graph patterns. These patterns define the relationships that must exist between entities of the model, both implied and explicit, when a condition is true. The dissertation investigates both the core set of problem types and Geometry Exemplars.