| 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. |
