Geometric reasoning for mechanical engineering design

Integration of design and manufacturing activities that require a global understanding of a part need an internal representation of the geometric structure, a formalism for elucidating the topology and geometric structure by way of queries posed to the internal representation, and procedures that will allow encoding of reasoning with the internal representation. This dissertation investigates a computational framework for representing spatial relationships and reasoning about the topology and geometric structure of mechanical parts.;Detail part design can be understood in terms of a vocabulary of features and a vocabulary of spatial relationships that occur between features. A hypothesis in the research is that spatial relationships can be expressed in a language made up of structural primitives and mathematically defined geometric primitives. Based on this hypothesis, a language, composed of structural and geometric primitives at an intermediate level of abstraction, is developed for the domain of standard cavity-type features encountered in discrete part manufacturing. The primitives have been implemented for prismatic parts on a 3D hybrid solid modeling system.;The use of solid models for integrated design and manufacturing will be of limited value if it is not possible to interrogate the solid model of a part for geometric and non-geometric data. Using the internal representation of the vocabulary of spatial relationships between features, a computational methodology for processing queries on the topology and geometric structure of 3D solid models is developed. The queries may be posed by designers or by semi-automated applications like process planning. A set-theoretic algebraic system, composed of relations and operations of relational algebra, provides the necessary "machinery" for query processing. The use of the language for abstracting spatial relationships and the computational methodology for geometric query processing is illustrated by applications in the areas of fixture design and process planning.