| The work reported in this dissertation develops a geometric model for dimensioning and tolerancing for mechanical components. The proposed model can (a) be used to mathematically model all tolerance classes, (b) be represented in a computer intelligible form, and (c) support tolerance analysis in three dimensional space. The proposed geometric model has been organized into two parts: the mathematical model and the representational model.;The math model provides the semantic definition and representation of each individual geometric tolerance class. Geometric building blocks (GBB) were developed for defining basic geometric relationships. GBBs are characterized by their shapes and degrees of freedom. Geometric tolerance classes are then synthesized with the GBBs. A geometric tolerance is modeled by a tolerance zone which is a region that encompasses all allowable deviations from the nominal geometry of the tolerance entity. Each tolerance class is defined by position of the appropriate. The tolerance zone is positioned relative to its datum coordinate. Both tolerance zone and datum coordinate system are constructed by the GBBs. For the convenience of computer representation, GBBs are represented in a parametric space, and tolerance zones are represented in transformation matrix form.;The representational model integrates each individual tolerance into a graph based system, the feature, dimension, and tolerance (FDT) graph. A FDT graph represents dimension relationships. It provides the topology connections between tolerance zones and datum coordinates.;The model encapsulates the semantics of geometric tolerances. It is capable of representing all ANSI Y14.5M geometric tolerances. It can identify interactions between different types of tolerance class. Additional tolerance classes can also be compassed. The model can provide the foundation for tolerance allocation, analysis, and error detection such as over and under-dimensioning, conflicting tolerances and improper datum specifications. |
