Representation and interpretation of geometric tolerances in a CAD system

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Uptal Roy


Tolerances, CAD, Polyhedral assemblies

Subject Categories

Computer Sciences | Mechanical Engineering


Development of a complete geometric tolerance representation scheme for assemblies is one of the important research topics in today's computer aided design area. It includes a part variation model, in which variations of part surfaces correspond to tolerance specifications, and a part position model, in which parts of an assembly are located one another by some geometric relations.

The main objective of this dissertation is to develop a tolerance model for polyhedral objects by introducing a surface-based variational model. Variations are applied to a part model by varying model variables of each part surface. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specification. To describe form tolerance, two different approximated simulations of the variant boundary surfaces are presented. A prototype software, written in LISP programming language, has been developed to implement the proposed concept in an object-oriented programming environment.

The relationships between parts with geometric variations have also been investigated in this research in order to position a part in an assembly. The positioning scheme for parts with nominal shape and size in assembly has been studied extensively. However, the real positions of variant parts and variant assembly configuration need to be studied for solving tolerancing problems. In both 2D and 3D polyhedral assemblies, the translational and rotational motion constraints are generated by analyzing geometric contact relations between variant parts. Assembly configuration uncertainties caused by part variations are fully investigated. The final mating configuration can be chosen by realizing a dimensional objective function. The proposed relative positioning scheme has been implemented in C++ programming language.


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