The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

PhD Thesis #8707

Title:Analysis of Uncertainties and Geometric Tolerences in Assemblies of Parts.
Date: 1987
Abstract:Computer models of the geometry of the real world have a tendency to assume that the shapes and positions of objects can be described exactly. However, real surfaces are subject to irregularities such as bumps and undulations and so do not have perfect, mathematically definable forms. Engineers recognise this fact and so assign tolerance specifications to their designs. This thesis develops a representation of geometric tolerance and uncertainty in assemblies of rigid parts. Geometric tolerances are defined by tolerance zones which are regions in which the real surface must lie. Parts in an assembly can also slop about and so their positions are uncertain. Tolerance parts and assemblies of toleranced parts are represented by networks of tolerance zones and datums. Each arc in the network represents a relationship implied by the tolerance specification or by a contact between the parts. It is shown how all geometric constraints can be converted to an algebraic form. Useful results can be obtained from the network of tolerance zones and datums. For example it is possible to determine whether the parts of an assembly can be guaranteed to fit together. it is also possible to determine the maximum slop that could occur in the assembly assuming that the parts satisfy the tolerance specification. Two applications of this work are (1) tolerance checking during design and (2) analysis of uncertainty build-up in a robot assembly plan. in the former, a designer could check a proposed tolerance specification to make sure that certain design requirements are satisfied. In the latter, knowledge of manufacturing tolerances of parts being manipulated can be used to determine the constraints on the position of the parts when they are in contact with other parts.

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