Toward a Theory of Geometric Tolerancing

TLDR

Manual drafting is being replaced by geometric modeling systems that are increasingly used in robotics and other industrial applications, yet these systems lack built‑in tolerancing capabilities essential for design and assembly planning. This paper proposes a mathematical theory of tolerancing that formalizes and generalizes existing practices to provide a foundation for integrating tolerances into geometric modeling systems. In the theory, a tolerance specification consists of geometric constraints on surface features, and an object is in tolerance when its features lie within tolerance zones formed by offsetting the nominal boundaries.

Abstract

Manual drafting is rapidly being replaced by modern, computerized systems for defining the geometry of mechanical parts and assemblies, and a new generation of powerful systems, called geometric (solid) modeling systems (GMSs), is entering industrial use. Solid models are beginning to play an important role in off-line robot programming, model- driven vision, and other industrial robotic applications. A major deficiency of current GMSs is their lack of facilities for specifying tolerancing information, which is essential for design analysis, process planning, assembly planning for tightly toleranced components, and other applications of solid modeling. This paper proposes a mathe matical theory of tolerancing that formalizes and generalizes current practices and is a suitable basis for incorporating tolerances into GMSs. A tolerance specification in the proposed theory is a collection ofgeometric constraints on an object's surface features, which are two-dimensional subsets of the object's boundary. An object is in tolerance if its surface features lie within tolerance zones, which are regions of space constructed by offsetting (expanding or shrinking) the object's nominal boundaries.