Modeling spaces for toleranced objects

Journal Article · Tue Oct 01 00:00:00 EDT 1991 · International Journal of Robotics Research; (United States)

DOI:https://doi.org/10.1177/027836499101000512· OSTI ID:5101599

Boyer, M; Stewart, N F ^[1]

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1. Univ. of Montreal, Quebec (Canada)

In this article the authors propose a modeling space for objects defined in terms of tolerances based on Requicha's suggestion of using variational classes. Variational classes are subsets of the hyperspace 2{sup En}, where E{sup n} is euclidean n-space. In order to motivate the ideas, the discussion involves the same simple example throughout: the specification of a ball bearing defined by position, size, and form constraints. They begin by discussing the relationship between Requicha's original proposal and their proposal for a definition of what should be viewed as a permissible variational class. They call such a permissible class, together with a nominal solid S, an R-class. They then introduce generalized versions of the regularized Boolean operations, which operate not on r-sets, but rather on R-classes. Just as the r-sets are closed under regularized Boolean operations, so the R-classes are closed under the generalized versions of the regularized Boolean operations. Finally, they discuss the relationship between the R-classes and the particular feature tolerancing methods proposed by Requicha.

• OSTI ID: 5101599
• Journal Information: International Journal of Robotics Research; (United States), Vol. 10:5; ISSN 0278-3649
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ROBOTS
COMPUTERIZED CONTROL SYSTEMS
BALL BEARINGS
CONTROL THEORY
EUCLIDEAN SPACE
MANIPULATORS
MATHEMATICAL MODELS
TOLERANCE
BEARINGS
CONTROL SYSTEMS
EQUIPMENT
LABORATORY EQUIPMENT
MATERIALS HANDLING EQUIPMENT
MATHEMATICAL SPACE
ON-LINE CONTROL SYSTEMS
ON-LINE SYSTEMS
REMOTE HANDLING EQUIPMENT
RIEMANN SPACE
SPACE
990200* - Mathematics & Computers