Tolerance Analysis by Polytopes

To determine the relative position of any two surfaces in a system, one approach is to useoperations (Minkowski sum and intersection) on sets of constraints. These constraints aremade compliant with half-spaces of R^n where each set of half-spaces defines an operandpolyhedron. These operands are gen...

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Bibliographic Details
Published in:arXiv.org 2015-09
Main Authors: Homri, Lazhar, Teissandier, Denis, Ballu, Alex
Format: Article
Language:English
Subjects:
Half spaces
Polyhedra
Polytopes
Tolerances
Topology
Online Access:Get full text
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Summary:To determine the relative position of any two surfaces in a system, one approach is to useoperations (Minkowski sum and intersection) on sets of constraints. These constraints aremade compliant with half-spaces of R^n where each set of half-spaces defines an operandpolyhedron. These operands are generally unbounded due to the inclusion of degrees ofinvariance for surfaces and degrees of freedom for joints defining theoretically unlimiteddisplacements. To solve operations on operands, Minkowski sums in particular, "cap" halfspacesare added to each polyhedron to make it compliant with a polytope which is bydefinition a bounded polyhedron. The difficulty of this method lies in controlling the influenceof these additional half-spaces on the topology of polytopes calculated by sum or intersection.This is necessary to validate the geometric tolerances that ensure the compliance of amechanical system in terms of functional requirements.
ISSN:2331-8422
DOI:10.48550/arxiv.1509.08763