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research-article

Tolerance analysis with polytopes in HV-description

[+] Author and Article Information
Santiago Arroyave-Tobon

Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France
santiago.arroyave-tobon@u-bordeaux.fr

Denis Teissandier

Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France
denis.teissandier@u-bordeaux.fr

Vincent Delos

CNRS, I2M, UMR 5295, F-33400 Talence, France
vincent.delos@u-bordeaux.fr

1Corresponding author.

ASME doi:10.1115/1.4036558 History: Received October 04, 2016; Revised April 13, 2017

Abstract

This article proposes the use of polytopes in HV-description to solve tolerance analysis problems. Polytopes are defined by a finite set of half-spaces representing geometric, contact or functional specifications. However, the list of the vertices of the polytopes are useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the V-description of polytopes in R^n from its H-description. It is detailed how intersections of polytopes can be calculated by means of the truncation algorithm. Minkowski sums as well can be computed using this algorithm making use of the duality property of polytopes. Therefore, a Minkowski sum can be calculated intersecting some half-spaces in the dual space. Finally, the approach based on HV-polytopes is illustrated by the tolerance analysis of a real industrial case using the open source software PolitoCAT and politopix.

Copyright (c) 2017 by ASME
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