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Tolerance Analysis With Polytopes in HV-Description

[+] Author Affiliations
Santiago Arroyave-Tobón, Denis Teissandier, Vincent Delos

University of Bordeaux, Talence, France

Paper No. DETC2016-59027, pp. V01AT02A001; 10 pages
doi:10.1115/DETC2016-59027
From:
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1A: 36th Computers and Information in Engineering Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5007-7
  • Copyright © 2016 by ASME

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 poly-topes are useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the V-description of polytopes in ℝn 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 © 2016 by ASME

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