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Operations on polytopes: application to tolerance analysis

Abstract : This article presents numerical methods in order to solve problems of tolerance analysis. A geometric specification, a contact specification and a functional requirement can be respectively characterized by a finite set of geometric constraints, a finite set of contact constraints and a finite set of functional constraints. Mathematically each constraint formalises a n-face (hyperplan of dimension n) of a n-polytope (1 ≤ n ≤ 6). Thus the relative position between two any surfaces of a mechanism can be calculated with two operations on polytopes : the Minkowski sum and the Intersection. The result is a new polytope: the calculated polytope. The inclusion of the calculated polytope inside the functional polytope indicates if the functional requirement is satisfied or not satisfied. Examples illustrate these numerical methods.
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Submitted on : Thursday, June 30, 2011 - 9:53:56 AM
Last modification on : Friday, December 3, 2021 - 2:10:02 PM
Long-term archiving on: : Saturday, October 1, 2011 - 2:21:39 AM


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  • HAL Id : hal-00604749, version 2
  • ARXIV : 1106.6148



Denis Teissandier, Vincent Delos, Yves Couétard. Operations on polytopes: application to tolerance analysis. 6th CIRP Seminar on CAT, Mar 1999, Enschede, Netherlands. pp.425-433. ⟨hal-00604749v2⟩



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