Operations on polytopes: application to tolerance analysis

Denis Teissandier (1) , Vincent Delos (1) , Yves Couétard (1)

1 LMP - Laboratoire de Mécanique Physique

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.

Mots clés: Three-dimensional Dimension; Chain; Geometric Specification; Contact Specification; Functional Requirement; Polytope; Tolerance

Domaines: Logiciel mathématique [cs.MS]; Génie mécanique [physics.class-ph]; Génie mécanique [physics.class-ph]

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⟩