  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 {\leq} n {\leq} 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.
