  The aim of this paper is to show through a simple assembly a method of
tolerancing analysis (coherent with GPS) developed at LM\'ecA and based on the
model of clearance and deviation domains. Tolerancing is an important step in
the product design because on it will depend the functionality of the mechanism
its assemblibility but also its cost: manufacturing cost increases with the
precision of tolerances values. In our model, each feature specification is
translated into tolerance zone. This zone limits displacements of the
toleranced feature. Limitations of this small displacements are expressed in a
mathematical form by a 6-polytope in a 6 dimensions space (3 rotations and 3
translations). In the same way, contact conditions in joints allow to write
linear inequalities which can be translated by 6-polytopes. Each domain is
defined by a set of vertices and a system of inequalities. Considering a chosen
tolerancing, the method allows to verify the mechanism assemblibility but also
several functional requirements. The example of a minimal clearance requirement
between two surfaces will be treated. We will show the residual clearance zone
associated to these surfaces considering tolerances on parts and clearances in
joints. With such a tool, the designer will be able to modify values of the
tolerances and thus to reduce the manufacturing cost while guaranteeing the
functionality of the mechanism.
