Geometric tolerancing analysis consists of simulating the behavior of a mechanical system according to geometric defects in the constituent parts. The aim is to verify system compliance in terms of the functional requirements for its expected operation. When carrying out the simulation the geometric specifications of the constituent parts and specifications of parts potentially in contact must be taken into account. One approach using polytopes consists of characterizing the specifications of the parts, the specifications of the contacts and the functional requirements of the mechanical system using sets of geometric constraints. This article describes modeling different sets of constraints manipulated by polytopes. We introduce the operations that are applied (Minkowski sum and intersection) to determine the relative position of any two surfaces of a mechanical system. Finally, tolerancing analysis of a simple mechanical system is described.
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