As far as the demand in quality and cost of manufacturing increase, the optimal qualification and quantification of acceptable defects is essential. Tolerancing is the means of communication between all actors of manufacturing. An optimal tolerancing is the right compromise between manufacturing cost and quality of the final product. Tolerancing is based on three major issues: The specification (standardization of a complete and unequivocal language), synthesis and analysis of the tolerancing. We suggest in this thesis some new analysis and synthesis of the three-dimensional tolerancing. These methods are based on a geometric model define by the deviations and clearances domains developed on the laboratory. The first step consists in determining the elementary topology that composes a three-dimensional mechanism. For each kind of these topologies one resolution method is defined. In worst case, the condition of functional requirement respect is traduced by existence and inclusions conditions on the domains. Then these domains equations can be translated in inequalities system of scalar. The statistical analysis uses the Monte-Carlo simulation. The random variables are the small displacements components of the deviation torsor which is defined inside its tolerance area (model by a deviations domain) and the geometrics dimensions which set the extent of clearance (size of the clearance domain). Thanks to statistical simulation, it is possible to estimate the non-quality rate in regards to the defined tolerancing. The development of a new representation of clearances and deviations domains most suitable, allows us to simplify the calculation for tolerancing problems. The local treatment of elementary topology makes enables the global treatment of complex three-dimensional mechanisms with take into account of clearances.
