A review of two models for tolerance analysis of an assembly: Jacobian and torsor

The dimensional and geometrical variations of each part of an assembly have to be limited by tolerances able to ensure both a standardized production and a certain level of quality, which is defined by satisfying functional requirements. The appropriate allocation of tolerances among the different parts of an assembly is the fundamental tool to ensure assemblies that work rightly at lower costs. Therefore, there is a strong need to develop a tolerance analysis to satisfy the requirements of the assembly by the tolerances imposed on the single parts. This tool has to be based on a mathematical model able to evaluate the cumulative effect of the single tolerances. Actually there are some different models used or proposed by the literature to make the tolerance analysis of an assembly constituted by rigid parts, but none of them is completely and univocally accepted. Some authors focus their attention on the solution of single problems found in these models or in their practical application in computer-aided tolerancing systems. But none of them has done an objective and complete comparison among them, analyzing the advantages and the weakness and furnishing a criterion for their choice and application. This paper briefly introduces two of the main models for tolerance analysis, the jacobian and the torsor. These models are briefly described and then compared showing their analogies and differences. The evolution of these two models, known as unified jacobian-torsor model, is presented too.