Review of variational models for tolerance analysis of an assembly

The tolerance analysis of assemblies, which is carried out during the design stage, is the basic tool to simulate the effects of the assigned tolerances on the required functionality, and then, to define the appropriate allocation of the tolerances. This tool has to be based on a mathematical model able to evaluate the effect that each single tolerance has on the whole assembly. There are some different models proposed in the literature to carry out the tolerance analysis of an assembly, 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. None of them has done an objective and complete comparison among them, analysing the advantages and the weakness and furnishing a criterion for their choice and application. The present paper briefly introduces one of the main models for tolerance analysis, the variational model. The variational model is a family of schemes developed by different authors; the two most developed schemes are that involving rotational and translational parameters and that involving only translational parameters. These two models are briefly described herein and then compared to show their analogies and differences.