Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Many existing tolerancing models deal with the tolerance analysis of mechanical assemblies using linear stack-up function, which will cause truncation errors for nonlinear assembly problem. This article proposes a new method for describing the variation propagation based on the product of exponentials formula. Both the length deviations and the angle deviations are uniformly represented by twist coordinates. Accordingly, the nonlinear stack-up functions relating the assembly functional requirements to the manufacturing variations can be derived, and no truncation errors generated. A three-dimensional assembly case is studied exploiting the proposed method and the direct linearization method, respectively. It appears that the product of exponentials formula can bring consistent tolerance analysis results with the exact geometric solutions, whereas there are some small errors in the analysis results of direct linearization method. The precision of tolerance estimation via the product of exponentials formula...