Manufacturing tolerances and joint clearances are the two major factors affecting mechanism accuracy. As error analysis is one of the bottlenecks of precision machinery design, methods for geometric tolerance analysis must be investigated for mechanism design. This paper describes an approach for analyzing errors caused by geometric tolerances and clearances in mechanism design. The method consists of three parts: variational kinematic models for geometric tolerances, a systematic geometric dimensioning and tolerancing (GD&T) representation scheme, and computation methods for interval and statistical tolerances. Variational models are based on differential transformation to model kinematic errors caused by tolerances and clearances. The model is consistent with error models used in typical mechanical devices. The GD&T scheme, called the Tolerance Network (TN), employs graph theory for representing GD&T as well as fitting specifications of a design is described. Errors are propagated by traversal throughout the network and stack-up of these variational models along the dominate path in the TN. Error computation methods for both interval and statistical tolerance types are discussed. A method for computing central moments, rather than analytical distributions, of statistical tolerances is developed to reduce the computation complexity. A five-degree-of-freedom robot is used as an example at each step to illustrate this approach.

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