The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For mis, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions-normal, Weibull and beta distributions-were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.