In order to quantify the effect of mixed uncertainties on the reliability of mechanisms, this paper proposes a method for analyzing the reliability of mechanisms with mixed uncertainties using polynomial chaos expansion. Based on the performance margin theory, a mechanism reliability model considering mixed uncertainties is developed, and the Sobol indices can be easily calculated by an arbitrarily polynomial chaos expansion (aPCE) of the reliability function to quantify the independent contribution of each parameter to the global sensitivity and the effect of parameter coupling. Additionally, this paper also introduces a mixed uncertainties propagation method based on PCE, which treats cognitive uncertainties as fuzzy variables, converts the fuzzy variable into an interval variable using cut set theory, and transforms the PCE containing interval uncertainties into a Bernstein polynomial to calculate the membership function of the output quantity and the non-probabilistic reliability index by area method. The final case study of a simplified automaton motion mechanism illustrates that the proposed method is effective and convincing, and the mechanism reliability decreases with increasing mixed uncertainties. The mechanism reliability index considering mixed uncertainties will give a more conservative reliability estimation.