<p>Inevitable joint clearances occur within mechanical systems. The nonlinear contact dynamics within these clearances exert a notable impact on kinematic reliability. However, investigations into this phenomenon are sparse. As such, dynamic analysis is utilized in the present study to evaluate time-dependent reliability, accounting for the nonlinear behavior of joint clearances. Firstly, a dynamic model of a mechanism was built, in which the contact behavior in the joints was modeled using the Lankarani and Nikravesh force model and the modified Coulomb friction model. On this basis, two time-dependent reliability analysis methods were established. One method was based on the Monte Carlo simulation (MCS), which can provide “precise solutions”. For the other method, an effective time-dependent reliability evaluation method is proposed based on the extreme-value motion error model and Kriging approximation. In the method, by dividing the concerned time interval into multiple subintervals and removing less important subintervals, the nonlinearity of the extreme-value motion error is decreased. Subsequently, an active learning strategy was formulated to pinpoint the subinterval with the greatest influence on failure probability, circumventing the need to solve the intricate dynamic model across the entire time span. Additionally, experiments were conducted to explore the nonlinear behavior of clearances within joints. Numerical investigations of the propulsion mechanism of a flapping wing aircraft demonstrate that the proposed approach achieves superior accuracy and efficiency compared to existing methods.</p>