Time-space-dependent kinematic reliability of planar mechanism considering joint clearance

In practical engineering, failure modes exhibiting spatiotemporal variability are inherent to the complexities of mechanical systems. However, contemporary analyses of kinematic reliability often overlook the simultaneous impact of spatial parameters, such as input angles, and temporal parameters, such as motion cycles, on the performance of mechanisms. Specifically, motion cycles influence the mechanism's output at various cycles due to joint wear, while input angles affect the output at different positions within each cycle. To address these challenges, this study employs the space-time-dependent outcrossing rate (STOR) method for conducting a space-time-dependent kinematic reliability analysis of motion mechanisms. Initially, a decoupling approach is proposed to isolate motion errors attributable to input angle and wear factors. Subsequently, the STOR method is enhanced to estimate the maximum failure probability, significantly reducing computational demands. Building on this, the Armijo-based adaptive stability transformation method (AASTM) is refined to augment the efficacy of the Hasofer-Lind-Rackwitz-Fiessler (HL-RF) method in identifying the most probable point (MPP). Upon establishing the outcrossing rates, the upper bound of failure probability is efficiently computed through the application of the Gauss-Legendre (GL) quadrature. The precision and effectiveness of the proposed methodology are validated through comparative analysis with the Monte Carlo simulation (MCS) method.