An Improved Envelope Method for Time-Dependent Mechanism Reliability

The time-dependent kinematic reliability of a mechanism is the probability that the motion error of the mechanism is less than a prespecified error tolerance for a given period of time. For the time-dependent kinematic reliability analysis, the envelope method outperforms the sampling (Monte Carlo simulation) method because of its higher efficiency. This study further enhances the envelope method with improved accuracy. The improvement is achieved by keeping all the expansion points in the approximation of the limit-state function, some of which are discarded by the original envelope method to avoid numerical singularity. A new equivalent component reliability method is developed in this study so that the dimensions of the motion errors at all the expansion points are reduced to a degree that does not cause any numerical singularity. With the use of all the expansion points, the improved envelope method produces higher accuracy without increasing computational effort in calling the limit-state function. Three examples of four-bar linkage mechanisms demonstrate the better performance of the improved envelope method. © 2024 by ASME.