A new non-probabilistic time-dependent reliability model for mechanisms with interval uncertainties

•The non-probabilistic interval process of the mechanism motion error.•Two most probable points (MPPs) of outcrossing are defined.•A non-probabilistic time-dependent reliability index is proposed.•Computational strategies of the proposed reliability index.•The time-dependent problems are transformed into time-independent problems. This paper proposes a new non-probabilistic time-dependent reliability model for evaluating the kinematic reliability of mechanisms when the input uncertainties are characterized by intervals. Based on the introduction of the non-probabilistic interval process of motion error, the most probable point of an outcrossing is defined to transform the complicated time-dependent problem into a concisely time-independent problem. A non-probabilistic time-dependent reliability index is proposed to evaluate the kinematic reliability of various mechanisms, and two computational strategies are designed to calculate the index. Then, the proposed reliability model is applied to a numerical example, a typical four-bar linkage mechanism and a car rack-and-pinion steering linkage mechanism, to demonstrate the significance of the proposed reliability model. The results show that the proposed model provides an effective tool for making reliability evaluation of time-dependent problems.