Time-dependent probabilistic synthesis for function generator mechanisms

In traditional probabilistic mechanism synthesis, point kinematic reliability is employed. Point kinematic reliability is the probability that the motion error is within a specified limit at a specific instant of time regardless if the mechanism failed before that instant. For function generator mechanisms, using the point kinematic reliability cannot satisfy the reliability requirement for the time interval where the desired function is defined. In this work a probabilistic mechanism synthesis method is proposed with the interval (or time-dependent) kinematic reliability, which is the probability of the motion error less than the specified limit over the time interval where the mechanism is supposed to perform its intended function. As a result, the new synthesis method can guarantee the satisfaction of the kinematic reliability requirement not only over the time interval but also at all the points within the interval. The interval reliability is calculated with the integration of the First Order Second Moment method and the first-passage Poisson approximation method. The method is demonstrated by the synthesis of a four-bar function generator mechanism.