Probabilistic mechanism analysis with bounded random dimension variables

In the traditional probabilistic mechanism analysis, random dimension variables are typically assumed to be normally distributed. This treatment may not be practical because a normal random variable is unbounded, changing from negative infinity to positive infinity, but an actual dimension variable is bounded with its tolerance range. This work intends to remedy this problem. The approach is to treat dimension variables as truncated random variables within their tolerance bounds. Since the traditional methods are not accurate for truncated random variables, a new probabilistic mechanism analysis method is developed. Its major steps include the linearization of the motion error with respect to truncated random variables, followed by the application of the Saddlepoint Approximation. The proposed method can accurately estimate the probability distribution of the motion error. The proposed method is applied to probabilistic mechanism analyses of a slider-crank mechanism and a four-bar mechanism.