Abstract: Considering the randomness of the parameters of planar compliant mechanisms with single-axis flexure hinges, the mean value and variance of displacement amplification, input stiffness, output stiffness and additional restrictions are obtained by Monte Carlo simulation, on the basis of which a mathematical model for the optimal design of the planar flexure-based compliant mechanisms based on probability are built, where the optimal compound performance is taken as the objective function, meeting reliability requirements of each minimum and maximum limits of the design parameters and additional restrictions as constraints. The approach of Lagrange’s multipliers is adopted during optimization. The distribution function method is used to display the reliability constraints in the optimal design model, and then the probability constraints are converted into convention constraints. Displacement amplification and stiffness are calculated according to the optimal design vectors achieved via the optimization design. It is shown that when the variances of parameters increase, the optimal design results are conservative.

Key words: random parameters, flexure hinge, compliant mechanism, Monte Carlo simulation