Analytical modeling and computational optimization for a 1-DOF compliant mechanism

The first natural frequency directly affects the operational conditions of compliant mechanisms in precision engineering systems. To address this challenge, a computational method based on the surface response method is proposed to optimize the frequency of a new one degree of freedom (DOF) compliant mechanism. Initially, a 1-DOF 3D model of a compliant mechanism is built. The dynamic equation and the frequency response are formulated via equivalent stiffness and the Lagrange method. Subsequently, a series of numerical simulations are conducted to find the fundamental frequency of the mechanism. The initial dimensions of the flexible joints are determined, and the initial frequency is analyzed by using finite element analysis. Next, the flexible joints in the designed mechanism are optimized by a variant of the genetic algorithm. The optimized dimensions of the mechanism are found with the thickness of the circular joint of 1.10 mm, the thickness of the leaf joint of 1.19 mm, and the length of the leaf joint of 54.50 mm. The optimized result showed that there is a significant improvement in the frequency of the mechanism, increasing from an initial design of 53.218 Hz to an optimal design of 75.927 Hz with an improvement of 42.6%. This study provides important reference materials for future research on compliant mechanisms.