Behavior Analysis of a Flexure Hinge Array

Compliant mechanisms have been well designed to reach an ultra-high accuracy in positioning systems. However, the displacement of compliant mechanisms is still a major problem that restricts practical applications. Hence, a new flexure hinge array (FHA) is proposed to improve its displacement in this article. This paper is aimed to design and optimize the FHA. The structure of FHA is constructed by series-parallel array. Analytical calculations of the FHA are derived so as to analyze the stiffness and deformation. The displacement of the FHA is optimized by moth-flame optimization algorithm. The results determined that optimal parameters are found at Lt1 of 20.58 mm, wt1 of 1.92 mm, and wt2 of 2.29 mm. Besides, the optimal displacement is about 27.02 mm. Through Kruskal–Wallis test, the results verified that the proposed MFO outperforms other optimization algorithms in terms of searching the largest displacement. Validations of the analytical models are verified through simulations and experiments. The theoretical results are close to the experimental results. Additionally, the displacement of the FHA is superior that of existing joints. The displacement in the z-direction is approximately 32 mm according to a displacement of 12 mm in the x-direction.