柔性铰链是高精度柔性机构的关键部件, 其运动精度与运动范围影响着柔性机构的性能, 本文对圆弧柔性铰链进行了柔度矩阵推导, 并依据柔度方程进行优化设计。采用结构矩阵法建立了圆弧柔性铰链的柔度方程, 对矩形截面的翘曲抗扭刚度进行推导, 得到了约束扭转状态下的扭转柔度近似方程。为相对长度较小铰链的扭转刚度精确求解提供了依据。对比理论计算结果与有限元分析结果, 结果显示扭转柔度的最大相对误差在10%左右, 其余方向柔度相对误差低于6%, 验证了柔度方程的准确性。采用正交试验直观分析法得到柔性铰链各设计参数对转动刚度的灵敏度, 并利用多目标遗传算法对柔性铰链的转动柔度以及轴向刚度两个目标进行了参数优化。通过优化结果与设计经验选取参数的对比, 发现优化后圆弧柔性铰链的弯曲柔度提升了5.12%, 同时铰链的轴向刚度提升了4.72%, 证明针对圆弧柔性铰链的优化设计具有明显效果。

Flexure hinges are the key components of high-precision flexible mechanisms. Their motion precision and range affect the performance of flexible mechanisms. Herein, the flexibility matrix of a circular flexure hinge was derived for optimal design. The flexibility equation of the circular flexure hinge was established using the structure matrix method. The warping and torsional stiffness of the rectangular section was deduced. The approximate equation of torsional flexibility under constrained torsional state was obtained, providing a basis for the exact solution of torsional stiffness of the hinge with small relative length. Compared with the finite element method, the maximum relative error of torsional flexibility is approximately 10%, and the relative error of the remaining flexibility is less than 6%, which verifies the accuracy of the flexibility equation. The sensitivity of the design parameters of the flexure hinge to rotational stiffness was obtained by the orthogonal experimental design. The rotation ability and axial stiffness of the flexure hinge were optimized by the multi-objective genetic algorithm. By comparing the optimization results with the parameters selected according to the design experience, it is found that the bending flexibility of the optimized circular flexure hinge increased by 5.12% and the axial stiffness of the hinge increased by 4.72%. It is proved that the optimal design of the circular flexure hinge has obvious effects.