Abstract: To realize the requirements of a certain optical instrument for flexural hinges， a new type of cross-spring flexural hinge was proposed， and the design method was studied by using the Castiglianos second theorem. First， the Castiglianos second theorem was used to derive the flexibility calculation formula of the cross-spring flexural hinges to determine the axial rigidity and rotational rigidity of the hinges. Then， a case design was carried out and the finite element analysis was used for simulation. Finally， an optical test platform was set up and the rotation stiffness of the example was measured. The results show that the analytical solution， the simulation solution and the experimental data are in good agreement， and the relative error is as 8.7%. Using the Castiglianos second theorem as a design tool， the designer may determine the dimensional parameters according to the rigidity and structural requirements of the cross-spring flexural hinges， and the design of the cross-spring flexural hinges provides a new approach method for other hinges. 

Key words: cross-spring flexural hinge, finite element analysis, the Castiglianos second theorem, rotational stiffness

摘要： 针对某光学仪器对光学元件柔性支撑的要求，提出了一种新型交叉簧片型柔性铰链，利用卡氏第二定理研究了设计方法。首先，利用卡氏第二定理推导交叉簧片型柔性铰链的柔度计算公式，确定铰链的轴向刚度与转动刚度，分析了直梁长度、直梁高度和空心圆柱壁厚对其刚度的影响；然后，进行了实例设计，并利用有限元软件进行了分析；最后，搭建光学测试平台，对实例进行了转动角度和转动刚度的测量。结果表明：解析解、仿真解和实验测量数据一致性较好，最大相对误差为8.7%。使用卡氏第二定理作为设计工具，设计者可根据交叉簧片柔性铰链的刚度与结构应力等要求确定几何参数，而且交叉簧片柔性铰链的设计为其他铰链的结构形式提供了新的思路。

关键词: 交叉簧片柔性铰链, 有限元分析, 卡氏第二定理, 转动刚度