基于椭圆弧柔性铰链兼顾了直梁型柔性铰链运动范围大和圆弧型柔性铰链运动精度高的特点，设计了基于椭圆弧柔性铰链的二维快速控制反射镜系统两轴柔性支撑平台。为使柔性支撑平台快速响应性好，即使其低阶固有频率最大化，对该柔性支撑平台进行了结构优化设计。理论推导了单个柔性铰链最大刚度与许用应力、转角和铰链参数的理论计算公式。然后，采用集**数的分析方法，得出了两轴柔性支撑平台低阶最大固有频率的理论计算公式。由公式可知：在转动惯量一定的情况下，低阶固有频率最大化即为工作方向刚度最大化。最后，通过有限元仿真和实验检测验证了理论计算的准确性， 得到的结果显示：柔性支撑平台的最大固有频率和最大应力的理论值与仿真值的相对误差小于5%，平台工作刚度的理论值与仿真值、实测值的相对误差分别为3.86%和5.75%。仿真和实验结果表明：利用本文推导的理论公式进行柔性支撑平台刚度优化设计，既可以满足工程设计要求，又能省去繁杂的有限元计算。

Elliptic flexure hinges have both advantages of larger moving ranges and higher moving accuracy from right-angle flexure hinges and circular flexure hinges. Therefore, this paper designs a two axis flexible supporting platform with an elliptic flexure hinge used in a fast steering mirror system. For a fast response required by the system, the flexible supporting platform needs to maximize its natural frequency within the material's allowable stress. Firstly, the theoretical formulas of the maximum stiffness including the parameters of the allowable stress and rotating angle are deduced. The lumped parameter analysis method is adopted to obtain the relationship between the stiffness of flexible supporting platform and the stiffness of single flexure hinge. Then, the closed-form solution about the low order natural frequency of the two axis flexible support platform is deduced. A finite element model are created to perform experiments to assess those equations . The results compared by finite element analysis and theoretic calculation show that the relative error of the platform's natural frequency and maximum stress is within 5%. The relative errors of platform's stiffness got by the experiment, simulation and the theoretic calculation are 3.86% and 5.75%, respectively. These results indicate that the theoretical formula proposed in this paper is benefit for engineering structural design，it not only meets the requirements of engineering design, but also saves a lot of time .The most important thing is that it can help to achieve the optimal stiffness in theory.