柔性铰链转动刚度计算公式的推导

柔性铰链作为无摩擦的支点有着成千上万的应用，以力学的基本公式和微积分为基础，给出了一般柔性铰链转动刚度计算公式的推导过程。在此基础上，得出了常用的直圆柔性铰链的设计计算公式，计算公式是精确的推导结果，且在表达上较迄今沿用的Paros给出的柔性铰链精确设计计算公式来得简洁，有利于柔性铰链及其机构的计算和分析。当直圆柔性铰链的切割半径与最小厚度相当时，Paros给出的简化公式存在一定的误差，这里的计算公式尤其适用于该类直圆柔性铰链。

Deduction of Design Equation of Flexure Hinge

Flexure hinges are used as friction-free pivots in thousands of applications. Based on the basic equations of mechanics and calculus, this paper presents the deduction process of design equation for calculating the rotation compliance or spring rate of flexure hinge. In the same time, this paper also presents the rotation compliance equation of right circular flexure hinge which is the most popular used flexure hinge, the equation is exact and more concise in expression than the wildly used exact rotation compliance equation of Paros, so it is more convenient to use it in calculating and analyzing flexure hinges and flexure hinge mechanisms. While the minimum hinge thickness of right circular flexure hinge approaches cutting radius of right circular flexure hinge, the simplified rotation compliance equation in the paper of Paros is not suitable. The design equation in this paper is very useful.