基于闭环柔度解析式的双曲线形柔性铰链研究

提出了一种新型的单轴柔性铰链结构型式一单边双曲线形柔性铰链。以力学卡氏第二定理和微积分为理论基础，推导了单边双曲线形柔性铰链柔度的闭环解析公式，在此基础上，推导出单边双曲线形柔性铰链的转动精度公式，对单边双曲线形柔性铰链的性能进行分析，得出了结构参数对其柔度性能的影响关系。并通过对双边双曲线形柔性铰链比较，分析了单边双曲线形柔性铰链的转动能力、转动精度和对轴向载荷的影响等性能，利用有限元和实验的方法对单边柔性铰链的柔度公式进行校验，结果表明有限元与闭环解析式的偏差小于8％，实验结果和解析式的偏差在7％以内，为柔性铰链在结构紧凑、大位移场合的工程应用提供了有价值的参考。

Research on half hyperbolic flexure hinge based on closed-form compliance equations

A novel single axis flexure hinge named half hyperbolic flexure hinge is introduced.Based on the Castigliano's second theorem and calculus,closed-form equations are derived for compliance of half hyperbolic flexure hinge.The rotation accuracy of half hyperbolic flexure hinge is also evaluated in terms of compliances.A unitary compliance-based analysis is performed by means of two-dimensional geometric parameters.Compared with symmetric hyperbolic flexure hinge,the performance of the half hyperbolic flexure hinge can be evaluated in terms of flexibility,precision of rotation center and sensitivity to axial load effects.Finite element analysis and experimental method were used to verify the compliance equations.The deviation between the results from finite element analysis and the compliance equations is less than 8%;and the deviation between the results from experiments and the compliance equations is within 7%.So the half hyperbolic flexure hinge is suitable for engineering applications where large displacement and compact mechanism are needed.