Abstract This paper presents the closed-form compliance equations of elliptic-revolute notch type multiple-axis flexure hinges undergoing small displacement for three-dimensional applications. Analytical compliance equations in six degrees of freedom are explicitly derived based on the beam theory. Comparisons with existing compliance equations of revolute flexure hinges are carried out. The presented compliance equations for the elliptic-revolute flexure hinges can result in the compliance equations for the cylindrical- and circular-revolute flexure hinges. Finite element analyses are performed to verify the developed equations. Numerical simulation is conducted to test the compliance characteristics of the elliptic-revolute flexure hinges. The simplified coefficients between the compliances of the elliptic- and circular-revolute flexure hinges are established. The presented compliance equations are helpful for designing spatial compliant mechanisms based on the elliptic-revolute flexure hinges.

中文翻译：

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椭圆-旋转凹口型多轴挠性铰链的闭式柔量方程

摘要 本文提出了椭圆-旋转凹口型多轴挠性铰链在三维应用中的小位移闭式柔量方程。六自由度的解析柔度方程是基于梁理论明确推导出来的。与现有的旋转挠性铰链柔度方程进行了比较。椭圆-旋转挠性铰链的柔度方程可以得到圆柱和圆形-旋转挠性铰链的柔度方程。进行有限元分析以验证开发的方程。通过数值模拟测试了椭圆-旋转挠性铰链的柔顺特性。建立了椭圆和圆形旋转挠性铰链的柔量之间的简化系数。提出的柔量方程有助于设计基于椭圆-旋转挠性铰链的空间柔顺机构。