This paper introduces a new planar flexible hinge of fractal configuration to be incorporated in out-of-plane-motion compliant stages that cover a wide stiffness range. The large-displacement fractal hinge consists of a series of scaled-down, concentric, circular-axis flexible segments that are connected in a folded manner by radial rigid links. In-plane and out-of-plane compliance matrices are derived for fractal hinges with variable planar geometry features. The flexible hinges are assembled in a radial architecture to form compliant stages that can be utilized for piston-type, out-of-plane sensing or actuation. The analytical model calculates the stage active, out-of-plane stiffness, as well as its parasitic, in-plane stiffness. The stage analytical stiffness is confirmed by the experimental testing of a prototype and by finite element simulation. Furthermore, analytical-model simulation is performed to evaluate the variations in the active and parasitic stiffnesses with key geometric parameters, which also enables optimization.

中文翻译：

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具有大运动折叠分形柔性铰链的平面外运动平台的刚度

本文介绍了一种新的分形构型平面柔性铰链，该铰链可用于覆盖广泛刚度范围的平面外运动顺应级。大位移分形铰链由一系列按比例缩小的同心圆轴柔性段组成，这些段通过径向刚性连杆以折叠方式连接。平面内和平面外柔量矩阵是为具有可变平面几何特征的分形铰链导出的。柔性铰链组装成径向结构，形成可用于活塞式、平面外传感或驱动的柔性级。分析模型计算平台活动的平面外刚度，以及它的寄生平面内刚度。舞台分析刚度通过原型的实验测试和有限元模拟得到确认。此外，执行分析模型模拟以评估具有关键几何参数的主动刚度和寄生刚度的变化，这也可以实现优化。