Multi-degree-of-freedom (multi-DOF) nanopositioning stages (NPSs) have rapidly growing applications in the spatial micro-/nano-machining and manipulation. Compliant parallel mechanisms (CPMs) demonstrate advantages to achieve a large output stiffness and high payload. A four-DOF NPS based on six-branched-chain CPMs is proposed in this paper. First, a mechanism design approach is introduced. One primary vertical DOF is generated using three parallel-kinematic lever amplifiers. A three-revolute-revolute-revolute mechanism acts as the kinematic configuration to produce three secondary planar DOFs. Three types of single-axis and one type of double-axis notch flexure hinges (NFHs) are employed to realize the nanoscale displacement/movement guiding, transferring, and decoupling. Second, a stiffness modeling approach is derived. Combined with exact compliance matrices of 54 NFHs and 95 flexible beams, a four-DOF high-efficiency stiffness model of the six-branched-chain CPM is built. The calculation procedure of the whole input/output stiffnesses and coupling ratios takes 12.06 ms. Simulation and prototype test results validate the calculation accuracy. For example, the maximum calculation deviation of input stiffnesses is verified to be 4.52% and 8.18%, respectively. The two proposed approaches contribute to the statics parameter optimization of spatial multi-DOF NPSs.

中文翻译：

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基于六支链柔性并联机构的四自由度纳米定位平台的设计与刚度建模

多自由度 (multi-DOF) 纳米定位台 (NPS) 在空间微/纳米加工和操纵中的应用迅速增长。兼容并联机构 (CPM) 展示了实现大输出刚度和高有效载荷的优势。本文提出了一种基于六支链 CPM 的四自由度 NPS。首先，介绍了一种机制设计方法。使用三个平行运动杠杆放大器生成一个主要垂直自由度。三旋转-旋转-旋转机构作为运动配置产生三个次级平面自由度。采用三种单轴和一种双轴槽口挠性铰链（NFH）实现纳米级位移/运动引导、传递和解耦。其次，推导出刚度建模方法。结合54个NFH和95个柔性梁的精确柔度矩阵，建立了六支链CPM的四自由度高效刚度模型。整个输入/输出刚度和耦合比的计算过程需要12.06 ms。仿真和样机测试结果验证了计算的准确性。例如，经验证，输入刚度的最大计算偏差分别为 4.52% 和 8.18%。提出的两种方法有助于空间多自由度 NPS 的静力学参数优化。例如，经验证，输入刚度的最大计算偏差分别为 4.52% 和 8.18%。提出的两种方法有助于空间多自由度 NPS 的静力学参数优化。例如，经验证，输入刚度的最大计算偏差分别为 4.52% 和 8.18%。提出的两种方法有助于空间多自由度 NPS 的静力学参数优化。