Jiang Yao, Li Tie-Min, Wang Li-Ping
Manufacturing Engineering Institute, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, People's Republic of China.
Rev Sci Instrum. 2015 Sep;86(9):095109. doi: 10.1063/1.4930884.
This paper investigates the stiffness modeling of compliant parallel mechanism (CPM) based on the matrix method. First, the general compliance matrix of a serial flexure chain is derived. The stiffness modeling of CPMs is next discussed in detail, considering the relative positions of the applied load and the selected displacement output point. The derived stiffness models have simple and explicit forms, and the input, output, and coupling stiffness matrices of the CPM can easily be obtained. The proposed analytical model is applied to the stiffness modeling and performance analysis of an XY parallel compliant stage with input and output decoupling characteristics. Then, the key geometrical parameters of the stage are optimized to obtain the minimum input decoupling degree. Finally, a prototype of the compliant stage is developed and its input axial stiffness, coupling characteristics, positioning resolution, and circular contouring performance are tested. The results demonstrate the excellent performance of the compliant stage and verify the effectiveness of the proposed theoretical model. The general stiffness models provided in this paper will be helpful for performance analysis, especially in determining coupling characteristics, and the structure optimization of the CPM.
本文基于矩阵法研究柔顺并联机构（CPM）的刚度建模。首先，推导了串联柔性链的通用柔顺矩阵。接下来，考虑外加载荷与所选位移输出点的相对位置，详细讨论了CPM的刚度建模。所推导的刚度模型形式简单且明确，CPM的输入、输出和耦合刚度矩阵能够轻松获得。将所提出的解析模型应用于具有输入输出解耦特性的XY并联柔顺平台的刚度建模和性能分析。然后，对平台的关键几何参数进行优化，以获得最小输入解耦度。最后，研制了柔顺平台样机，并测试了其输入轴向刚度、耦合特性、定位分辨率和圆轮廓跟踪性能。结果表明该柔顺平台性能优异，验证了所提理论模型的有效性。本文提供的通用刚度模型将有助于进行性能分析，特别是在确定耦合特性以及CPM的结构优化方面。
