Abstract: To avoid vibrations and abrasions caused by the rotation of a planar spring in the deformation processes, a new planar spring was proposed based on LEMs. The planar spring with advantages including a small volume, easy to fabricate, a simple structure and no revolution during the deformation, etc. might be fabricated from planar materials and might emerge out of the fabricated planar materials. Firstly, the stiffness of the planar spring was deduced based on the flexural cantilever model and the pseudo-rigid-body model respectively. In order to verify the correctness of the theoretical stiffness formulations, the ANSYS model for this planar spring was established and the FEA was compared with theoretical results calculated by the flexural cantilever model and the pseudo-rigid-body model, respectively. The results indicate that the formula derived from model of cantilever leads to the calculation with higher accuracy when the deformation is small. In contrary, the formula derived from pseudo-rigid-body model applying to large deformation is better. Finally, the applicable ranges for the two above mentioned models were analyzed separately and a numerical example was given to demonstrate their correctness.

Key words: lamina emergent mechanisms(LEMs), planar spring, pseudo-rigid-body model, finite element analysis(FEA)

摘要： 针对常规平面弹簧变形过程中运动端容易产生周向旋转从而造成振动和磨损的问题，设计了一种基于LEMs的平面弹簧，该弹簧由平面薄板加工成形且能实现平面外运动，具有体积小、易加工，结构简单及变形过程中运动端不发生周向旋转等优点。首先，基于悬臂梁模型和伪刚体模型分别推导了LEMs平面弹簧的刚度计算公式。其次，为验证所推导公式的正确性，建立了LEMs平面弹簧的ANSYS仿真模型，并将有限元分析结果与上述两种理论模型的计算结果进行了对比。结果表明，在变形较小的情况下由悬臂梁模型所推导的公式计算精度更高，在变形较大的情况下使用由伪刚体模型所推导的公式更为合适。最后，通过大量实例分析推导了两个公式的适用范围，并用一组数值算例证明了其正确性。

关键词: 平面折展机构, 平面弹簧, 伪刚体模型, 有限元分析