Equations for Load-Displacement Characterization in Three Degrees of Freedom for General LET Arrays

Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load-displacement for general serial-parallel formulations of LET arrays for three degrees of freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis and, to show variability of the LET array design space, several validation plots over a range of parameters are provided. The equations are reproduced here as MATLAB scripts.

适用于折纸类应用的层状突出扭转（Lamina Emergent Torsion, LET）关节，可实现面板的折叠功能。将LET关节以串联与并联的方式组合（即构建LET阵列），能够拓展设计空间，使其在保持折叠能力的同时，还可在其他方向上实现可调的刚度特性。本文给出了适用于三自由度LET阵列通用串并联构型的弹性载荷-位移特性解析方程，涵盖绕指定轴旋转、面内旋转以及拉伸/压缩三种运动模式。借助这些解析方程，可针对包括折纸机构在内的多种应用场景开展LET阵列的设计工作。本文采用有限元分析对上述通用解析方程进行了验证；同时为展示LET阵列设计空间的多样性，还提供了多组参数下的验证绘图结果。本文附带的MATLAB脚本中复现了这些解析方程。