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.