Flexible origami is suitable for designing deployable mechanisms due to its ability to transform from a flat or compactly folded geometry to a more extended geometry. Non-Euclidean origami can help by splitting folding branches of origami vertices, leading to kinematically determinate behaviour. This paper presents two novel finite element modelling procedures for analysing flexible non-Euclidean origami, fabricated using 2D manufacturing techniques. The finite element modelling procedures presented in this work are a step towards the implementation of flexible non-Euclidean origami in functional applications, such as deployable mechanisms.

The use of origami-based mechanisms in the engineering field is growing as their advantages are better understood. Origami-based mechanisms have the advantage of being lightweight, compact, and their ability to transform from a flat sheet into complex three-dimensional structures makes them a source of inspiration to meet design challenges. A fold in paper is realized by a localized reduction in thickness, which reduces stiffness. Since most materials do not exhibit this property when folded, other techniques are used to facilitate this stiffness reduction. These include sandwiching a thinner material between rigid facets, or by thinning to create a groove joint (notch joint). The drawbacks of these techniques are that the first technique requires assembly, and the second technique requires complex material removal. Another technique has been proposed to reduce stiffness with simpler manufacturing methods, namely lamina emergent joints. These joints require cutting through the material, which can be done using well-established sheet manufacturing methods, such as laser cutting or stamping. However, the removal of material involves a trade-off between range of motion and stiffness in directions other than the desired bending motion. Initial research indicates that the groove joint is able to maintain the highest stiffness and range of motion, thus outperforming the lamina emergent joint. Therefore, the objective of this paper is to design an improved lamina emergent joint that approaches the performance of the groove joint. This is achieved by quantifying and evaluating the stiffness performance and range of motion of existing lamina emergent joints and then combining them on strong features. Improved designs are proposed that made an approach toward the groove joint and the best design was selected for optimization. The results showed that the selected design was not able to outperform the groove joint on both stiffness and range of motion. However, it was able to achieve similar in-plane shear stiffness and higher torsion stiffness than a groove joint with a lower thickness ratio. However, this also allowed more range of motion for the groove joint. So figuring out this trade-off between stiffness and range of motion is challenging and essential to design suitable joints in the future.