Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns

Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, metamaterials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.