Connecting the Branches of Multistable Non-Developable Origami Using Crease Stretching

Reconfigurable origami systems show great promise for expanding the functionality of adaptive structures. However, the myriad folding pathways makes it difficult to control the trajectory during reconfiguration. Multistable origami systems simplify the control problem, however they rely on flexible and stretchable facets to resolve geometric frustration. This excludes materials that cannot accommodate large strains, including electronics based on brittle semi-conductors. Traditional origami methods have been used to achieve multiple stable states without facet stretching, but rely on precise relative tuning of the crease stiffness. By relaxing the requirement that the system be folded from a flat sheet of paper, so called “Non-Euclidian Origami” has achieved multiple stable states with the use of a single torsional spring. Specifically, for a 4-facet origami system, it has been shown that these stable states lie on two disconnected branches. In this work, we take a 4-facet origami system and permit crease stretching in addition to bending to enable the continuous folding between these otherwise disconnected branches. The crease stretching, or Spring Origami, is inspired by the wing deployment mechanism in the Earwig. Using spherical geometry, we develop a mapping between the kinematic space and the energetic space of the 4-facet origami system. We show that a single 4-facet origami unit can exhibit up to 3 stable states, with 2 distinct folding pathways between each state. This analysis provides a simple analytic method to predict which equilibrium angles which result in mono-, bi-, tri-stable behavior. Ultimately, we lay the groundwork for controlling the folding pathways and stable shapes of stiff reconfigurable origami systems without additional control complexity.