Non-Euclidean origami

Connecting the branches of multistable non-Euclidean origami by crease stretching

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected solution branches each with the same angular deficiency but opposite handedness. We show that these regions can be connected via "crease stretching," wherein the creases exhibit extensibility in addition to torsional stiffness. We further reveal that crease stretching acts as an energy storage method capable of passive deployment and control. Specifically, we show that in a Miura-Ori system with a single stretchable crease, this is achieved via two unique, easy to realize, equilibrium folding pathways for a certain wide set of parameters. In particular, we demonstrate that this connection mostly preserves the stable states of the non-Euclidean system, while resulting in a third stable state enabled only by the interaction of crease torsion and stretching. Finally, we show that this simplified model can be used as an efficient and robust tool for inverse design of multistable origami based on closed-form predictions that yield the system parameters required to attain multiple, desired stable shapes. This facilitates the implementation of multistable origami for applications in architecture materials, robotics, and deployable structures.

Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean

We derive algebraic equations for the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to elegant equations for the general developable degree-4 case. We compare our equations to previous results in the literature and provide two examples of how the equations can be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode.

An additive algorithm for origami design

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

Wrinkling of liquid-crystal elastomer disks caused by light-driven dynamic contraction

The trigger time of light-driven wrinkling is very critical for accurate active control in photo-powered machines. In this paper, the wrinkling of liquid-crystal elastomer disks caused by light-driven dynamic contraction is theoretically studied, and the critical times for appearance and disappearance of the wrinkles are numerically calculated. The light-driven prebuckling stress can be significantly adjusted by changing the contraction coefficient, while controlled within a certain limit by tuning the light intensity and illumination time. There exists a critical contraction coefficient for triggering the wrinkling of the disk, and the second-order mode of wrinkling is the most unstable mode, which is most easily induced for the illumination radius ratio 0.69. The critical times for the appearance and disappearance of wrinkling can be significantly changed by the contraction coefficient, while regulated only within a certain range by the light intensity and the illumination radius ratio. These results have potential applications for accurate active control in the fields of soft robotics, active microlens, smart windows, and tunable surface patterns.