# Helical Miura Origami

## TL;DR

This paper comprehensively characterizes the phase-space of Helical Miura Origami, revealing their rigidity, multistability, and potential for reconfigurability, with applications in actuators and metamaterials.

## Contribution

It introduces a detailed framework for understanding and designing Helical Miura Origami structures, including their compatibility conditions and reconfigurability strategies.

## Key findings

- Helical Miura Origami are generally rigid but multistable.
- Two reconfigurability strategies: slip and phase transformation.
- Provides quantitative design guidance for origami-based actuators and metamaterials.

## Abstract

We characterize the phase-space of all Helical Miura Origami. These structures are obtained by taking a partially folded Miura parallelogram as the unit cell, applying a generic helical or rod group to the cell, and characterizing all the parameters that lead to a globally compatible origami structure. When such compatibility is achieved, the result is cylindrical-type origami that can be manufactured from a suitably designed flat tessellation and "rolled-up" by a rigidly foldable motion into a cylinder. We find that the closed Helical Miura Origami are generically rigid to deformations that preserve cylindrical symmetry, but multistable. We are inspired by the ways atomic structures deform [1] to develop two broad strategies for reconfigurability: motion by slip, which involves relaxing the closure condition; and motion by phase transformation, which exploits multistability. Taken together, these results provide a comprehensive description of the phase-space of cylindrical origami, as well as quantitative design guidance for their use as actuators or metamaterials that exploit twist, axial extension, radial expansion, and symmetry.