Geometry and design of origami bellows with tunable response

TL;DR

This paper develops a geometric framework to analytically understand the mechanics of origami bellows, revealing how to design and fabricate cylinders with tunable deployability for applications in space and medicine.

Contribution

It introduces a new set of geometrical tools to analytically solve for all rigid-face states of origami cylinders, enabling tunable deployability in practical designs.

Findings

Analytic solutions for all rigid-face states of origami cylinders.

Identification of parameters controlling bistability.

Demonstration of tunable deployability in fabricated bellows.

Abstract

Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight and medicine. In spite of this interest, a general understanding of the mechanics of an origami folded cylinder has been elusive. With a newly developed set of geometrical tools, we have found an analytic solution for all possible cylindrical rigid-face states of both Miura-ori and triangular tessellations. Although an idealized bellows in both of these families may have two allowed rigid-face configurations over a well-defined region, the corresponding physical device, limited by nonzero material thickness and forced to balance hinge and plate-bending energy, often cannot stably maintain a stowed configuration. We have identified the parameters that control this emergent bistability, and have demonstrated the ability to design and fabricate bellows with tunable deployability.