Generalized Bistability in Origami Cylinders

Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight, medicine, and even experimental nuclear physics. In spite of this interest, a general understanding of the dynamics of an origami folded cylinder has been elusive. By solving the fully constrained behavior of a periodic fundamental origami cell defined by unit vectors, we have found an analytic solution for all possible rigid-face states accessible from a cylindrical Miura-ori pattern. Although an idealized bellows has two rigid-face configurations over a well-defined region, a physical device, limited by nonzero material thickness and forced to balance hinge with plate-bending energy, often cannot stably maintain a stowed configuration. We have identified and measured the parameters which control this emergent bistability, and have demonstrated the ability to fabricate bellows with tunable deployability.