  Snapping of a slender structure is utilized in a wide range of natural and
man-made systems, mostly to achieve rapid movement without relying on
muscle-like elements. Although several mechanisms for elastic energy storage
and rapid release have been studied in detail, a general understanding of the
approach to design such a kinetic system is a key challenge in mechanics. Here
we study a twist-driven buckling and fast flip dynamics of a geometrically
constraint ribbon by combining experiments, numerical simulations, and
analytical theory. We identify two distinct types of shape transitions; a
narrow ribbon snaps, whereas a wide ribbon forms a pair of localized helices.
We construct a phase diagram and explain the origin of the boundary, which is
determined only by geometry. We quantify effects of gravity and clarify time
scale dictating the rapid flipping. Our study reveals the unique role of
geometric twist-bend coupling on the fast dynamics of a thin constrained
structure, which has implications for a wide range of biophysical and applied
physical problems.
