Structure, design, and mechanics of a paper spring

A paper spring is a simple paper craft popular with children. It can be constructed by interfolding and gluing two long strips of paper of equal sizes, with the simplest possible crease patterns. In addition to its curious springy response, this origami-based composite exhibits a twist deformation during its extension. Although its interlocking structure is expected to underly the strong stretch-twist coupling, a detailed understanding of it remains elusive. Here we quantify the kinematics and mechanics of a paper spring during its extensional actuation by combining experimental, numerical, and analytical approaches. We directly link the nonlinear mechanics of a paper spring with its structural design and the sheet elasticity. We show that the unique interlocking provides an enhanced structural rigidity because the thin sheets suffer from geometric frustrations and must locally bend and stretch during extension. This structural design allows for a reversible transformation between the rotatory and linear motions solely by controlling forces and moments applied at the ends of the structure. Such deployment kinematics could provide a unique avenue of the mode conversion for potential applications and will broaden the possibilities of future designs of origami-based springs with tunable functionalities.