Large-Curvature Deployable Developable Structures via Lamina Emergent Arrays

A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures that are also deployable. By exploiting the ruling lines in developable surfaces, this method enables developable structures that can be manufactured with two-dimensional geometry and yet have a greater range of elastic motion than is possible with a solid sheet of material. A mathematical model is developed to describe the resulting stiffness of the structure employing the lamina emergent arrays and equations are derived to facilitate stress analysis of the structure. Finite element results show the sensitivity of alignment of the elements in the array to the stress present in the developed structure. A specific technique for creating an array pattern for conical developable surfaces is described. Examples of developable structures, including curved-fold origami models transitioned to thick materials, are also examined.