Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays

A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures suited to deployable applications. By exploiting the ruling lines in developable surfaces, this method enables developable structures and mechanisms 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. Aligning the joints to the ruling lines also biases the structure to a specific deployment path. 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 and mechanisms, including curved-fold origami models transitioned to thick materials and two origami-inspired mechanisms, are examined.