Kinematic behaviour of origami combining two four-crease vertices

Abstract

The simplest rigidly foldable single-vertex origami structure is a four-crease origami (single 4C). It is a 1 DOF spherical linkage which possesses geometric properties that allow its copies to be combined into more complex rigidly foldable origami such as the Miura-ori. Merging two identical flat-foldable single 4Cs together produces a new construction, called the double 4C. We discover that this composite structure has some unique kinematic properties. Apart from being rigidly foldable and flat-foldable with 1 DOF, both single 4Cs in the double 4C are always in identical folded states. Moreover, it actually couples some panels together to form scissor-like mechanisms without physically crossing the panels. The double 4C can also have its kinematically equivalent thick-panel counterpart. By dissecting the double 4C and its thick panel counterpart, we find the constituent mechanisms forming them. We uncover how the constituent mechanisms evolve. Since the double 4C are fundamental units in many stackable tessellation origami structures, our kinematic analysis gives insight into the kinematic behaviour of these structures. Not only can the findings be used to guide the creation of thick panel counterparts of the stackable origami, but it may also enable the creation of new origami structures with single DOF by mimicking the vast number of deployable structures that contain scissor-like elements.