Folding arrays of uniform-thickness panels to compact bundles with a single degree of freedom

Flat arrays consisting of panels of finite thickness are widely used in aerospace applications such as solar panels and reflectarray antennas. Packaging them into compact bundles without any voids and then deploying them bi-directionally to flat, continuous and accurate surfaces with a single degree of freedom (DoF) has challenged engineers for decades. Here, we present a solution based on origami of thick panels. In modular construction, we first created two deployable unit arrays, each of which comprises four eight-panel elements where panels in regular shapes are connected by simple but robust rotational joints. We prove that these units have only a single DoF, and they can be folded from a flat array to compact bundles without any voids. We then show that the units can be tessellated to form larger flat arrays where a single-DoF deployment and compact packaging properties are intact. A parametric study is carried out, which provides a precise design range that prevents the panels from physical interference during deployment. Physical models were constructed that have successfully validated the concepts. Our work is directly applicable to the design of future flat arrays that can be controlled with ease.