Folding Miura-ori of Uniform Thickness with One DoF

Abstract

The Miura-ori is an origami pattern with bi-directional folding capable of transforming a large thin sheet into a compact volume with a single degree of freedom (DoF). A common Miura-ori pattern consists of identical rigid parallelogram facets that can rotate about the creases without twisting or stretching. However, large gaps along the hinges or uneven surfaces in deployed states are inevitable when thick panels are used. In this paper, the authors add uniform thickness to a Miura-ori tessellation and connect the thick panels by revolute joints on either the top or the bottom facets of the panels for valley creases or mountain creases, respectively. To enable its folding, regular slits are made on some facets not only to remove the excess kinematic constraints but also to accommodate the panel thickness during the folding process. Having made the cuts, we demonstrate that the resultant assembly can fold into a compact package with one DoF. We further notice that although the slits open up during the folding process, they close in the deployed state of the assembly, giving flat and continuous surfaces on both the top and bottom sides. The same method can also be applied to fold the derivatives of the Miura-ori such as double corrugated patterns.