Thick-panel origami considers the panel thickness for engineering requirements such as solar arrays and reflectarray antennas, and is widely used in the aerospace field. However, it is still a challenge to generate the one-DOF hexagonal thick-panel origami with uniform thickness, flat deployable surface and compact folding.

         Recently, the team of Professor Yan Chen from Tianjin University, collaborating with Professor Zhong You from the University of Oxford, has constructed a series of one-DOF planar thick-panel origami mechanisms using one-DOF spatial 8R linkage networks and uniform-thickness regular hexagonal panels, which have flat surfaces and compact folding properties. This achievement was published online in the journal Mechanism and Machine Theory on October 10, 2025, with Professor Yan Chen as the corresponding author and Dr. Yuanqing Gu as the first author. The study was supported by the National Natural Science Foundation of China and New Cornerstone Science Foundation through the XPLORER PRIZE.

        The hexagon, as the fundamental geometric element of honeycomb patterns with excellent tessellation properties, is employed as the basic configuration for origami panels in this paper. As shown in Fig. 1, P₁, P₂, P₃, P₅, P₆, and P₇ are regular hexagonal panels, while P₄ and P₈ are combinations of two regular hexagonal panels respectively. A slit (shown in red) is arranged between panels P₁ and P₅, thus the above eight panels connected end-to-end can be equivalent to a spatial 8R linkage. As shown in its motion sequence, the six regular hexagonal panels can achieve orderly and compact folding between P₄ and P₈.

Fig. 1. The spatial 8R linkage based on uniform-thickness regular hexagonal panels

        Further, the tessellation and connection forms of the spatial 8R units are explored to construct large-scale planar arrays. First, as shown in Fig. 3(a), three units are tessellated horizontally, and two adjacent units share one panel (P₈/P₄) to construct assembly A and its identical assembly A′. Subsequently, according to the four connection forms shown in Fig. 3(b), the panels P₆ and P₇ of assembly A are connected to the panels P₂ and P₃ of assembly A′, and finally the four large-scale planar array construction cases in Fig. 3(c) are obtained.

Fig. 2. Construction cases of large-scale planar array based on assembly A

        Through the analysis of folding angles and kinematic coordination relationships, it is verified that construction cases 1.1 to 1.4 all have one DOF. In the corresponding spatial 8R mechanism network topology shown in Fig. 3, the mechanism network composed of two original folding units (U₁ and U₂) and two derived connection units (C₁ and C₂) can be regarded as the minimum one-DOF topological unit of this type of mechanism network, and has the ability of infinite planar tessellation.

Fig. 3. Construction of cases 1.1 to 1.4 and their mechanism network topologies

        Furthermore, flipping assembly A with 180 degrees around the x-axis or y-axis while maintaining all topological connections can generate assemblies B, C, and D, as shown in Fig. 4. Referring to the four connection forms of assembly A and assembly A′ in Fig. 2, assembly A can be connected to assemblies B, C, and D respectively in four forms to construct large-scale planar arrays. The specific construction cases and their one-DOF spatial 8R mechanism topologies are shown in Fig. 5, Fig.6 and Fig.7 respectively. So far, this paper has obtained a total of 16 planar thick-panel origami construction cases based on uniform-thickness regular hexagonal panels and 8 corresponding one-DOF mechanism topologies.

Fig.4. Assemblies A to D via rotational transformation around the x- and y-axis

Fig. 5. Construction cases 2.1 to 2.4 and their mechanism network topologies

Fig. 6. Construction cases 3.1 to 3.4 and their mechanism network topologies

Fig. 7. Construction cases 4.1 to 4.4 and their mechanism network topologies

        Finally, based on the obtained one-DOF mechanism topologies, further research is conducted on the surface integrity of the proposed planar thick-panel origami mechanisms. As shown in Figs. 8(a-b), by introducing additional hexagonal thick panels to fill the gaps between panels, two spatial 8R folding units with flat surfaces are obtained without physical interference during the entire movement. Taking case 1.4 as an example, Fig. 8(c) shows the planar thick-panel origami design method with a complete and flat surface, and the folding sequence of its physical model is shown in Fig. 8(d) (Video 1).

Fig. 8. Surface integrity design of hexagonal planar thick-panel origami

Video 1

        In summary, this work conducts the exploration of the one-DOF topological combinations of spatial 8R linkage. Based on uniform-thickness regular hexagonal panels, a series of planar thick-panel origami construction cases with uniform thickness, flat surfaces, compact folding, and one-DOF characteristics are proposed. This paper research various thick-panel folding cases and their mechanism topologies based on various panel connection forms. Future research can be extended to folding assemblies of other polygonal panels, thereby further enhancing the versatility and applicability of planar thick-panel origami mechanisms.

Yuanqing Gu, Li Wen, Jiayao Ma, Xiao Zhang, Zhong You, Yan Chen*. One-DOF hexagonal thick-panel origami with uniform thickness, flat deployable surface and compact folding. Mechanism and Machine Theory. 2025, 217, 106252.
(https://doi.org/10.1016/j.mechmachtheory.2025.106252)