Thick-panel origami is a special type of origami that considers the thickness of panels to satisfy engineering requirements. It not only inherits the advantages of zero-thickness origami including large folding ratio and tight folding, but also overcomes the serious physical interference caused by the panel thickness during the folding process. Compared to traditional zero-thickness origami, it retains excellent folding performance while considering material thickness, which can enhance structural stiffness and adapt to complex load environments. It has demonstrated application value in aerospace deployable structures, civil engineering and other fields.
1 Thick-panel origami theory
In order to apply rigid origami to engineering applications, we considered the thickness of rigid materials and developed a kinematic theory of single-vertex thick-panel origami based on spatial overconstrained linkages by replacing the spherical linkage of the original origami model with a spatial overconstrained linkage. For multi-vertex origami patterns, by analyzing the topology and kinematic compatibility conditions of the corresponding mobile assemblies, the complete folding motion of the thick-panel origami was described, and the implementation of kinematic equivalence between thick-panel and zero-thickness origami was explored. A design method for directly constructing equivalent thick-panel origami from zero-thickness origami was established, successfully solving the international problem of thick-panel origami. This theory breaks through the main bottleneck between origami science and its application, paving the way for engineering applications. The research outcomes were published in Science in 2015, as the first mechanism-related article published in this top research journal.
Science published "Origami of Thick Panels" online on 24th July 2015
Kinematic equivalence between various vertex models of zero-thickness sheets and thick panels.
2 Planar thick-panel origami
2.1 Equivalent transformation between multi-DOF planar rigid origami and single-DOF thick-panel origami
A thick-panel transformation method based on the thick-panel origami theory was established to address the problem that single-DOF folding of multi-DOF planar origami along symmetric paths is difficult to control. This method was successfully applied to classic multi-DOF six-crease waterbomb origami and triangular Resch origami, achieving single-DOF folding along a symmetric motion path. By analyzing and revealing the geometric conditions for the bifurcation path of waterbomb thick-panel origami, a motion path selection strategy was proposed to avoid physical interference of structural boundaries during the folding process. During the thick-panel transformation of Resch origami, some vertices were transformed into Bricard linkages, while other vertices maintain the spherical 6R linkages. This provides a new approach for exploring the equivalent transformation of single-DOF thick-panel origami from multi-DOF zero-thickness origami.
Two motion paths of zero-thickness waterbomb origami and its thick-panel form
Two motion paths of zero-thickness Resch origami and its thick-panel form
Yan Chen, Huijuan Feng, Jiayao Ma, Rui Peng, Zhong You* Symmetric waterbomb origami. Proc. R. Soc. A , 2016, 472, 20150846. (http://dx.doi.org/10.1098/rspa.2015.0846) (Journal cover paper)
Fufu Yang, Miao Zhang, Jiayao Ma, Zhong You, Ying Yu, Yan Chen*, Paulino G*. Design of single degree-of-freedom triangular Resch patterns with thick-panel origami, Mechanism and Machine Theory, 2022, 169: 104650. ( https://doi.org/10.1016/j.mechmachtheory.2021.1046505)
2.2 Thick-panel origami with a flat unfolded surface
For the demand of flat working surfaces in aerospace deployable structures, and the problem of uneven surface caused by the convex structure used for arranging hinges on the unfolded surface of thick-panel origami, three methods have been proposed: a method for constructing flat surfaces in thick-panel origami based on the parameter analysis of spatial overconstrained mechanism networks, a single-DOF compact folding thick-panel origami method with flat unfolded surfaces based on the combined design of creases and cuts, and a convex structure removal method based on kinematically equivalent replacement of mechanisms. Starting from diamond origami, 2-DOF composite units with crease and slits, Miura-ori thick-panel origami, etc., a series of thick-panel origami structures with flat unfolding surfaces and large folding ratio were designed, laying a theoretical foundation for the application of thick-panel origami in the field of aerospace as planar array antennas.
Diamond thick-panel origami with flat working surface
Compact folding thick-panel origami with flat unfolded surfaces based on combined creases and cuts
Four-crease thick-panel origami with rectangular flat working surface
Xiao Zhang, Yan Chen*. The diamond thick-panel origami and the corresponding mobile assemblies of plane-symmetric Bricard linkages. Mechanism and Machine Theory, 2018, 130, 585-604. (https://doi.org/10.1016/j.mechmachtheory.2018.09.005)
Jingyi Yang, Xiao Zhang, Yan Chen, Zhong You, Folding arrays of uniform-thickness panels to compact bundles with a single degree of freedom. Proceedings of the Royal Society A, 2022, 478: 20220043. ( http://doi.org/10.1098/rspa.2022.0043)
Chenjie Zhao#, Ming Li#, Xin Zhou, Tianming Liu, Jian Xing, Yan Chen, Xiao Zhang*. Deployable structure based on double-layer miura-ori pattern. Mechanics Research Communications, 2023, 131, 104152. ( https://doi.org/10.1016/j.mechrescom.2023.104152)
3 Three-dimensional thick-panel origami
3.1 Thick-panel origami tube
The thick-panel origami tube composed of four-crease vertices has non-developable four-crease origami vertices, which makes it difficult to transition to thick-panel form. We started from a zero-thickness origami tube, and found there were multiple motion paths sharing a common bifurcation configuration in a single origami tube. By using thick-panel origami theory and kirigami techniques, a thick-panel origami that can be reconfigured between specified configurations was constructed. By designing a single motor actuation scheme, a fast and accurate switching between the contraction mode and the shear mode of the thick-panel origami tube was realized. The research is conducive to the application of thick-panel origami in scenarios with multi-function requirements, such as reconfigurable antennas and metamaterials.
Reconfigurable thick-panel origami tube
Weiqi Liu, Yuxing Song, Yan Chen*, Xiao Zhang*. Reconfigurable thick-panel structures based on a stacked origami tube. Journal of Mechanisms and Robotics, 2024, 16(12): 121005. ( https://doi.org/10.1115/1.4064836)
3.2 Thick-panel origami cube
To overcome the mathematical bottleneck that prohibits rigid folding of closed polyhedral origami structures, a design strategy combining creases and cuts was developed to construct a zero-thickness cubic origami structure with a minimum number of creases and cuts, which is flat-foldable with a single degree of freedom. Furthermore, for non-developable 3D origami vertices, thick-panel transformation was performed based on spatial mechanisms, and corresponding kinematic models were established. The compatibility of the nonlinear folding motions among multiple spatial mechanisms corresponding to multiple polyhedral vertices was solved, leading to a design methodology for kinematically equivalent mechanisms. This provides a theoretical basis for the innovative design of three-dimensional thick-panel origami.
Two types of flat-foldable origami cubes with a single DOF
A flat-foldable origami cube and its thickness panel form with a single DOF
Yuanqing Gu, Yan Chen*. Origami cubes with one-DOF rigid and flat foldability. International Journal of Solids and Structures, 2020, 207, 250-261. (https://doi.org/10.1016/j.ijsolstr.2020.09.008)
