Resch pattern, a family of origami tessellations, was discovered by Professor Ronald Dale Resch, a famous artist, computer scientist, and applied geometrist in 1960s. Among these tessellations, triangular Resch pattern has attracted much attention in a lot of research areas thanks to its higher stiffness and the capability of forming several shapes. However, its application is limited due to the property of multi-DOF which renders the difficulty to control. Therefore, it is challenging and significant to find the one-DOF form of the triangular Resch pattern.
        Recently, the team of Professor Yan Chen at Tianjin University (The first author, Dr. Fufu Yang, works at Fuzhou University as a lecturer recently), and Professor Zhong You at the University of Oxford, as well as Professor G. H. Paulino at Princeton University, who is also a member of US National Academy of Engineering (NAE), proposed two thick-panel counterparts to realise one-DOF folding.
        According to the geometric property, there are three kinds of vertices in a triangular Resch pattern, and each kind of vertex is transformed to its potential thick-panel forms at first by the technique of thick-panel origami. Then, all vertices are tried to be transformed to their thick-panel forms at the same time but an immobile structure is obtained due to overconstraint. Finally, two mobile schemes with one-DOF were obtained by releasing some constraints. The results were demonstrated by the derivation of the analytical expressions among all kinematic variables. Meanwhile, two groups of prototypes were fabricated to validate the results too.

(a)

(b)

(c)

One-DOF forms with (a) Scheme I and its equivalent linkage, (b) Scheme II and its equivalent linkage, validated by (c) two groups of prototypes folding like the original zero-thickness triangular pattern.

        This paper was accepted by Mechanism and Machine Theory, the official journal of IFToMM, on Oct. 9, 2021, and has been published online on Dec. 2, 2021. It provides a new design idea for exploring the single-degree-of-freedom form of multi-degree-of-freedom origami, and lays the foundation for the further application of rigid origami.

Fufu Yang, Miao Zhang, Jiayao Ma, Zhong You, Ying Yu, Yan Chen*, G. H. Paulino*, 2022, Design of Single Degree-of-Freedom Triangular Resch Patterns with Thick-panel Origami, Mechanism and Machine Theory, 169, 104650.
(https://doi.org/10.1016/j.mechmachtheory.2021.104650)