Rigid origami has been widely used in the innovative design of developable structures in recent years because of its excellent folding characteristics and abundant folding methods, and the kinematical equivalence to a mobile assembly of linkages. It is of great significance to design the developable structure with single degree of freedom (DOF) and a large deployable rate based on origami.
        Professor Chen Yan's team from School of Mechanical Engineering of Tianjin University cooperated with Shanghai Institute of Astronautical System Engineering to carry out the research on the innovative design of developable structure based on the variant unit of Plane linkage origami. First, a closed-loop mesh origami with a stable deploying process was proposed by changing the crease arrangement, as shown in the figure below. Then, considering the multi-DOF problem of the zero-thickness origami, the DOF is reduced to 1 by constructing its thick-panel origami form, and it is proved that the regular hexagonal thick-panel origami is kinematically equivalent to the zero-thickness origami with symmetric constraints. Furthermore, the analytical relationship between the deployable rate and the height and thickness of the triangular element was established. Through a reasonable selection of geometric parameters, a one-DOF deployable structure with a deployable ratio of 16.3 was designed.

The regular hexagon origami pattern with three DOFs.

The motion sequences of a regular hexagon thick-panel origami

        Considering that the deployable structure in engineering application usually has a flat working surface on one side, Bricard linkage and Waldron linkage were used to replace Bennett linkage at some vertices to remove the stairs on the working surface of regular hexagon thick-panel origami. Then, the thick-panel origami with a flat developed surface on one side is obtained, which provides technical support for its practical application.

The process of transformation from Bennett linkage to Bricard linkage

The process of combining Bennett linkage into Waldron linkage

A regular hexagon thick-panel origami with a flat developed surface on one side

        This work was accepted by the Journal of Mechanical Engineering on April 16, 2021, and published online on April 21, which provides a new idea for the subsequent design of novel deployable structures with flat developed surfaces based on origami.

张霄，李明，崔琦峰，陈学松，马家耀，陈焱. 基于正六边形折纸的单自由度可展结构[J].机械工程学报，2021，57：1-12.
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