Origami is the traditional art of paper folding into sculpture, and rigid origami is a particular form of origami in which each surface surrounded with crease lines is not stretching and bending. Hence, by taking the panels as links and the creases as revolute joints, a degree-4 rigid origami vertex can be regarded as a spherical 4R linkage, and an rigid origami pattern formed by degree-4 vertexes can be regarded as a mobile assembly of spherical 4R linkages. Rigid origami patterns can therefore be obtained according to the kinematical analysis of spherical linkages. However, the method mentioned above requires solution of complex nonlinear equations, which may limit the design of rigid origami patterns. Simplifying the mechanism model of rigid origami patterns is helpful to solve the problem.
        Professor Yan Chen and her students Weilin LV and Rui Peng from School of Mechanical Engineering of Tianjin University and Prof. Guowu Wei from School of Science, Engineering and Environment of University of Salford presented kinematics of a single loop spherical 4R linkage, and by merging four identical spherical 4R linkages into a single loop, three basic mobile assemblies are constructed and the one-degree-of-freedom kinematic compatibility condition is formulated. Through alteration of the four vertex linkages in the three basic assemblies, variations of the basic assemblies are generated, and this method simplified the mechanism model of rigid origami pattern. Consequently, by adding further geometric conditions, a novel rigid origami pattern called the helical pattern is obtained. The results were published in volume 142 of Mechanism and Machine Theory on Sep. 25, 2019.

a single loop formed by four identical spherical 4R linkages

a novel rigid origami pattern (the helical pattern)

        This paper provides a novel approach for generating new rigid origami patterns which can lead to the development of foldable structures and tessellations with potential applications in robotics, smart architectures, mechanical metamaterials and space exploration.

Yan Chen, Weilin Lv, Rui Peng and Guowu Wei, 2019, Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns, MMT, Volume 142, 103613
(https://doi.org/10.1016/j.mechmachtheory.2019.103613)