Thick-Panel Origami-Inspired Multiple Metamorphic Mechanisms with Planar-Spherical-Bennett Bifurcated Cycle

The intricate relationship between origami and mechanism underscores the fertile ground for innovation, which is particularly evident in the construction theory of thick-panel origami. Despite its potential, thick panel origami remains relatively unexplored in the context of single-loop metamorphic mechanisms. Drawing inspiration from thick-panel origami, particularly Miura origami, this study proposes a pioneering single-loop 6R multiple metamorphic mechanism. Through rigorous mathematical modeling (including the construction and resolution of the D-H closed-loop equation) and leveraging advanced analytical tools such as the screw theory and Lie theory, this study meticulously elucidates the planar, spherical, and Bennett motion branches of the mechanism. Furthermore, it delineates all the three bifurcation points between the motion branches, thereby providing a comprehensive understanding of the kinematic behavior of the mechanism. A metamorphic network can be constructed by applying several single-loop mechanisms to a symmetrical layout. Owing to its metamorphic properties, this network can act as a structural backbone for deployable antennas, aerospace shelters, and morphing wing units, thereby enabling a single mechanism to achieve multiple folding configurations. This paper not only introduces innovative metamorphic mechanisms but also suggests a promising method for uncovering and designing metamorphic mechanisms by developing new mechanisms from thick-panel origami.