Foldability Analysis of Thick-panel Origami Mechanism with Third-order Magic Square Topology

doi:10.3901/JME.2023.11.201

Abstract

Abstract: Rigid foldability of the origami mechanism is directly affected by the crease pattern. Firstly, components of the origami crease pattern with third-order magic square topology are examined with topology theory. To represent the crease assignment features of the origami topology, the mesh circuit vector and the crease assignment matrix are constructed. Secondly, the origami topology is identical before and after the operations of rotating, flipping, and mirroring for two hundred and fifty-six topology configurations. Following isomorphism determination, twenty-three topological configurations are obtained and classified as three types named square-twist type, axisymmetric type, and irregular type. Finally, to determine whether the thick-panel origami mechanism can achieve rigid folding, the single-vertex four-crease mechanism is equivalent with the Bennett linkages kinematically. A general formula of kinematic compatibility is established by introducing the sector angle parameter matrix, the dihedral angle eigen matrix, and the sector angle eigen matrix. The coefficient of kinematic compatibility is proposed and it can be used to determine whether a thick-panel origami mechanism is rigidly foldable or not. Nineteen of the twenty-three topological configurations are available for rigidly foldable thick-panel modules. These modules can be used to construct large scale deployable mechanisms with their mirrored counterpart which have a great prospect.

Key words: deployable mechanism, origami mechanism, topology, rigid foldability, kinematic compatibility

CLC Number:

TH112

CHANG Boyan, ZHANG Haonan, LIANG Dong, JIN Guoguang. Foldability Analysis of Thick-panel Origami Mechanism with Third-order Magic Square Topology[J]. Journal of Mechanical Engineering, 2023, 59(11): 201-212.

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