Analytical and numerical investigation of second-order infinitesimal mechanism in rigid origami

Abstract

This study investigates second-order infinitesimal mechanisms and bifurcation paths of rigid origamis with multiple-degree-of-freedom mechanisms. A truss model, consisting of pin-connected rigid bars, is employed for the infinitesimal mechanism analysis. The conditions for the existence of a second-order infinitesimal mechanism are analytically solved to investigate the combinations of the infinitesimal mechanism modes that are the potential finite mechanisms. Analytical solutions for simple crease patterns show the bifurcation of the deformation paths at the flat state, some disappeared combinations of the mechanism modes in a single path, and the relationship between the nodal displacement and axial force distribution. This comprehensive analysis, using analytical solutions, lays the foundation for understanding bifurcation and finite mechanism of rigid origami, which have not yet been fully explored. These properties are also verified in the finite deformation paths generated by large deformation analysis of a frame model consisting of frame members and hinges, which is suitable for the analysis using general-purpose finite element analysis software. The second-order infinitesimal mechanisms found in this study are confirmed to be able to be extended to the finite mechanisms.