Rigid- and flat-foldable grid origami structure exhibiting bifurcation of mechanism in non-flat state

This study investigates a novel origami-based flat-foldable structure for its rigid-folding mechanism and elastic deformation using two models: a panel-pin model and a finite element model. The entire proposed structure consists of unit structures arranged in a grid pattern on a plane. Each unit is a ring of eight right-angled isosceles triangular panels connected by hinges. The single unit has the same configuration as a single layer of the well-known Yoshimura tube. The infinitesimal mechanism analysis of the structure using a panel-pin model with the three units in both grid directions reveals that the proposed structure exhibits a single-degree-of-freedom mechanism except in the flat-folded states and a single isolated non-flat singular state where the rigid-folding mechanism bifurcates. Notably, the bifurcated mechanism in the non-flat singular state is only a first-order infinitesimal mechanism and cannot lead to a finite mechanism. By contrast, the stiffness in the direction of this bifurcated mechanism, investigated through the eigenvalue analysis of the tangent stiffness matrix of the panel-pin model, is the smallest among those in the directions of eigenmodes. This is also confirmed in the natural frequency analysis of the finite element model consisting of shell and hinge elements. Furthermore, the uniform panel thickness can be simply assigned to the proposed structure, and the single-degree-of-freedom rigid-folding mechanism is consistent in the presence of any panel thickness. These distinctive properties offer promising potential for innovative deployable, morphing, and bending active structures.