A mechanical method for folding simulation of rigid and non-rigid origami based on planar tensegrity models

Origami-inspired engineering structures enable large, continuous shape changes and have found wide applications in deployable systems and mechanical metamaterials. Efficient folding simulation remains challenging for truss-based models, as planar truss facets with more than three edges inherently lack out-of-plane stiffness, leading to spurious infinitesimal mechanisms. To address this while retaining the original nodal degrees of freedom and using only axial members, this study models an origami as a tensegrity structure, composed of planar tensegrity units representing the polygonal origami panels. For instance, a quadrilateral panel is represented as an X-form tensegrity unit. Owing to prestress stability, the out-of-plane infinitesimal mechanisms of the proposed model are stabilized by the prestress-induced geometric stiffness. Furthermore, the existence of prestress provides persistent out-of-plane stiffness proportional to the prestress level. Based on this model, this study develops an enforced-displacement nonlinear analysis framework as well as a rotation-controlled rigid-folding simulator featuring a linear predictor and a constrained form-finding corrector. Numerical examples, including Miura-ori, square twist, and Resch’s patterns, are presented to demonstrate the capability of the proposed method in simulating both rigid and non-rigid origami folding.