Folding Simulation of Square Twist Origami using Planar Tensegrity Model

Rigid paper panels are commonly modeled using truss or panel-hinge structures in origami folding simulations. The traditional truss model with more than three edges, such as quadrilaterals with members along the four edges and two diagonals, is unstable due to out-of-plane mechanisms. This paper proposes modeling quadrilateral papers as planar (X-form) tensegrity structures to address instability issues. Prestress in planar tensegrities ensures stability and planarity by eliminating redundant infinitesimal mechanisms. The strain energy of tensegrity can easily check the rigidity after the equilibrium condition is strictly satisfied. This paper proposed two methods, incremental enforced displacement and repeated form-finding, that simulated non-rigid and rigid folding of the square twist origami. For the rigid folding, the strain energy remains unchanged. For the non-rigid one, the strain energy reveals bistable equilibrium states of the tensegrity, corresponding to the flat-unfolded and flat-folded states of origami at the start and end of folding.