Dynamics of flexible multi-stable origami with bio-inspired creases

Origami, an ancient art form, has attracted immense interest from scientists and engineers. However, the design space of corresponding structures is significantly limited by the rotation assumption of rigid origami creases. This study proposes a novel origami structure with multi-stable mechanisms by introducing extensible-torsional creases like natural folding structures, enhancing the geometric flexibility of classic four-crease vertex origami. A three-degree-of-freedom geometric model is developed to characterize the structural deformation. It is reduced to two degrees of freedom with the fixed-free geometric boundary conditions. The nonlinear dynamic equations of the system are derived using Lagrange's Equation and solved by fourth-order Runge-Kutta method. The theoretical predictions are consistent with simulation results in ADAMS. With the dedicated theoretical model, multiple deformation paths of the origami structure corresponding to different configurations are discovered, as well as configuration transitions with supercritical pitchfork and saddle-node bifurcations. The origami structures with five and six stable equilibria are demonstrated. The bifurcations of their equilibria and corresponding inherent properties are investigated. Nonlinear dynamic behaviors, including period-doubling and chaotic motions, are explored. Experimental results further illustrate configuration transformations in the bi-stable and tri-stable structures under dynamic excitations. This work opens up new possibilities for designing innovative origami structures with multi-stable mechanisms, paving the way for advanced engineering applications such as deployable structures, metamaterials and robotics.