A general formulation for simulating the dynamic deployment of thick origami

The deployment of origami is usually a rapid and complicated dynamic process. However, little has been done to simulate the entire deployment process of thick origami which is a typical over-constrained mechanical system. Based on the constrained Hamilton's equations in conjunction with the natural coordinate formulation, a general formulation capable of tracing the dynamic deployment of thick origami is established. Particular efforts are paid to dealing with the problems including geometric description, redundant constraint, large rotational angle, and possible bifurcation paths. The proposed formulation is applied to three thick origami structures: thick Miura-ori, thick diamond origami, and thick waterbomb origami. The results show that the dynamic characteristics during the deployment can be successfully obtained, and the numerical accuracy is also validated by the ADAMS simulation and prototype experiments. Furthermore, parametric analyses are performed to investigate the effects of actuating positions and geometric parameters on deployment behaviors. The proposed formulation provides a clear view of the deployment process for thick origami structures, which will benefit the optimal design in practical applications.