Nonlinear dynamics of an origami tessellation based on the waterbomb pattern

Abstract

Origamis have been inspiring new adaptive structures, such as micro robots, solar panels and energy harvesting. One of the challenges of the design of origami structures is the large number of degrees of freedom (DoF) associated with such complex structures, including variables associated with creased folds and hidden variables associated with the bending and twisting of panels. Closed tessellations have a reduced number of DoF when compared to open ones. Symmetries allow the description of the structure from reducedorder models. This work presents an overview of origami structures, with special interest on waterbomb pattern and related tessellations. A unit cell is studied establishing a comparison with kinematic and mechanical formulations. The study is expanded to tessellations, considering open and closed cases. Reduced-order models are proposed in order to describe the mechanical behavior of the origamis, verifying their validity from a comparison with more sophisticated models. Nonlinear dynamics of origamis is explored by investigating an origami wheel, a modified closed waterbomb tessellation. Finally, a two-wheel autonomous robot with origami wheel is analyzed, investigating the maneuverability and responsiveness from the deformation of the wheels. Numerical simulations related to operational conditions are performed for different thermal and mechanical loads, showing rich behaviors with periodic and chaotic responses.