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Origami has emerged as a promising tool for the design of mechanical structures that can be folded into small volume and expanded to large structures, which enables the desirable features of compact storage and effective deployment. Most attention to date on origami deployment has been on its geometry, kinematics, and quasi-static mechanics, while the dynamics of deployment has not been systematically studied. On the other hand, deployment dynamics could be important in many applications, especially in high speed operation and low damping conditions. This research investigates the dynamic characteristics of the deploying process of origami structures through investigating a Miura-Ori sheet (Fig. 1(b, c)). In this study, we have utilized the stored energy in pre-deformed spring elements to actuate the deployment. We theoretically model and numerically analyze the deploying process of the origami sheet. Specifically, the sheet is modeled by bar-and-hinge blocks, in which the facet and crease stiffnesses are modeled to be related to the bar axial deformation and torsional motion at the creases. On the other hand, the structural inertia is modelled as mass points assigned at hinges. Numerical simulations show that, apart from axial contraction and expansion, the origami structure can exhibit transverse motion during the deploying process. Further investigation reveals that the transverse motion has close relationship with the controlled deploying rate. This research will pave the way for further analysis and applications of the dynamics of origami-based structures. 

Origami designs have attracted significant attention from researchers seeking to develop new types of deployable structures due to their ability to undergo large and complex yet predictable shape changes. The Kresling pattern, which is based on a natural accumulation of folds and creases during the twistbuckling of a thin-walled cylinder, offers a great example for the design of deployable systems that expand uniaxially into tubes or booms. However, much remains to be understood regarding the characteristics of Kresling-based deployable systems, and their dynamics during the deployment process remain largely unexplored. Hence this research investigates the deployment of Kresling origami-inspired structures, employing a full sixdegree- of-freedom truss-based model to study their dynamics under different conditions. Results show that tuning the initial rotation angle of a structure gives rise to several qualitatively distinct mechanical properties and stability characteristics, each of which has different implications for the design of the deployable systems. Dynamic analyses reveal the robustness of Kresling structures to out-of-axis perturbations while remaining compliant in the axial direction. These findings suggest that Kresling-based designs can form the basis for the development of new types of deployable structures and systems with tunable performance. 

Origami provides a flexible platform for constructing three-dimensional multi-stable mechanical metamaterials and structures. While possessing many interesting features originating from folding, the development of multi-stable origami structures is faced with tremendous demands for acquiring tunability and adaptability. Through an integration of origami folding with magnets, this research proposes a novel approach to synthesize and harness multi-stable magneto-origami structures. Based on the stacked Miura-ori and the Kresling ori structures, we reveal that the embedded magnets could effectively tune the structure’s potential energy landscapes, which includes not only altering the position and the depth of the potential wells but essentially eliminating the intrinsic potential wells or generating new potential wells. Such magnet-induced evolutions of potential energy landscapes would accordingly change the origami structure’s stability profiles and the constitutive force–displacement relations. Based on proof-ofconcept prototypes with permeant magnets, the theoretically predicted effects of magnets are verified. The exploration is also extended to the dynamics realm. Numerical studies suggest that the incorporated magnets not only could translate the critical frequencies for achieving certain dynamical behaviors but also fundamentally adjust the frequency-amplitude relationship. Overall, this study shows that the proposed approach would provide a novel means to control the stability profile as well as the mechanics and dynamic characteristics of origami structures, and thus, inspire new innovations in designing adaptive mechanical metamaterials and structures.