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1. Exploring the dynamic characteristics of degree-4 vertex origami metamaterials

   https://doi.org/10.1115/SMASIS2017-3810  

   Xia, Yutong ; Fang, Hongbin ; Wang, K.W. ( September 2017 , ASME section IX)

   Origami-inspired mechanical metamaterials could exhibit extraordinary properties that originate almost exclusively from the intrinsic geometry of the constituent folds. While most of current state of the art efforts have focused on the origami’s static and quasi-static scenarios, this research explores the dynamic characteristics of degree-4 vertex (4-vertex) origami folding. Here we characterize the mechanics and dynamics of two 4-vertex origami structures, one is a stacked Miura-ori (SMO) structure with structural bistability, and the other is a stacked single-collinear origami (SSCO) structure with lockinginduced stiffness jump; they are the constituent units of the corresponding origami metamaterials. In this research, we theoretically model and numerically analyze their dynamic responses under harmonic base excitations. For the SMO structure, we use a third-order polynomial to approximate the bistable stiffness profile, and numerical simulations reveal rich phenomena including small-amplitude intrawell, largeamplitude interwell, and chaotic oscillations. Spectrum analyses reveal that the quadratic and cubic nonlinearities dominate the intrawell oscillations and interwell oscillations, respectively. For the SSCO structure, we use a piecewise constant function to describe the stiffness jump, which gives rise to a frequencyamplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenariomore »because locking is not triggered, and the other with large amplitude and significant nonlinear characteristics. The method of averaging is adopted to analytically predict the piecewise stiffness dynamics. Overall, this research bridges the gap between the origami quasi-static mechanics and origami folding dynamics, and paves the way for further dynamic applications of origami-based structures and metamaterials.« less
2. Heterogeneous origami-architected materials with variable stiffness

   https://doi.org/10.1038/s43246-021-00212-4  

   Miyazawa, Yasuhiro ; Yasuda, Hiromi ; Kim, Hyungkyu ; Lynch, James H. ; Tsujikawa, Kosei ; Kunimine, Takahiro ; Raney, Jordan R. ; Yang, Jinkyu ( November 2021 , Communications Materials)

   Origami, the ancient art of paper folding, has shown its potential as a versatile platform to design various reconfigurable structures. The designs of most origami-inspired architected materials rely on a periodic arrangement of identical unit cells repeated throughout the whole system. It is challenging to alter the arrangement once the design is fixed, which may limit the reconfigurable nature of origami-based structures. Inspired by phase transformations in natural materials, here we study origami tessellations that can transform between homogeneous configurations and highly heterogeneous configurations composed of different phases of origami unit cells. We find that extremely localized and reprogrammable heterogeneity can be achieved in our origami tessellation, which enables the control of mechanical stiffness and in-situ tunable locking behavior. To analyze this high reconfigurability and variable stiffness systematically, we employ Shannon information entropy. Our design and analysis strategy can pave the way for designing new types of transformable mechanical devices.
3. ON THE DEPLOYMENT OF MULTISTABLE KRESLING ORIGAMI-INSPIRED STRUCTURES

   https://doi.org/10.1115/DETC2019-97427  

   Kidambi, Narayanan ; and Wang, K.W. ( August 2019 , ASME section IX)

   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.
4. Designing continuous equilibrium structures that counteract gravity in any orientation

   https://doi.org/10.1038/s41598-023-34760-1  

   Redoutey, Maria ; Filipov, Evgueni T. ( May 2023 , Scientific Reports)

   This paper presents a framework that can transform reconfigurable structures into systems with continuous equilibrium. The method involves adding optimized springs that counteract gravity to achieve a system with a nearly flat potential energy curve. The resulting structures can move or reconfigure effortlessly through their kinematic paths and remain stable in all configurations. Remarkably, our framework can design systems that maintain continuous equilibrium during reorientation, so that a system maintains a nearly flat potential energy curve even when it is rotated with respect to a global reference frame. This ability to reorient while maintaining continuous equilibrium greatly enhances the versatility of deployable and reconfigurable structures by ensuring they remain efficient and stable for use in different scenarios. We apply our framework to several planar four-bar linkages and explore how spring placement, spring types, and system kinematics affect the optimized potential energy curves. Next, we show the generality of our method with more complex linkage systems that carry external masses and with a three-dimensional origami-inspired deployable structure. Finally, we adopt a traditional structural engineering approach to give insight on practical issues related to the stiffness, reduced actuation forces, and locking of continuous equilibrium systems. Physical prototypes support the computational resultsmore »and demonstrate the effectiveness of our method. The framework introduced in this work enables the stable, and efficient actuation of reconfigurable structures under gravity, regardless of their global orientation. These principles have the potential to revolutionize the design of robotic limbs, retractable roofs, furniture, consumer products, vehicle systems, and more.

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5. Untethered control of functional origami microrobots with distributed actuation

   https://doi.org/10.1073/pnas.2013292117  

   Novelino, Larissa S. ; Ze, Qiji ; Wu, Shuai ; Paulino, Glaucio H. ; Zhao, Ruike ( September 2020 , Proceedings of the National Academy of Sciences)

   Deployability, multifunctionality, and tunability are features that can be explored in the design space of origami engineering solutions. These features arise from the shape-changing capabilities of origami assemblies, which require effective actuation for full functionality. Current actuation strategies rely on either slow or tethered or bulky actuators (or a combination). To broaden applications of origami designs, we introduce an origami system with magnetic control. We couple the geometrical and mechanical properties of the bistable Kresling pattern with a magnetically responsive material to achieve untethered and local/distributed actuation with controllable speed, which can be as fast as a tenth of a second with instantaneous shape locking. We show how this strategy facilitates multimodal actuation of the multicell assemblies, in which any unit cell can be independently folded and deployed, allowing for on-the-fly programmability. In addition, we demonstrate how the Kresling assembly can serve as a basis for tunable physical properties and for digital computing. The magnetic origami systems are applicable to origami-inspired robots, morphing structures and devices, metamaterials, and multifunctional devices with multiphysics responses.