devices, [26,27] to small-scale nano- [28][29][30] and DNA origamis. [31] A common theme in these studies is to exploit the sophisticated shape transformations from folding. For example, an origami robot is typically fabricated in a 2D flat configuration and then folded into the prescribed 3D shape to perform its tasks. The origamis have been treated essentially as linkage mechanisms in which rigid facets rotate around hingelike creases (aka "rigid-folding origami"). Elastic deformation of the constituent sheet materials or the dynamics of folding are often neglected. Such a limitation in scope indeed resonates the origin of this field, that is, folding was initially considered as a topic in geometry and kinematics.However, the increasingly diverse applications of origami require us to understand the force-deformation relationship and other mechanical properties of folded structures. Over the last decade, studies in this field started to expand beyond design and kinematics and into the domain of mechanics and dynamics. Catalyzed by this development, a family of architected origami materials quickly emerged (Figure 1). These materials are essentially assemblies of origami sheets or modules with carefully designed crease patterns. The kinematics of folding still plays an important role in creating certain properties of these origami materials. For example, rigid folding of the classical Miura-ori sheet induces an in-plane deformation pattern with auxetic properties (aka negative Poisson's ratios). [32,33] However, elastic energy in the deformed facets and creases, combined with their intricate spatial distributions, impart the origami materials with a rich list of desirable and even unorthodox properties that were never examined in origami before. For example, the Ron-Resch fold creates a unique tri-fold structure where pairs of triangular facets are oriented vertically to the overall origami sheet and pressed against each other. Such an arrangement can effectively resist buckling and create very high compressive load bearing capacity. [34] Other achieved properties include shape-reconfiguration, tunable nonlinear stiffness and dynamic characteristics, multistability, and impact absorption.Since the architected origami materials obtain their unique properties from the 3D geometries of the constituent sheets or modules, they can be considered a subset of architected cellular solids or mechanical metamaterials. [35][36][37][38][39] However, the origami materials have many unique characteristics. The rich geometries of origami offer us great freedom to tailor targeted Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geomet...
This study investigates a unique asymmetric quasi-zero stiffness (QZS) property from the pressurized fluidic origami cellular structure, and examines the feasibility and efficiency of using this nonlinear property for low-frequency vibration isolation. This QZS property of fluidic origami stems from the nonlinear geometric relationships between folding and internal volume change, and it can be programmed by tailoring the constituent Miura-Ori crease design. Different fluidic origami cellular structure designs are introduced and examined to obtain a guideline for achieving QZS property. A proof-of-concept prototype is fabricated to experimentally validate the feasibility of acquiring QZS. Moreover, a comprehensive dynamic analysis is conducted based on numerical simulation and harmonic balance method approximation. The results suggest that the QZS property of fluidic origami can successfully isolate base excitation at low frequencies. In particular, this study carefully examines the effects of an inherent asymmetry in the force-displacement curve of pressurized fluidic origami. It is found that such asymmetry could significantly increase the transmissibility index with certain combinations of excitation amplitude and frequency, and it could also induce a drift response. Outcome of this research can lay the foundation for new origami-inspired multi-functional metamaterials and meta-structures with embedded dynamic functionalities. Moreover, the investigations into the asymmetry in force-displacement relationship provide valuable insights for many other QZS structures with similar properties.
This research investigates the potential effects of utilizing nonlinear springs on the performance of robotic jumping mechanisms. As a theoretical example, we study dynamic characteristics of a jumping mechanism consisting of two masses connected by a generic nonlinear spring, which is characterized by a piecewise linear function. The goal of this study is to understand how the nonlinearity in spring stiffness can impact the jumping performance. To this end, non-dimensional equations of motion of the jumping mechanism are derived and then used extensively for both analytical and numerical investigations. The nonlinear force-displacement curve of the spring is divided into two sections: compression and tension. We examine the influences of these two sections of spring stiffness on the overall performance of the jumping mechanism. It is found that compression section of the nonlinear spring can significantly increase energy storage and thus enhance the jumping capabilities dramatically. We also found that the tension section of the nonlinear force-displacement curve does not affect the jumping performance of the center of gravity, however, it has a significant impact on the internal oscillations of the mechanism. Results of this study can unfold the underlying principles of harnessing nonlinear springs in jumping mechanisms and may lead to the emergence of more efficient hopping and jumping systems and robots in the future.
Via numerical simulation and experimental assessment, this study examines the use of origami folding to develop robotic jumping mechanisms with tailored nonlinear stiffness to improve dynamic performance. We propose a multifunctional structure where the load-carrying skeleton of the structure acts as the energy-storage medium at the same time. Specifically, we use Tachi–Miura polyhedron (TMP) bellow origami—which exhibits a nonlinear ‘strain-softening’ force-displacement curve—as a jumping robotic skeleton with embedded energy storage. TMP’s nonlinear stiffness allows it to store more energy than a linear spring and offers improved jumping height and airtime. Moreover, the nonlinearity can be tailored by directly changing the underlying TMP crease geometry. A critical challenge is to minimize the TMP’s hysteresis and energy loss during its compression stage right before jumping. So we used the plastically annealed lamina emergent origami (PALEO) concept to modify the TMP creases. PALEO increases the folding limit before plastic deformation occurs, thus improving the overall strain energy retention. Jumping experiments confirmed that a nonlinear TMP mechanism achieved roughly 9% improvement in air time and a 13% improvement in jumping height compared to a ‘control’ TMP sample with a relatively linear stiffness. This study’s results validate the advantages of using origami in robotic jumping mechanisms and demonstrate the benefits of utilizing nonlinear spring elements for improving jumping performance. Therefore, they could foster a new family of energetically efficient jumping mechanisms with optimized performance in the future.
This research investigates a quasi-zero stiffness (QZS) property from the pressurized fluidic origami cellular solid, and examines how this QZS property can be harnessed for low-frequency base excitation isolation. The QZS property originates from the nonlinear geometric relations between folding and internal volume change, and it is directly correlated to the design parameters of the constituent Miura-Ori sheets. Two different structures are studied to obtain a design guideline for achieving QZS: one is identical stacked Miura-Ori sheets (ismo) and the other is non-identical stacked Miura-Ori sheets (nismo). Further dynamic analyses based on numerical simulation and harmonic balance method, indicate that the QZS from pressurized fluidic origami can achieve effective base excitation isolation at low frequencies. Results of this study can become the foundation of origami-inspired metamaterials and metastructures with embedded dynamic functionalities.
In this study, we examine a rapid and reversible origami folding method by exploiting a combination of resonance excitation, asymmetric multi-stability, and active control. The underlying idea is that, by harmonically exciting a multi-stable origami at its resonance frequencies, one can induce rapid folding between its different stable equilibria without the need for using responsive materials. To this end, we use a bi-stable water-bomb base as an archetypal example. Via numerical simulation based on a new dynamic model and experimental testing, we show that the inherent asymmetry of waterbomb bi-stability can enable dynamic folding with relatively low actuation requirements. For example, if the water-bomb initially settles at its "weak" stable state, one can use a base excitation to induce the intra-well resonance. As a result, the origami would fold and remain at the other "strong" stable state even if the excitation does not stop. The origami dynamics starting from the strong state, on the other hand, is more complicated. The water-bomb origami is prone to show inter-well oscillation rather than a uni-directional switch due to a nonlinear relationship between the dynamic folding behavior, asymmetric potential energy barrier, the difference in resonance frequencies, and excitation amplitude. Therefore, we develop an active feedback control strategy, which cuts off the base excitation input at the critical moment to achieve robust and uni-directional folding from the strong stable state to the weak one. The results of this study can apply to many different kinds of origami and create a new approach for rapid and reversible (self-)folding, thus advancing the application of origami in shape morphing systems, adaptive structures, and reconfigurable robotics. I. INTRODUCTIONOrigami-the ancient art of paper folding-has received a surge of interests over the past decade from many research communities, such as mathematicians, material scientists, biotics researchers, and engineers ([27]). A key driving factor underneath such interests is the seemingly infinite possibilities of developing three-dimensional shapes from folding a simple flat sheet. The kinematics (or shape transformation) of origami is rich and offers many desirable characteristics for constructing deployable aerospace structures ([40]), kinetic architectures ([7, 17]), self-folding robots ([16]), and compact surgery devices ([24, 33]). The mechanics of origami offers a framework for architecting material systems ([27]) with unique
This research investigates the feasibility of utilizing origami folding techniques to create an optimized jumping mechanism. As a theoretical example, we study the dynamic characteristics of a jumping mechanism consisting of two masses connected by a Tachi-Miura Polyhedron (TMP) origami structure with nonlinear stiffness characteristics. We show how the desired “strain-softening” effects of the TMP structure can lead to design of jumping mechanisms with optimized performance. The kinematics of TMP origami structure is reviewed and a modified model of its reaction-force displacement curve is presented. We derive the equations of motion of the jumping process and use their numerical solutions extensively for design optimization. Through this process we are able to obtain optimum geometrical configurations for two different objectives: The maximum time spent in the air and the maximum clearance off the ground. Results of this study can lead to emergence of a new generation of more efficient jumping mechanisms with optimized performance in the future.
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