This research explores a segmented parabolic antenna that can change its physical shape via shape memory alloy actuators, thereby altering its radiation pattern when transmitting a signal. The parabolic dish has been discretized into an origami pattern to make use of the naturally compliant fold regions, about which shape memory alloy wires create moments. Modeling of antenna deformation is accomplished via Abaqus considering SMA wires contracting due to temperature change as a manifestation of the shape memory effect. An electromagnetic analysis of the deformed antenna follows in ANSYS-HFSS to determine the antenna gain in all directions around the structure. The computed radiation pattern is projected onto a goal shape (e.g. the contiguous United States) to determine the degree to which the shaped broadcast pattern matches that of a desired broadcast area. Finally, the design is iterated using an efficient global optimization algorithm to ascertain an actuation schedule that generates the most conformal broadcast pattern. Traditional optimization algorithms such as genetic or particle swarm may require thousands of designs, particularly when many design variables are considered. The efficient global optimization algorithm employs far fewer designs by fitting surrogate models to the data and only testing points where large improvement is expected, thus reducing design optimization time. The evolution and improvement to an antenna will be discussed for an antenna making use of eight, 16, and 24 SMA linear actuators to most optimally broadcast to only the United States while avoiding signal spill-over into other regions, and the lessons learned can then applied to match broadcast pattern based on other countries as well.

Origami-inspired structures and material systems have been used in many engineering applications because of their unique kinematic and mechanical properties induced by folding. However, accurately modeling and analyzing origami folding and the associated mechanical properties are challenging, especially when large deformation and dynamic responses need to be considered. In this paper, we formulate a high-fidelity model — based on the iso-parametric Absolute Nodal Coordinate Formulation (ANCF) — for simulating the dynamic folding behaviors of origami involving large deformation. The center piece of this new model is the characterization of crease deformation. To this end, we model the crease using rotational spring at the nodes. The corresponding folding angle is calculated based on the local surface normal vectors. Compared to the currently popular analytical methods for analyzing origami, such as the rigid-facet and equivalent bar-hinge approach, this new model is more accurate in that it can describe the large crease and facet deformation without imposing many assumptions. Meanwhile, the ANCF based origami model can be more efficient computationally compared to the traditional finite element simulations. Therefore, this new model can lay down the foundation for high-fidelity origami analysis and design that involve mechanics and dynamics.

An origami design pattern is integrated to an active control system through camber morphing for vibration suppression and gust load alleviation in a typical wing section. Origami design parameters are optimized to have high sensitivity in chordwise fold angle and a maximum camber of 10% chord. A LQR controller is used to achieve the desired vibration suppression in a lightly damped aeroelastic system. The desired vibration suppression is achieved with change in camber of below 5% chord for an initial displacement condition induced vibration and less than 1% chord for gust excited vibration. Results also show that camber morphing is effective in suppressing vibration in both pitch and plunge degrees of freedom simultaneously.

In the growing field of origami engineering, self-folding is of a high regard. The latter is regularly used by nature as an efficient approach for autonomous growing and reorganizing. In this work, we present a self-folding approach based on Electro-Active Polymer (EAP), especially Conductive Polymers (CP). This approach proposes lightweight, compact and energy efficient self-folding structures, as well as large angle and reversible folding. We study the behavior of a three-segment milli-structure containing two passive segments made of paper, separated by an active segment made of CP. The folding motion of the structure was modeled and experimentally validated. Furthermore, as a proof of concept, a self-folding origami cube is presented.

Recent work has used self-folding origami inspired composites to produce complex, scalable, affordable, and lightweight morphing structures [1]. These characteristics are of interest for engineering applications, in fields including aerospace [2] and medical devices [3]. Due to these advantages, research on self-folding smart composites has grown, with a particular focus on the use of laminate manufacturing techniques that stack layers of heterogeneous materials to generate functional composites. Previous work used this approach to manufacture self-folding origami inspired robots [1]. A simple shape memory composite design consists of a smart material (e.g. a one-way shape memory polymer, or SMP) sandwiched between patterned rigid layers. These SMPs change their shape in response to an external stimulus (e.g. temperature). Upon heating above the phase transition temperature of the polymer ( Tt ), the SMP contracts, causing the laminate to fold. The SMPs used in self-folding laminate composites are unidirectional and thus the laminate is unable to recover its original state without application of external force. In this work, we study the use of thermal responsive liquid crystal elastomers (LCE) for reversible self-folding and actuation of origami inspired composites using laminate manufacturing. LCEs are smart materials that exhibit reversible deformation, good strain recoverability, and tailorable properties (i.e. phase transition temperature, strain, and orientation of deformation) [4–6]. We explore two composite hinge designs using laminate manufacturing process [1, 7] with a Joule heating layer to enable self-folding: one where the LCE acts as a tensile actuator connected only on the edges of the rigid layer, which we call a tensional hinge, and a second where the LCE is attached along the patterned rigid layer hinge, which we call a flexural hinge. The angular displacements of these two hinge designs are estimated using geometric models that account for the contraction of the LCE upon heating, and compared against experimental measurements. The maximum blocked torque of the composite hinges is also measured experimentally. To demonstrate the use of LCE as an active layer for origami inspired composites, we also present a laminate crawler robot. The crawling locomotion is controlled with an electrical heating layer laminated on the LCE. These results demonstrate the possibility of using LCE to achieve rapid, reversible folding and to generate similar torques, as compared to previous work in origami inspired self-folding composite.

This manuscript investigates the flexural wave propagation behavior of a foldable metamaterial structure. Origami-inspired foldable structures are making inroads into many engineering applications — deployable solar cell arrays, foldable telescope lenses, foldable automotive airbags, to name a few; driven primarily by some of the remarkable mechanical properties (high stiffness, negative Poisson’s ratio, bistability etc.) of these structures. The chief motivation of this research is a comprehensive analysis of flexural wave propagation in such foldable structures. The repeating unit cell of the structure consists of an Euler-Bernoulli beam and a torsion spring. Transfer Matrix (TM) method is used to analyze the vibration attenuation properties of the structure and it is shown that the structure exhibits bandgap behavior. The obtained bandgaps are validated using Finite Element Analysis (FEA). Using the characteristic equation of the transfer matrix, we derive a transcendental equation for the bandgap edge frequencies. We show that for the n th band gap, the second band edge frequency is always equal to the natural frequency of the n th modeshape of the constituent beam under the simply supported condition. This frequency, therefore, is independent of the torsion spring constant. In addition, a detailed parametric study of the variation in band edge frequencies when the geometric and material parameters of the structure (Young’s modulus of beam, torsional spring constant, width and thickness of beam etc.) are varied is conducted. It is concluded that the ratio of flexural rigidity of the beam to the torsion spring constant (EI/k t ) is an important parameter affecting the width of the bandgap. For low values of the ratio, i.e., low beam flexural rigidity and high torsional stiffness, the first band edge frequency is almost equal to the second band edge and, effectively, no bandgap exists. As the stiffness ratio increases, i.e. high flexural rigidity (EI of the beam) and low torsional stiffness k t , the first band edge frequency assumes progressively lower values relative to the second band edge and we obtain a relatively large bandgap over which no flexural waves propagate. This has important ramifications for the design of foldable metamaterial structures.

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.

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 locking-induced 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, large-amplitude 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 frequency-amplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenario 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.

The design of compliant mechanisms made of Nickel Titanium (NiTi) Shape Memory Alloys (SMAs) is considered to exploit the superelastic behavior of the material to achieve tailored high flexibility on demand. This paper focuses on two-stage design optimization of compliant mechanisms, as a systematic method for design of the composition of the functionally graded NiTi material within the compliant mechanism devices. The location, as well as geometric and mechanical properties, of zones of high and low flexibility will be selected to maximize mechanical performance. The proposed two-stage optimization procedure combines the optimization of an analytical model of a single-piece functionally graded unit, with a detailed FEA of a continuous compliant mechanism. In the first stage, a rigid-link model is developed to initially approximate the behavior of the compliant mechanism. In the second stage the solution of the rigid-link problem serves as the starting point for a continuous analytical model where the mechanism consists of zones with different material properties and geometry, followed by a detailed FEA of a compliant mechanism with integrated zones of superelasticity. The two-stage optimization is a systematic approach for compliant mechanism design with functional grading of the material to exploit superelastic response in controlled manner. Direct energy deposition, as an additive manufacturing technology, is foreseen to fabricate assemblies with multiple single piece functional graded components. This method could be applied to bio-inspired structures, flapping wings, flexible adaptive structures and origami inspired compliant mechanisms.

Origami provides inspiration and solutions to the fabrication and functionality of various structures. Origami design methods in the literature are limited to the idealization of the folds as creases of zeroth-order geometric continuity. This idealization is not proper for origami structures having non-negligible fold thickness or maximum curvature at the folds restricted by material or structural limitations. For these structures, the folds are not accurately represented as creases but instead as bent regions of higher-order geometric continuity. These fold regions of arbitrary order of continuity are denoted in this work as smooth folds. A method for the design of a single planar sheet and its associated pattern of smooth folds that morphs into a given three-dimensional goal shape represented as a polygonal mesh is proposed. The parameterization of the planar sheet and the constraints allowing for a valid smooth fold pattern and matching of the goal shape in a folded configuration are presented. The folding deformation of the determined sheet designs is simulated using a previously derived kinematic model for origami with smooth folds. Various testing examples considering diverse goal shapes are presented. The results demonstrate that each considered sheet design matches its corresponding goal shape in a known folded configuration having fold angles determined from the geometry of the goal mesh. The proposed method can be used for the design of origami structures having folds of arbitrary order of geometric continuity such as origami-inspired active structures.

With the development of smart materials such as electroactive polymers and magnetoactive elastomers, active origami structures, where desired folded shapes can be achieved using external electric and magnetic stimuli, are showing promising potential in many engineering applications. In this study, finite element analysis (FEA) models are developed in 3-D using COMSOL Multiphysics software for unimorph bending and folding actuated using a single external field, and a bi-fold configuration which is actuated using multi-field stimuli. The objectives of the study are: 1) to investigate folding behavior and effects of geometric parameters, and 2) to maximize actuation for a given stimulus. Experimentally determined mechanical pressures and moments are applied as external loads to simulate electric and magnetic fields, respectively. Good agreement is obtained in the tip displacement and folding angles between the simulation and experiments, which demonstrates the effectiveness of the FEA model.

Robert Lang has brought functionality to origami, the art of paper folding, by developing an extensive series of “action origami” figures. As the name suggests, these figures can perform actions and produce an output motion with the help of manual actuation, unlike traditional origami. For instance, different figures can bite, row, and fly. The goal of this research study is to adapt a few of these action origami figures put forth by Robert Lang to create ‘active’ action origami; these systems, instead of relying on manual actuation for motion, will rely on electro-mechanical actuation. This electro-mechanical actuation will be achieved through the judicious use of an electroactive polymer known as P (VDF-TrFE-CTFE) terpolymer. The terpolymer’s in-plane motion in response to an electric field is converted into bending using a unimorph configuration. This bending motion is exploited to actuate three so-called “action origami” structures: the flapping butterfly, the catapult, and the barking dog. Based on knowledge of the kinematics of the origami structures, multilayered terpolymer actuator is placed strategically on the origami figures with an aim to maximize the resulting actuation motion. In order to understand the behavior, capabilities, and limitations of the terpolymer as an active material, both qualitative and quantitative data are collected from the actuation of these three different action origami structures as a function of number of terpolymer layers, applied electric field and frequency of the applied field. The goal is to find the suitable shapes and crease patterns of the structures as well as the configurations with the terpolymer film to maximize the actuation. These three structures are tested and results show that PVDF-terpolymer is an effective actuator with ability to deform a substrate to a desired shape in the presence of an electric field: the butterfly was able to flap, the mouth of the dog was able to “bark,” and the catapult was able to launch a small ball of paper. Through experimentation, it was determined what parameters affect actuation and furthermore what values of those parameters will maximize the actuation.

The Starshade is a future exoplanet discovery mission consisting of a satellite and a 34 meter diameter starshade used to block the light of a star of interest, enhancing visualization of the orbiting planets. The starshade itself is composed of a number of 7 meter long petals surrounding a 20 meter diameter optical shield. A critical design requirement of the optical shield is stowage in a 3 meter diameter area during launch. Origami has been investigated as a means of collapsing the optical shield, specifically a family of action origami models known as “flashers.” In this paper a dynamic model of an optical shield design candidate based on a flasher pattern is created in Adams 2014. As these patterns can have many parts and joints, a method for the automatic creation of dynamic models using information about the geometry of the crease pattern is utilized. As the fabricated optical shield panels will be somewhat flexible, each quadrilateral panel is modeled as two rigid triangles connected with a joint. The effect of joint stiffness on the forces and torques developed during deployment is investigated. It is found that the optical shield design is rigid foldable if the panel flexibility is taken into account by additional joints, which are found to bend from 10° – 40°. Joint forces are predicted over the deployment, and maximum and average joint forces are tabulated. These and other insights gained from the dynamic model can help guide future Starshade design decisions, and similar analyses can be performed for other origami-inspired deployable structures.

Origami-inspired active structures have important characteristics such as reconfigurability and the ability to adopt compact flat forms for storage. A self-folding shape memory alloy (SMA)-based laminated sheet is considered in this work wherein SMA wire meshes comprise the top and bottom layers and a thermally insulating compliant elastomer comprises the middle layer. Uncertainty in various parameters (e.g. material properties) may affect the performance of the sheet, which is explored here. Different modeling approaches are studied in order to compare their accuracy and computational cost. A numerical approach based on the Euler-Bernoulli beam theory is selected due to its accuracy when compared to higher fidelity finite element simulations and its low computational cost, necessary to perform a large number of design evaluations as required for uncertainty analysis. Optimization is performed considering uncertainty in the material properties. Failure probabilities under mechanical constraints and expected values of fold curvature and blocking moment are considered during optimization of the self-folding sheet. The multiobjective genetic algorithm for technology characterization P3GA is used to obtain the Pareto dominant designs. Most designs forming the Pareto frontier have the same values for certain design parameters such as the distance between the wires in the SMA meshes non-dimensionalized by SMA wire thickness, elastomer layer thickness non-dimensionalized by SMA wire thickness, and applied temperature. The design parameter deciding the trade-off between fold curvature and blocking moment is found to be the SMA wire thickness.

Origami inspired structures possess attractive characteristics such as the potential to be reconfigurable and the capability to be folded into compact forms for storage. Self-folding structures, which are systems able to perform folding operations without external mechanical input, are desirable in certain circumstances such as remote applications (e.g., space applications, underwater robotics). A self-folding structural sheet consisting of two outer layers of shape memory alloy (SMA) orthogonal wire meshes separated by an inner insulating layer is considered in this work. The inner layer consists of ABS plastic columns that connect the SMA wire mesh intersections of the top and bottom layers, which are co-located and co-oriented (denoted sparse middle layer/aligned meshes design). Significant reduction on the heat transfer between the SMA layers is expected in this design compared to previously considered designs with continuous or perforated elastomeric middle layers. The geometric and power input parameters of the sparse middle layer/aligned meshes design are optimized under mechanical and thermal constraints considering finite element and reduced order analytical models. The optimal folding performance of the sparse middle layer/aligned meshes design is compared to that of the previous designs. The results show that the sparse middle layer/aligned meshes design has promising characteristics as a self-folding structural sheet and provides for tighter folds compared to the designs with elastomeric middle layers.

The goal of this research is to experimentally characterize the capabilities of a concept for a self-folding reconfigurable sheet for use in origami-inspired engineering design and to use this characterization to validate simulations of physics-based models of the sheet. The sheet consists of an active, self-morphing laminate that contains two shape memory alloy (SMA) mesh layers and a passive compliant medium between these layers. The SMA layers are thermally actuated, allowing bending to occur in both positive and negative directions to create soft hill and valley folds. These folds are completely reversible, allowing the structure to fold and unfold without permanent deformation. Unlike past work on self-folding structures, these sheets can have folds along any line, be subsequently unfolded, and then be folded again in a new way. To explore the effect of changing design parameters on the performance metrics of the sheet, it is desirable to use Finite Element Analysis (FEA) simulations instead of relying on time consuming experiments. Such models have been created incorporating user material subroutines (UMATs) in an FEA solver such as Abaqus to capture material behavior, but these must now be validated against experimental data to establish how well they match experimental performance. The primary performance metric of the sheet was chosen to be the radius of curvature measured perpendicularly to the line of heating. Both experiment and simulation focus on the radius of curvature achieved by the sheet for a given set of design parameters and actuation path. The goal of validation is to achieve a desirable level of agreement and repeatability in these results. To measure the deformation and curvature in the sheet as it actuates, a 3D Digital Image Correlation (3D DIC) system is employed to track the movement of points along the surface of the sample as it is heated to a temperature above the transformation temperature of the SMA and allowed to fully actuate. These tools are utilized for a number of samples so that validation of the sheet encompasses multiple values for each of the primary design parameters.

We are investigating the use of dielectric elastomers (DE) to realize origami-inspired folding and unfolding of structures. DEs are compliant materials where the coupled electro-mechanical actuation takes advantage of the low modulus and high breakdown strength of the elastomer. Until recently, pre-straining of relatively thick DE materials was necessary in order to achieve the high electric fields required to trigger electrostatic actuation. However, the current availability of thinner DE materials (ex: VHB 9469PC-130μm, VHB 9473 PC −260 μm) has enabled their actuation at achievable electric fields without the need to pre-strain. In this work, an exhaustive study on the fundamentals of DE actuation is done by exploring thickness actuation mechanism and studying the change in dielectric permittivity; we also take advantage of the thin DEs to build actuators with very large bending angles. In particular, we relate the electrostatically-induced thickness contraction in a DE monomorph to the resulting bending once an inactive substrate is added. Both statically and dynamically induced electromechanical thickness strains are measured, and the experimental data is used as an input to a bender model to predict and optimize bending response; variables such as type of inactive material, number of DE layers, and type of electrodes are examined. We will also experimentally track the changes in the dielectric constant as a function of strain, electrode type, and applied electric field; the measured behavior will be used to model thickness and bending actuation. These fundamental studies are necessary to determine ability and limitation of DE materials in a bender configuration. Finally, bending of the DE actuator is transformed into folding by a novel geometric approach, where different shaped notches are introduced in the inactive substrate. The folding configuration is a step towards realizing active origami structure.

The objective of this paper is to show the development of a compact, self-deploying array based on the tapered map fold. The tapered map fold was modified by applying an elastic membrane to one side of the array and adequately spacing the panels adjacent to valley folds. Through this approach, the array can be folded into a fully dense volume when stowed. The panels are dimensioned to account for the panel thickness when folded, which otherwise would prevent the model from reaching a fully dense form. The folding motion is achieved by creating a rigid-foldable model of the origami-inspired crease pattern. The paper discusses a variety of approaches for creating rigid origami from the map fold, including pleat hinges and spacer panels. The tapered map fold is rigid-foldable through the incorporation of tapered spacer panels. By choosing appropriate values for the angles and tapered spacer panel dimensions, the tapered map fold is fully dense when stowed. The tapered spacer panels also enable the model to have a single degree of freedom of actuation. Stored strain energy in the elastic membrane enables self-actuation of the model. Applying a membrane also simplifies fabrication of the array. Potential applications for the array include a collapsible solar array, or other military or backpacking applications.

This paper presents the conceptualization and modeling of a compliant forceps design, which we have called Oriceps, as an example of origami-inspired design that has application in a variety of settings including robotic surgeries. Current robotic forceps often use traditional mechanisms with parts that are difficult to clean, wear quickly, and are challenging to fabricate due to their complexity and small size. The Oriceps design is based on the spherical kinematic configurations of several action origami models, and can be fabricated by cutting and folding flat material. This design concept has potential implementation as surgical forceps because it would require fewer parts, be easier to sterilize, and be potentially suitable for both macro and micro scales. The folded and planar characteristics of this design could be amenable to application of smart materials resulting in smaller scale, greater tool flexibility, integrated actuation, and an adaptability to a variety of tool functions. The suitability of shape-memory materials for use in Oriceps is discussed.