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Zipper-coupled tubes are a unique structure consisting of two tubes with zig-zag walls that, when coupled in a zipper fashion, resist compression in the normal direction. A wider application of zipper-coupled tubes, however, is precluded by their angular form. By focusing on a subset of zipper-coupled tubes with parallel and coplanar creases constructed by repeating asymmetric degree-four vertex cells, we design a smooth sheet attachment that lies flat when the asymmetric zipper-coupled tubes are fully deployed, increasing the utility of the otherwise jagged tubes. Furthermore, we provide an explicit mathematical model of the motion of the resulting mechanism, thereby demonstrating its rigid-foldability.

Small-scale flexible (or compliant) mechanisms are valuable in replacing rigid components while retaining comparable motion and behavior. However, fabricating such mechanisms on this scale (from 0.01 to 10 cm) proves difficult, especially with thin sheet metals. The manufacturing method of laser forming, which uses a laser to cut and bend metal into desired shapes, could facilitate this fabrication. However, specific methods for designing mechanisms formed by lasers need to be developed. This work presents laser forming as a means for creating compliant mechanisms on this scale with thin sheet metal. The unique challenges for designing mechanisms to be laser formed are explored, and new adaptations of existing designs are fabricated and discussed. The design of basic “building-block” features is developed for several mechanisms: a parallel-guided mechanism, a cross-axis flexural pivot, a lamina emergent torsional (LET) joint array, a split-tube flexure, and a bi-stable switch. These mechanisms are shown to perform repeatable behavior and motion comparable to existing nonlaser-formed versions. The further possibilities for fabricating compliant mechanisms with laser forming are explored, as advanced applications can benefit from using lasers to create compliant mechanisms from thin sheet metal.

Deployable origami-based arrays can offer many benefits for a wide variety of engineering applications. However, alignment in the deployed state is a primary challenge of these arrays; in optical systems, local (single panel) and global (entire array) misalignment can drastically reduce performance. The objective of this work is to compare the relative sensitivities of different degrees-of-freedom (DOFs) of misalignment in deployable origami-based optical arrays and specify which have the greatest effect on performance. To accomplish this, we suggest a practice for defining local and global misalignment in deployable origami-based arrays, we simulate misalignment perturbations and record the resulting power output, and we use compensation techniques to restore as much lost power as possible. We use a deployable LiDAR telescope based on the hexagonal twist origami pattern as a case study, though the conclusions could be extended to other origami-based systems. From simulation, we find that the DOFs which are the most sensitive to misalignment and for which compensation is not effective are the local decenter X (467% power loss per mm misalignment), local decenter Y (463% power loss per mm misalignment), local tilt (357% power loss per degree misalignment), and local tip (265% power loss per degree misalignment) misalignments. These results could help minimize the need for compensation or position sensing and help optical systems designers to know which DOFs should be carefully controlled to maximize energy output.

In this paper we develop techniques for designing stable flat-foldable wooden furniture. Thickness-accommodation techniques used to enable folding of origami from thick materials are shown to also be applicable to wood. Specifically, wood may be used in (and is stable in) the unique load-bearing conditions of vertical lamina emergent torsional (LET) joints and arrays and angled-from-vertical modified origami tessellations, which utilize membrane joints to accommodate thickness. We present and analyze data for LET arrays of various heights in compression. In addition to being unique in load-bearing conditions, the presented structures are unique in that they are collapsible and deployable and fold from their deployed state to a completely flat state. The viability of using LET arrays as load-supporting joints — both in vertical and horizontal orientations — is also discussed. We present a design for a deployable stool and chair which gain their movement from carefully-placed LET joints and may be manufactured with a CNC mill from a single sheet of plywood. A design for a deployable chair based on an origami tessellation is also presented, which consists of six wooden panels cut on a CNC mill, and has a comparatively small surface area in its flat-folded state and may thus be more easily transported.

Zipper-coupled tubes constructed from Miura-ori cells are a unique structure consisting of two tubes which, when coupled in a zipper fashion, resist compression in the normal direction. A wider application of zipper-coupled tubes, however, is precluded by their angular form and symmetry. We demonstrate the construction of asymmetric zipper-coupled tubes based on an asymmetric degree-four vertex, along with a smooth sheet attachment that is flat when the asymmetric zipper-coupled tubes are fully deployed. Furthermore, we provide a mathematical model of the motion of the resulting mechanism, thereby demonstrating the rigid-foldability of the entire mechanism.

Design projects in childcare settings present unique design challenges because of their function, size, and specific safety concerns. In selecting effective childcare furniture, stowage space, safety, and ease of access for childcare furniture are important considerations. Origami-inspired design can be useful in addressing these issues in an innovative way by introducing flat-foldability and deployability into childcare furniture. Fundamental design considerations for childcare furniture and mechanical design principles for deployable furniture are examined in order to understand how to make safe and functional furniture pieces. Childcare furniture must be very child-safe. This means that origami principles used must not add safety concerns like decreased stability or pinch points. Nonhazardous, durable, and comfortable materials must be used. Extra precaution must be taken when designing folding structures for use in a childcare environment. Mechanical principles for such systems, including folding methods and thickness accommodation, are examined in the context of childcare spaces. Various types of joints are also examined and the M-LET compliant joint is shown as a potential replacement for rigid hinges in folding furniture. Using this understanding, this work presents two simple flat-folding techniques and a compliant joint suitable for a childcare setting and demonstrates these principles through functional “safe space” furniture.

Deployable origami arrays have been used to increase the aperture areas of spacecraft instruments. Folds within these patterns allow the arrays to fold compactly, but can also cause un-desired folding when in the deployed state. In addition, there is a need to deploy them with mechanisms that are light and small. This paper introduces a strain-energy storing joint that can be used to deploy and stiffen foldable origami arrays, called the Lenticular Lock (LentLock). The LentLock hinge design includes compliant flexures with geometry based on the Euler spiral. When panels are folded, the flexures are deflected flat and lie in-plane with the panels, storing strain energy. During deployment, the panels are released and the stored strain energy in the flexures opens the folded hinge. Simultaneously, the out-of-plane displacement of the deployed flexures is used to create beneficial interference to stabilize the array and prevent undesired refolding of the mechanism. In this paper, the geometry of the LentLock is introduced and performance of the joint is shown. The Lent-Lock is integrated into several folding mechanisms including a single fold, a single origami vertex, a Z-fold, and a multi-vertex origami array. Proof-of-concept prototypes of each folding pattern are shown.

This work introduces methods of developing embedded straight-line and linear-motion mechanisms on right circular cylinders. Developable surfaces, particularly right circular cylinders, are the manufactured embodiment of many products. Functional linkages are traditionally not geometrically constrained to a body and often dictate the final shape of the housing they reside in. This work explores the idea of mapping straight-line and linear-motion mechanisms onto cylinders for practical design purposes. Potential applications of embedded cylindrical developable mechanism capable of deployment and generation of linear motion would be useful are discussed. A design guideline is provided outlining the utility of using various linkages to complement a particular engineering design criteria.

Origami-inspired mechanisms can produce compact, easily-manufacturable designs. Compliant mechanisms have been used to create surrogate folds in many kinds of engineering materials by allowing large deflections without yielding. LET arrays are best used as surrogate folds when the regions being folded on each other have parallel sides, keeping the LET joint segment geometry constant. This consistency allows for homogeneous stresses/strains throughout the joint and constant curvature along the joint is achieved. However, when panel sides are irregular, optimal LET design is not necessarily obvious. This paper presents an exploration into characterizing folding motions of LET joints to achieve arbitrary curvatures of the folded region. Curvatures are obtained through variations in joint segment geometry whether length, width, thickness, or a combined approach. Testing of several specimens is conducted and the results are consistent with the analysis.

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano's first theorem and the Crotti-Engesser theorem, which don't require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

The field of foldable and physically reconfigurable antennas has recently attracted significant interest from diverse scientific communities, including researchers on antennas, material science, mechanical engineering and numerical modeling. Deployable, packable and multifunctional systems are very important for many applications, including satellite communications, UAVs, CubeSats as well as airborne and spaceborne communication systems. Foldable and physically reconfigurable antennas, particularly origami-based antennas, can provide new capabilities for the aforementioned applications. In this work, we present emerging research on foldable and physically reconfigurable antennas. Such antennas morph their shape to adapt and reconfigure their EM performance (e.g., frequency of operation, bandwidth, polarization, beamwidth, etc.). Also, origami antennas provide ultra-compact stowage, easy deployment, reduced weight, enhanced EM performance and multifunctional utility.

Origami patterns have been used in the design of deployable arrays. In engineering applications, paper creases are often replaced with surrogate folds by providing a hinge-like function to enable motion. Overconstraint observed in multivertex origami patterns combined with imperfect manufacturing may cause the resulting mechanisms to bind. The removal of redundant constraints decreases the likelihood of binding, may simplify the overall system, and may decrease the actuation force by reducing friction and other resistance to motion. This paper introduces a visual and iterative approach to eliminating redundant constraints in origami-based mechanisms through joint removal. Several techniques for joint removal are outlined and illustrated to reduce overconstraints in origami arrays.

A fully compliant multistable mechanism is a monolithic structure that is capable of staying at multiple positions without power input, and has many applications including switches, valves, positio...

An origami-based foldable and reconfigurable Reflectarray Antenna (RA) with multiple apertures is proposed for CubeSat applications. The proposed configuration consists of a central RA embedded in folding panels using Lamina Emergent Torsional (LET) joints based on compliant mechanisms. Depending on the folding direction of these panels (forward or backward), a new RA aperture is formed. The proposed RA along with its folding panels and hinges is fabricated using only a single PCB. A prototype of such an RA with two foldable panels is fabricated and measured. This RA operates in the Ku-band at 16 GHz and provides two pencil beams pointing at ( $\theta = 30^{\circ }$ , $\varphi = 0^{\circ }$ ) and ( $\theta = -30^{\circ }$ , $\varphi = 0^{\circ }$ ), and a dual-beam pointing at ( $\theta = +27^{\circ }$ , $\varphi = 0^{\circ }$ ) and ( $\theta = -29^{\circ }$ , $\varphi = 0^{\circ }$ ). The proposed RA provides a gain of 25 dB and 19 dB in its single- and dual-beam operations, respectively. For CubeSat applications, the key advantages of this RA are its small stowed volume, reconfigurable EM performance, beamsteering capabilities, monolithic construction, low fabrication cost, and reduced complexity.

This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of < 0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

The hexagonal twist origami pattern has characteristics that made it a candidate for next-generation deployable space arrays. It has a deployed area that is up to 3.3 times larger than the stowed area, has a single-degree-of-freedom which simplifies actuation, it is flat-foldable making flat positions possible in both stowed and deployed positions, and its rigid foldability means that its motion is enabled by rotation about distinct axes without deformation of its panels. Although the pattern shows promise for deployable systems, it cannot be directly applied with thick materials because of the self-intersection of nesting panels. This paper presents the kinematics and mechanical advantages of the hexagonal twist pattern, addresses the self-intersection problem by implementing five different thickness accommodation techniques and provides metrics for comparing thickness accommodation techniques to determine which would be best suited for a given application. The concepts are demonstrated through two applications: a deployable reflectarray antenna and a LiDAR telescope.

Deployable Euler spiral connectors (DESCs) are introduced as compliant deployable flexures that can span gaps between segments in a mechanism and then lay flat when under strain in a stowed position. This paper presents models of Euler spiral beams combined in series and parallel that can be used to design compact compliant mechanisms. Constraints on the flexure parameters of DESCs are also presented. Analytic models developed for the force-deflection behavior and stress were compared to finite element analysis and experimental data. A spinal implant and a linear ratcheting system are presented as illustrative applications of DESCs.

Folding is a manufacturing method which can create complex 3D geometries from flat materials and can be particularly useful in cost-sensitive or planar-limited fabrication applications. This paper introduces compliant mechanisms that employ folding techniques from origami to evolve from a flat material to deployed state. We present origami-inspired sacrificial joints, joints which have mobility during assembly of the mechanism but are rigid in their final position, to create regions of high and low stiffness and the proper alignment of compliant flexures in folded mechanisms. To demonstrate the method we fold steel sheet to create some well-known and complex compliant mechanisms.

The ability of origami to alter its properties and behaviors with its shape makes it an elegant source of inspiration for many engineering designs challenges. Fold states specify the shape of the origami – its facets, creases, and fold angles. Origami research recognizes several acknowledged fold states: the unfolded, fully folded, and flat-folded states. However, these fold states are not comprehensive, excluding some of the most predominant fold states in origami-based devices. In this paper we propose a comprehensive list of fold states based on fold angles. We support the method of categorizing fold states by evaluating the functions and fold states of a large sample of origami-based devices. These correlations provide insight for selecting fold states for origami-based design. We discuss properties and behaviors of the fold states individually and provide a process for fold-state selection.

This paper proposes a novel mechanically frequency reconfigurable high-gain Reflectarray Antenna (RA) design, which is based on the Augmented Square Twist (AST) origami folding pattern. The RA was designed to operate at two operating frequencies, 20 GHz (lower band) and 40 GHz (upper band) in its unfolded and folded states, respectively. The main beam is directed along φ = 90°, θ = 30° at the lower band and φ = 90°, θ = 20° at the upper band. The RA was excited by a 15 dBi linearly polarized standard gain horn antenna positioned at a focal distance of 9.6λ with a 20° offset angle. The proposed origami RA achieved a gain of 27.0 dBi and 28.6 dBi at its unfolded and folded states, respectively.

A novel foldable and reconfigurable reflectarray antenna (RA), operating at 8.425GHz for deep space communications based on an extended Miura-Ori origami pattern is presented. The aperture leverages the properties of subdivision and a folding feature to create a packable and reconfigurable antenna capable of changing its beam from a single pencil beam to a multi-beam aperture with beamsteering ability. A mechanical and theoretical EM analysis is carried out supported by a numerical algorithm using array theory. The results show that the proposed reflectarray can achieve a high packing efficiency of 92%. This RA provides a pencil beam in the broadside at (θ = 0°, ϕ = 0) in its flat configuration and multi-beam (dual, triple and quad-beams) depending on its folding angle. For CubeSat applications, the key advantages of this RA are its decreased stowage volume, reconfigurable EM performance, beamsteering capabilities, low fabrication cost, and reduced complexity.