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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.

Design parameters of the origami flasher pattern can be modified to meet a variety of design objectives for deployable array applications. The focus of this paper is to improve the understanding of design parameters, objectives, and trade-offs of origami flasher pattern configurations. Emphasis is placed on finite-thickness flasher models that would enable engineering applications. The methods presented aim to provide clarity on the effects of tuning flasher parameters based on existing synthesis tools. The results are demonstrated in the design of a flasher-based deployable LiDAR telescope where optimization is used to converge on optimal design parameters and the results are implemented in proof-of-concept hardware.

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...

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.

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.

Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved Lamina Emergent Torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.

We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this article have motion paths that necessarily contain bifurcation points, which lead to an unbounded array of motion paths in the parameterization plane.

The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional optimization algorithm is presented to place joints to minimize the error from the rigid-link approximation and account for additional manufacturing and stress considerations in the torsion bars. A proof is presented to show that equal torsion spring spacing along the horizontal axis of deployed parabolic profiles will result in minimizing the area between the model’s rigid-link approximation and smooth curve. The model is demonstrated through the physical construction of a deployable airfoil surface and a metallic deployable parabolic reflector.

We present a resource for designing bistable developable mechanisms (BDMs) that reach their second stable positions while exterior or interior to a cylindrical surface. Analysis of the necessary conditions to create extramobile and intramobile cylindrical BDMs is conducted through a series of three tests. These tests contain elements of both existing and new mechanism design tools, including a novel graphical method for identifying stable positions of linkages using a single dominant torsional spring, called the principle of reflection. These tests are applied to all possible mechanism cases and configurations to identify why certain configurations will always, sometimes, or never be a BDM. Two tables summarize these results as a guide when designing extramobile and intramobile BDMs. The results are compared and demonstrated with a numerical simulation of 30,000+ mechanisms, including several example mechanisms that illustrate the concepts discussed in the work. Discussion is then provided on the implication of these results.

This work develops and presents design concepts and models of thickness-utilizing deployable hard stops (ThUDS) which can be incorporated into origami-based design applications to provide stability in specific fold states. A ThUDS, like a lamina-emergent mechanism, emerges from a flat state and can reside within a sheet. A variety of planar and spherical ThUDS configurations are developed and presented, using diagrams, equations, and prototypes. Examples of ThUDS applications are given and attributes are discussed. Considerations for the design of a ThUDS are discussed. This work outlines how a ThUDS can maintain foldability while improving stability and utilizing thickness. Parameter values for prototypes are also given for reader reproduction.

Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load–displacement for general serial–parallel formulations of LET arrays for three degrees-of-freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis, and to show variability of the LET array design space, several verification plots over a range of parameters are provided.

This paper presents the development of an origami-inspired support system (the OriGuide) that enables the insertion of flexible instruments using medical robots. Varying parameters of a triangulated cylindrical origami pattern were combined to create an effective highly compressible anti-buckling system that maintains a constant inner diameter for supporting an instrument and a constant outer diameter throughout actuation. The proposed origami pattern is composed of two repeated patterns: a bistable pattern to create support points to mitigate flexible shaft buckling and a monostable pattern to enable axial extension and compression of the support system. The origami-based portion of the device is combined with two rigid mounts for interfacing with the medical robot. The origami-based portion of the device is fabricated from a single sheet of polyethylene terephthalate. The length, outer diameter, and inner diameter that emerge from the fold pattern can be customized to accommodate various robot designs and flexible instrument geometries without increasing the part count. The support system also adds protection to the instrument from external contamination.

We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multiloop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of planar unfolded state, parallel-stacked panels in the flat-folded state and kinematic single-degree-of-freedom motion from the flat-unfolded to the flat-folded state. The paper develops the mathematics defining the necessary offsets, beginning with a symmetric bird’s-foot vertex, and then shows that the joints can be developed for asymmetric flat-foldable systems. Although in the general case there is no guarantee of achieving perfect kinematic motion, we show that for many cases of interest, the deviation is a tiny fraction of the plate thickness. Mechanical realizations of several examples are presented.

Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.

Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

This paper reports the study of a planar Cross-Axis Flexural Pivot (CAFP) comprising an additional contact pair. The proposed device may be useful for applications requiring a revolute joint that behaves differently when deflecting clockwise/anti-clockwise. The presence of the contact pair reduces the free length of one flexures, resulting in a considerable increment of the overall joint stiffness. The pivot behaviour is investigated, for different load cases, via the Chained-Beam-Constraint Model (CBCM), namely an accurate method to be applied in large deflection problems. A framework comprising Matlab and ANSYS is developed for testing the CAFP performances in terms of rotational stiffness, parasitic shift and maximum stress, with different combinations of geometrical aspect ratios and contact extensions. Results achieved via CBCM for a pure rotation applied to the CAFP’s output link are then verified through Finite Element Analysis. The resulting performance maps show good agreement between the numerical results. Furthermore, the CBCM shows an improved computational efficiency, which is a crucial aspect for preliminary design steps. At last, direct comparison between simulations and experiments, developed by means of two custom test rigs, confirms the efficacy of the proposed design method for the modeling of contacts in large deflection problems.

Kinetostatic analysis of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a kinetostatic modeling method for flexure-hinge-based compliant mechanisms with hybrid serial-parallel substructures is presented to provide accurate and concise solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of flexure hinges/flexible beams is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent two-node element simple. A general kinetostatic model of the whole compliant mechanisms is first established based on the equilibrium equation of the nodal force. Then, a condensed two-port mechanical network representing the input/output force-displacement relations of single-degree-of-freedom (DOF) compliant mechanisms and the Jacobian matrix for multi-DOF compliant mechanisms are respectively built. Comparison of the proposed method with the compliance matrix method in previous literature, finite element analysis and experiment for three exemplary mechanisms reveals good prediction accuracy, suggesting its feasibility for fast performance evaluation and parameter optimization at the initial stage of design.

Light-weight origami-inspired mechanisms can provide advantages in deployable space systems and other applications. However, a significant challenge in their design is ensuring that they are sufficie...

The potential of compliant mechanisms and related origami-based mechanical systems to store strain energy make them ideal candidates for applications requiring an actuation or deployment process, such as space system arrays, minimally invasive surgical devices and deployable barriers. Many origami structures can be thought of as a compliant mechanism because, like compliant mechanisms, its function is performed through the elastic deformation of its members. This stored strain energy could prove useful. There are opportunities using strain energy to develop approaches to deploy particular mechanical systems. In order to better understand the principles of self-actuation and promote the designs of such systems, a taxonomy of deployable origami mechanisms is presented. This taxonomy demonstrates that there are several different types of deployable origami mechanisms and provides an organizational method to better understand the design space. Characteristics of self deployment in concentrated, deployable origami strain energy mechanisms with internal actuation are identified and examples of strain energy based deployment are provided.

Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural—or lowest energy—configurations that physical models will preferentially assume. We present normalized coordinate equations—equations that relate fold surface properties to their edge of regression—to simplify curved-fold relationships. An energy method based on these normalized coordinate equations is developed to identify natural configurations of general curved folds. While it has been noted that natural configurations have nearly planar creases for curved folds, we show that nonplanar behavior near the crease ends substantially reduces the energy of a fold.

This work introduces a type of motion termed “conceal-and-reveal” which is characterized by a state that protects a payload, a state that exposes the payload, and coupled motions between these two states. As techniques for thick, rigid origami-based engineering designs are being developed, origami is becoming increasingly more attractive as inspiration for complex systems. This paper proposes a process for designing origami-based conceal-and-reveal systems, which can be generalized to design similar thick, rigid origami-based systems. The process is demonstrated through the development of three conceal-and-reveal systems that present a luxury product to the consumer. The three designs also confirm that multiple origami crease patterns can be used to initiate viable approaches to achieving conceal-and-reveal motion.

The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces "developable mechanisms" as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.

A fully compliant constant-force mechanism that uses an initially angled parallel-guiding mechanism is proposed. A pseudo-rigid-body model (PRBM) of the mechanism is developed and validated using both finite element models and experimental prototype testing. The PRBM is used as a preliminary design tool to identify parameters that result in a constant-force mechanism. An adjustable version of the mechanism is also proposed and is used to assess the range of validity of the PRBM and highlights how the system response can be varied by changing the flexible beams inclination. A finite element based optimization is used to create a modified version of the mechanism that incorporates beam-end rotation effects and offers greater performance. Potential applications for the mechanism are discussed and it is demonstrated as a component of a statically balanced system.

This work details the integration of three distinct methods for altering the stiffness of compliant joints: lattice flexures, compound joints, and static balancing. The methodology for applying these strategies is discussed in detail. Lattice flexures are a flexure modification that leads to low motion-direction bending stiffness. Compound joints improve a compliant joint's load-carrying ability and off-axis stiffness. Static balancing in this case is achieved through the addition of an auxiliary energy storage device. To statically balance a compound lattice-flexured cross-axis flexural pivot, the load-dependent stiffness behavior of a cross-axis flexural pivot (CAFP) with two lattice flexure types is determined. A balancer spring design is developed that is fully 3D-printable. The balancer is combined with a compound lattice-flexured CAFP. Physical hardware is 3D printed in titanium and its torque-displacement behavior is measured. The resulting device requires 1% of the actuation energy of a conventional CAFP of the same dimensions and material.

Similar to the general class of metamaterials, compliant arrays (CAs) are engineered from an array of subelements that combine to produce a response that is typically not available from a flat panel made of a single material. As such, analysis and design of CA systems requires the integration of both the material and geometrical properties of the array. This paper proposes a convenient and efficient method of combining these essential elements using analytically derived shape factors for bending modes. The approach is validated experimentally, and used to demonstrate large regions of previously inaccessible property combinations in material selection charts that become attainable using carefully design CAs. Keywords: Shape factor, Bending, Material selection, Compliant, Stiffness, Metamaterials

Several methods have been developed to accommodate for the use of thick materials in origami models which preserve either the model's full range of motion or its kinematics. The offset panel technique (OPT) preserves both the range of motion and the kinematics while allowing for a great deal of flexibility in design. This work explores new possibilities for origami-based product applications presented by the OPT. Examples are included to illustrate fundamental capabilities that can be realized with thick materials such as accommodation of various materials in a design and manipulation of panel geometry resulting in an increased stiffness and strength. These capabilities demonstrate the potential of techniques such as the OPT to further inspire origami-based solutions to engineering problems.

This work describes a deployable compliant rolling-contact element joint (D-CORE joint) that employs curved-folding origami techniques to enable transition from a flat to deployed state. These deployable joints can be manufactured from a single sheet of material. Two fundamental configurations of the D-CORE are presented. The first configuration allows for motion similar to that of a Jacob's ladder when the joint is in a planar state while achieving the motion of a CORE when in the deployed state. The second configuration constrains all degrees of freedom to create a static structure when the joint is in the planar state and allows for the motion of a CORE in the deployed state. Curved-folding origami techniques can be used with both configurations to control the cam radius and range of motion of the D-CORE. Physical models are demonstrated in Tyvek®, polycarbonate, polypropylene, and metallic glass. A deployable translating platform constructed of an inversion of the D-CORE is also shown.

An approach for designing developable mechanisms on a conical surface is presented. By aligning the joint axes of spherical mechanisms to the ruling lines, the links can be created in a way that the mechanism conforms to a conical surface. Terminology is defined for mechanisms mapped onto a right cone. Models are developed to describe the motion of the mechanism with respect to the apex of the cone, and connections are made to cylindrical developable mechanisms using projected angles. The Loop Sum Method is presented as an approach to determine the geometry of the cone to which a given spherical mechanism can be mapped. A method for position analysis is presented to determine the location of any point along the link of a mechanism with respect to the conical geometry. These methods are also applied to multiloop spherical mechanisms.

Contact-aided compliant mechanisms (CCMs) utilize contact to achieve enhanced functionality. The contact phenomenon of CCMs increases the difficulties of their analysis and design, especially when they exhibit beam-to-beam contact. Considering the particularity of CCMs analysis, which is more about the mechanisms’ deformation, this paper presents a numerical method to analyze the large deflection and stress of the CCMs considering beam-to-beam contacts. Based on our previous work on beam-to-rigid contact, the large deformation of general beams in CCMs is modeled by using the chained pseudo-rigid-body model (CPRBM). An approximation based on the geometric information of CPRBM is proposed in this paper to rapidly determine the moving boundary curve for beam-to-beam contact constraints. The static equilibrium configuration of CCMs is solved by minimizing its potential energy function under the geometric constraints from the boundary curves of contacts. A formulation is also provided to evaluate the normal stress along the deformed beam based on the deformation of CPRBM’s torsional springs. Numerical examples and finite element analysis are used to verify the feasibility and accuracy of the proposed method.

Mechanical advantage is traditionally defined for single-input and single-output rigid-body mechanisms. A generalized approach for identifying single-output mechanical advantage for a multiple-input compliant mechanism, such as many origami-based mechanisms, would prove useful in predicting complex mechanism behavior. While origami-based mechanisms are capable of offering unique solutions to engineering problems, the design process of such mechanisms is complicated by the interaction of motion and forces. This paper presents a model of the mechanical advantage for multi-input compliant mechanisms and explores how modifying the parameters of a model affects their behavior. The model is used to predict the force-deflection behavior of an origami-based mechanism (Oriceps) and is verified with experimental data from magnetic actuation of the mechanism.

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

The Synchronized-offset-rolling-contact element (SORCE) technique for thickness accommodation in origami-inspired mechanisms combines selected strengths of several thickness-accomadation techniques but with the tradeoff of manufacturing complexity of rolling joints. This work presents principles to facilitate the construction of rolling joints suitable for applications like the SORCE technique. These include leveraging fold-angle multipliers of origami vertices, variations of flexure assembly, sunken flexures, and form-closed rolling joints. Prototypes of origami-mechanisms using the SORCE technique are constructed demonstrating these principles.

Lamina emergent compliant mechanisms (including origami-adapted compliant mechanisms) are mechanical devices that can be fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane. Lamina emergent compliant mechanisms often exhibit undesirable parasitic motions due to the planar fabrication constraint. This work introduces a type of lamina emergent torsion (LET) joint that reduces parasitic motions of lamina emergent mechanisms, and presents equations for modeling parasitic motion of LET joints. The membrane joint also makes possible one-way joints that can ensure origami-based mechanisms emerge from their flat state (a change point) into the desired configuration. Membrane-enhanced LET (M-LET) joints, including one-way surrogate folds, are described here and show promise for use in a wide range of compliant mechanisms and origami-based compliant mechanisms. They are demonstrated as individual joints and in mechanisms such as a kaleidocycle (a 6R Bricard linkage), degree-4 origami vertices (spherical mechanisms), and waterbomb base mechanisms (an 8R multi-degrees-of-freedom origami-based mechanism).

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the cross-section (i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.

We present a design technique for generating rigidly foldable quadrilateral meshes (RFQMs), taking as input four arrays of direction angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforcing the fold-angle multiplier condition at each vertex, it is possible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree-of-freedom (DOF). Furthermore, the design technique is computationally simple, reducing for some cases to a simple linear-programming problem. The resulting mechanisms have applications in architectural facades, furniture design, and more.

Origami is the art of folding paper. In the context of engineering, orimimetics is the application of folding to solve problems. Kinetic origami behavior can be modeled with the pseudo-rigid-body model since the origami are compliant mechanisms. These compliant mechanisms, when having a flat initial state and motion emerging out of the fabrication plane, are classified as lamina emergent mechanisms (LEMs). To demonstrate the feasibility of identifying links between origami and compliant mechanism analysis and design methods, four flat folding paper mechanisms are presented with their corresponding kinematic and graph models. Principles from graph theory are used to abstract the mechanisms to show them as coupled, or inter-connected, mechanisms. It is anticipated that this work lays a foundation for exploring methods for LEM synthesis based on the analogy between flat-folding origami models and linkage assembly.

This paper describes the conception, modeling, and development of a fully compliant two-degree-of-freedom pointing mechanism for application in spacecraft thruster, antenna, or solar array systems. The design objectives and the advantages of a compliant solution are briefly discussed. Detailed design decisions to meet project objectives are described. Analytical and numerical models are developed and subsequently verified by prototype testing and measurements in several iterations. A final design of the 3-D printed titanium monolithic pointing mechanism is described in detail and its performance is measured.

This work presents a general method of statically balancing flexural hinges. Using a set of non-dimensional parameters, we show that one can quickly design a statically balanced rotational flexure. First, a balancing method is developed for an idealized hinge/torsion spring system. This method is then extended to load-dependent systems and is demonstrated with the design of a balanced cross-axis-flexural pivot with stiffness that varies as a function of compressive preload. A physical prototype is built and tested to verify the design method. This method is general for any system that has a well understood stiffness response to an applied compressive load.

Tubular origami may provide both the needed deployment displacement and sufficient strength to be useful as deployable structures. This paper reviews origami tube-based deployable mechanisms and a structural optimization of FEA models is performed. Symmetric and non-symmetric 4-sided tubes are evaluated. Panel geometries and thicknesses are varied to produce rigidly foldable origami-tube-based mechanisms that are both strong and lightweight. The mechanical properties of these tubes over various deployment lengths are discussed. Three different configurations of this mechanism are compared and the advantages of each are discussed.