Origami has become a source of inspiration in a number of engineered systems. In most systems, non-paper materials where material thickness is non-negligible is required. In origami-inspired engineered systems where thickness is non-negligible, thickness-accommodation techniques must be utilized to overcome the issue of self-intersection. Many thickness-accommodation techniques have been developed for use in thick-origami-inspired-engineered systems. In this work several thickness-accommodation techniques are reviewed and discussed. New thickness-accommodation techniques including hybrid thickness-accommodation techniques and the split vertex technique are presented and discussed. These techniques enable new capabilities of thickness-accommodation in origami adapted design. Thickness-accommodation techniques have been developed in the context of developable origami patterns and the application of these techniques to non-developable patterns is introduced here. The capability of non-developable thick origami is demonstrated in an application example of a deployable locomotive nose-fairing.

Origami-adapted mechanisms form the basis of an increasing number of engineered systems. As most of these systems require the use of non-paper materials, various methods for accommodating thickness have been developed. These methods have opened new avenues for origami-based design. This work introduces approaches for the design of two new classes of thick-origami systems and demonstrates the approaches in hardware. One type of system, called "conceal-and-reveal,'' is introduced, and a method of designing these mechanisms is developed. Techniques are also developed for designing folding printed circuit boards which are fabricated from a single sheet of material. This enables areas of regional flexibility, leaving other areas stiff. This allows components to be attached to stiff regions and folding to occur at flexible regions. An optimization method is presented to design the geometry of surrogate hinges to aid in monolithic origami-based mechanisms such as flexible PCBs. Examples are shown which demonstrate each of these new techniques.

The objective of this research is to present a new model for predicting the piezoresistive effect in microflexures experiencing bending stresses. A linear model describing piezoresistivity exists for members in pure tension and compression. Extensions of this model to more complex loading conditions do not match experimental results. An accurate model of piezoresistivity in complex loading conditions would expand the design possibilities of piezoresistive devices. A new model to predict piezoresistive effects in tension, compression, and more complex loading conditions is proposed. The focus of this research is to verify a unidirectional form of this proposed model for microflexures in tension and bending. Implementation of the unidirectional form of the model involves geometric design, stress analysis, and electrical analysis. One of the ways to implement the model is with finite-element analysis (FEA). The piezoresistive FEA for flexures (PFF) algorithm is an FEA implementation of the unidirectional form of the model for flexures. A case study is then given in which the resistance curves of two test devices are predicted with the PFF algorithm. Results from the PFF implementation of the unidirectional form of the model show a close comparison between analytical prediction and experimental results. This new model could contribute to optimized sensors, feedback control of microdevices, nanopositioning, and self-sensing microdevices.

There are times when it is desirable for devices to be stowed compactly, ``transported'' to the location of their desired use, and then deployed to another stable shape or configuration to perform their designed function. Origami-based mechanisms are beneficial in these cases due to their compact, folded nature and large deployments. Unlike traditional mechanical design, compliant mechanism and origami-based design approaches inherently have coupled characteristics, creating complex design problems. The research presented here discusses metrics, methods, and designs to aid in the design of origami-adapted and compliant mechanisms, focusing on the design case of deployable space systems. First, the hexagonal twist origami pattern is used to develop performance metrics for next-generation deployable space arrays. These are shown using five different thickness accommodation techniques. The concepts are demonstrated through two applications: a deployable reflectarray antenna and a LiDAR telescope. Second, a highly compact stowable deployment is presented with the Deployable Euler Spiral Connectors (DESCs). These are compliant deployable flexures that can span gaps between segments in a mechanism and then lay flat when under strain in a stowed position. Additionally, a metamaterial is shown based on the combination of Euler spiral flexures (ESFs) to provide unique behaviors difficult to obtain in traditional materials, such as high compactability, decoupled motion and stiffness, tailorable Poisson's ratio, and multi-directional deployment. Third, this work presents a method for creating hinge-like motion for origami-adapted mechanisms using internal membranes attached between rigid panels. The goal is to remove adhesive requirements, preserve panel volume for use as hard stops, and reduce parasitic motion experienced by other membrane joint types, while keeping the stress in the membrane below the stress limits. Lastly, specific applications and examples of each of the above are shown throughout the work with a specific chapter highlighting more concise examples of creating metrics to determine the best origami patterns and to create compatible hinges. The presented techniques stand to greatly benefit the origami-adapted mechanisms design community.

The purpose of this research is the development of design concepts and models of large-angle, compliant, multistable, revolute joints. This research presents evidence of the capability of these models and concepts by presenting a case study in which the miniaturization of revolute joints are examined. Previous attempts at multistable revolute joints can be categorized into two categories: compliant and non-compliant mechanisms. Non-compliant multistable revolute joints are typified by a combination of pin-in-slot joints, springs, and detents. Due to factors inherit in design, noncompliant joints often succumb to friction, wear, and undesirable motion, that leads to a decline in performance. Compliant multistable joints, such as those discussed in this work, negate these issues by allowing deflection in one or more of their members. However, compliant mechanisms have challenges associated with large-angle revolutions, stress concentration, and, historically, they perform poorly in compression. The literature has been lacking information on the fabrication of compliant multistable revolute joints having more than two stable positions. This work develops a truly multistable compliant revolute joint that is capable of multiple stable positions, the multistable compliant rolling-contact element(CORE). A CORE is a contact-aided complaint mechanism that eliminates friction and wear by allowing two surfaces to roll on each other. Furthermore, the contact eliminates problems such as poor performance in compression, typically associated with compliant mechanisms. The device uses minima in potential energy to achieve multi-stability, through one of six mechanisms. The use of minima in the potential energy eliminates the need for detents and other fatigue prone devices. Multistability may be achieved by placing the CORE flexure into tension or using flexible segments attached to the foci; or by changing the initial curvature of the flexure, curvature of the CORE surface, cross sectional area of the flexure (both protagonistically or antagonistically), or material properties. The stability methods are evaluated via a Pugh scoring matrix and the most promising concept, stability through tension in the CORE flexures, examined further. The utility of mathematical models, developed in this work, that predict stress, strain, and activation force, are demonstrated via a case study. This work also demonstrates that the device is capable of large angle deflections (360) and that the provided models permit efficient engineering design with COREs.

The purpose of this research is to develop the tools necessary to create tristable compliant mechanisms; the work presents the creation of models and concepts for design and a demonstration of the feasibility of the designs through the fabrication of tristable compliant mechanism prototypes on the macro scale. Prior methods to achieve tristable mechanisms rely on detents, friction, or power input; disadvantages to these methods include a high number of parts, the necessity for lubrication, and wear. A compliant tristable mechanism accomplishes tristability through strain energy storage. These mechanisms would be preferable because of increased performance and cost savings due to a reduction in part count and assembly costs. Finite element analysis and the pseudo-rigid-body model are used to design tristable compliant mechanisms. The mechanisms are initially designed by considering symmetrical or nearly symmetrical mechanisms which achieve a stable position if moved in either direction from the initial (fabrication) position, thus resulting in a total of three stable positions. The mechanisms are fabricated and tested in both partially and fully compliant forms, and efforts to miniaturize the mechanism are discussed. The basic mechanism design is used as a starting point for optimization-based design to achieve tailored stable positions or neutrally stable behavior. An alternative to fabrication methods commonly used in compliant mechanisms research is introduced. This method integrates torsion springs made of formed wire into compliant mechanisms, allowing the desired force, stiffness, and motion to be achieved from a single piece of formed wire. Two ways of integrating torsion springs are fabricated and modeled, using either helical coil torsion springs or torsion bars. Because the mechanisms are more complex than ordinary springs, simplified models are presented which represent the wireform mechanisms as four-bar mechanisms using the pseudo-rigid-body model. The method is demonstrated through the design of mechanically tristable mechanisms. The validity of the simplified models is discussed by comparison to finite element models and experimental measurements. Finally, fatigue testing and analysis is presented.

Injury, instrumentation, or surgery may change the functional biomechanics of the spine. Spinal fusion, the current surgical treatment of choice, stabilizes the spine by rigid fixation, reducing spinal mobility at the cost of increased stress at adjacent levels. Recently, alternatives to spinal fusion have been investigated. One such alternative is total disc replacements. The current generation of total disc replacements (TDRs) focuses on restoring the quantity of motion. Recent studies indicate that the moment-rotation response and axis of rotation, or quality of motion (QOM), may have important implications in the health of adjacent segments as well as the health of the surrounding tissue of the operative level. This dissertation examines the use of compliant mechanism design theory in the design and analysis of spinal arthroplasty devices. Particularly, compliant mechanism design techniques were used to develop a total disc replacement capable of replicating the normal moment-rotation response and location and path of the helical axis of motion. Closed-form solutions for the device's performance are proposed and a physical prototype was created and evaluated under a modified F1717 and a single-level cadaveric experiment. The results show that the prototype's QOMclosely matched the selected force-deflection response of the specified QOM profile. The use of pseudo-rigid-body modeling to evaluate the effects of various changes on motion at adjacent segments is also investigated. The ability to model biomechanical changes in the spine has traditionally been based on animal models, in vitro testing, and finite element analysis. These techniques, although effective, are costly. As a result, their use is often limited to late in the design process. The pseudo-rigid-body model (PRBM) developed accurately predicted the moment-rotation response of the entire specimen and the relative contribution of each level. Additionally, the PRBM was able to predict changes in relative motion patterns of the specimen due to instrumentation.

Lamina Emergent Mechanisms (LEMs) are a class of compliant mechanisms that can be manufactured from sheet goods and possess motion out of the plane of fabrication. LEMs can be designed to perform sophisticated motions. This thesis expands LEM understanding and increases the ability to utilize them in applications by introducing the fundamentals of spherical LEMs, creating joints suitable for LEMs, and providing an example of a LEM application. In this thesis, the fundamentals of spherical LEMs are developed. This includes classification of all possible spherical 4R LEMs and a discussion of the motion characteristics of the various mechanisms. The motion characteristics associated with spherical 4R LEMs are then used to predict the motion of spherical 6R LEMs and arrays of spherical LEMs. Multiple spherical LEM prototypes are shown and discussed. A common difficulty of working with compliant mechanisms, especially LEMs, is creating suitable joints. There is often a trade off between flexibility in the desired direction of deflection, and stiffness in directions of undesired deflection. For this thesis, LEM joints that possess higher off-axis stiffness, especially in tension and compression, than previous designs were developed: the I-LET, the T-LET, and the IT-LET. Joint geometries were optimized and then modeled in commercial finite element analysis (FEA) software capable of nonlinear analysis. These models were used to predict the bending of tensile/compressive stiffnesses of the joints. As a benchmark, lamina emergent torsional (LET) joints were modeled and optimized for maximum tension and compression loading while maintaining the same bending stiffness as the joint being compared. Mechanisms that utilized the new joints were created and are briefly discussed. The use of these joints allows for minimized parasitic motion under tension and compression loads and expands the capability of LEM joints. The Lens Lift™ was developed to demonstrate an application of LEMs. The Lens Lift™ is a LEM device that allows for easier and more sterile use of disposable contact lenses. It possesses a monolithic structure and can be fabricated using simple manufacturing processes. As the contact lens user opens the blister pack used to store the lens, the lens is lifted out of the pack and presented to the user. The user can then lift the lens with one touch and place it in the eye. A provisional patent has been filed for the device and the device currently being evaluated by a major contact lens manufacturer for further development.

Origami, the Japanese art of paper folding, has been used previously to inspire engineering solutions for compact, deployable designs. Action origami, the subset of origami dealing with models designed to move, is a previously unexplored area for engineering design solutions that are deployable and have additional motion in the deployed state. A literature review of origami in engineering is performed, resulting in seven key areas of technical origami literature from a wide variety of disciplines. Spherical mechanisms are identified as the method by which most action origami models achieve complicated motion while remaining flat-foldable. The subset of action origami whose motion originates from spherical mechanisms is termed "kinematic origami''. Action origami is found to contain large coupled systems of spherical mechanisms. All possible action origami models are classified by their spherical mechanism structure, resulting in eight possible categories. Viewing action origami as spherical mechanisms allows the use of established equations for kinematic analysis. Several kinematic origami categories are used to demonstrate a method for the position analysis of coupled systems of spherical mechanisms. Input-output angle relationships and coupler link motions are obtained for a single spherical mechanism, two spherical mechanisms coupled together, and four spherical mechanisms coupled in a loop arrangement. This lays a groundwork from which it is possible to create compact, deployable mechanisms with motion in the deployed state.

This research presents methods for modeling and optimizing an origami design using compliant mechanisms, improving origami design processes, modeling and analyzing rolling behavior of compliant designs, and an antenna design for SmallSats. A framework for the optimization of the origami Flasher pattern to mitigate issues with rigid-foldability is shown, and several optimization solutions are presented to overcome these issues. An alternative design method is presented which allows designers to more accurately predict the characteristics of a design in the deployed state, and configurations are shown for an example use case. A model for rolled gossamer structures is presented which predicts the relative slippage that adjacent panels will experience, and slippage trends are correlated with key pattern parameters. Finally, a SmallSat antenna design is presented, which stows compactly, incorporates a unique hinge design, utilizes magnets for stabilization in the deployed state, and self-deploys using compliant mechanisms.