The design of structures and mechanisms subject to impact loading has historically involved designing in such a way as to minimize damage induced by the impact. This has historically been accomplished by absorbing and dissipating the energy of the impact. However, in some applications it is desirable to harness the energy and return it to the impacting object to maximize the coefficient of restitution (COR), resulting in large rebound velocities. The use of traditional rigid-body mechanisms to achieve high-COR mechanisms is limited by issues of friction, durability, poor strain-energy distribution and others. Compliant mechanisms do not possess the same limitations and are well-suited to these types of applications. The principles needed to realize these types of designs are found in existing literature but are confined to very specific applications such as hollow-body golf club heads. The contribution of this thesis is an approach to the generation and evaluation of compliant mechanism concepts for use in impact applications where a high COR is required. This approach is based loosely on common general concept development processes found in literature. This thesis describes the process of including the use of lumped mass or mechanical models, the categorization of strain-energy storage, the use of both closed-form and finite-element static models and the use of dynamic finite-element models to determine if a configuration is eligible to be used in a final design process. This thesis also contributes a case study in the development of configurations for metalwood golf club driver heads.

An increasing number of mechanical systems are being designed on the micro and meso scales. Assembly and maintenance become increasingly difficult as the size of mechanisms decrease, and the minimum size of traditional elements such as bearings and springs is limited. The backlash of bearings also limits their usefulness in applications where high precision and repeatability are needed. At small scales and for high precision applications, alternative, non-traditional elements are needed. The objective of this thesis is to develop reliable and scalable compliant components to replace bearings and helical springs. Components replacing springs must be able to produce specified torque/motion requirements. Components replacing bearings must permit sufficient motion about the axis of rotation, bear specified loads in the lateral directions, and fit within roughly the same design space as a bearing. Additionally, all components will be designed to be manufactured using in-plane fabrication processes. Practical application of the components will be demonstrated by their use in Sandia National Laboratory's Stronglink assembly. The concepts discussed in this thesis fall into three categories: mechanisms that replace 1) the helical spring, 2) the bearing, and 3) both the helical spring and the bearing. The serpentine flexure belongs to the first category, the compliant rolling-contact element (CORE), CORE bearing, and elliptical CORE bearing belong to the second, and the compliant contact-aided revolute (CCAR) joint belongs to the third category.

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.

There exists a great need for armor systems with greater mass efficiencies and ballistic limits. This thesis explores the development of a new field of armor capable of satisfying the increased demand for modern armor: Mechanically Reactive Armor or MRA. More specifically, the thesis focuses on Compliant MRA or CMRA. From the physics governing projectile-armor interactions, principles governing successful design of MRA are identified and presented. These principles or design approaches focus primarily on rejecting, minimizing, or absorbing the incoming projectile's kinetic energy. After identifying these principles, the specific mechanical functions required by the principles are isolated. These functions represent the physical behavior and capabilities of real mechanisms that satisfy the specific design principles. Using these mechanical functions and other benchmark concepts as a guide, established concept generation methodology is used to identify families of CMRA concepts that could supply the identified mechanical functions. These concept families are then narrowed by comparison of their respective ability to supply the required mechanical functions. The remaining concepts are selected for further study and simulation. In order to provide more detailed insight into the behavior of specific designs of these concepts, a quantitative model is developed. This simplified model is capable of predicting the behavior of the CMRA system when impacted by a ballistic projectile. After development, the model is then implemented to search the design space of the narrowed concepts. The search of the design space reveals important trends to be used in the design of CMRA elements. Finally, the feasibility of the specific designs is evaluated to judge their practicality in terms of practical materials and dimensions. It is shown that the concepts hold significant promise but require further design and development to provide the most desirable performance.

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.

This thesis introduces and presents the modeling of a novel compliant spinal implant designed to reduce back pain and restore function to degenerate spinal disc tissues as well as provide a mechanical environment conducive to healing the tissues. The initial objectives for this device development and the focus of this work are modeling and validation of the force-deflection relationships and stress analysis. Modeling was done using the pseudo-rigid-body model to create a 3 degree of freedom mechanism for flexion-extension (forward-backward bending) and a 5 degree of freedom mechanism for lateral bending (side-to-side). These models were analyzed using the principle of virtual work to obtain the force-deflection response of the device. The model showed good correlation to finite element analysis and experimental results. Also, described in this thesis is a model that incorporates an estimate of the combined stiffness of the biologic structures. This combined model is confirmed by cadaveric testing. A stress analysis of the implant for combined loading conditions is also presented. This work introduces and provides a foundation for the FlexSuRe™ spinal implant.

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.

Lamina emergent mechanisms (LEMs) are a subset of compliant mechanisms which are fabricated from planar materials; use compliance, or flexibility of the material, to transfer energy; and have motion that emerges out of the fabrication plane. LEMs provide potential design advantages by reducing the number of parts, reducing cost, reducing weight, improving recyclability, increasing precision, and eliminating assembly, to name a few. However, there are inherent design and modeling challenges including complexities in large, non-linear deflections, singularities that exist when leaving the planar state, and the coupling of material properties and geometry in predicting mechanism behavior. This thesis examines the planar and spherical LEMs and their relation to origami. Origami, the art of paper folding, is used to better understand spherical LEMs and flat-folding mechanisms in general. All single-layer planar four-bar LEMs are given with their respective layouts. These are all change-point pinned mechanisms (i.e. no slider cranks). Graph representations are used to show the similarities between action origami and mechanisms. Origami principles of flat-folding are shown to be analogous to principles of mechanisms including rules for assembly and motion.

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.