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.

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.

A review of current variable-stiffness actuators reveals a need for more simple, cost effective, and lightweight designs that can be easily incorporated into a variety of human-interactive robot platforms. This thesis considers the potential use of compliant mechanisms to improve the performance of variable-stiffness actuators. The advantages and disadvantages of various concepts using compliant mechanisms are outlined, along with ideas for further exploration. A new variable-stiffness actuator that uses a compliant flexure as the elastic element has been modeled, built, and tested. This new design involves a variable stiffness joint that makes use of a novel variable transmission. A prototype has been built and tested to verify agreement with the model which shows a reasonable range of stiffness and good repeatability. Ideas for further exploration are identified.

Static balance is the reduction or elimination of the actuating effort in quasi-static motion of a mechanical system by adding non-dissipative force interactions to the system. In recent years, there is increasing recognition that static balancing of elastic forces in compliant mechanisms leads to increased efficiency as well as good force feedback characteristics. The development of insightful and pragmatic design methods for statically balanced compliant mechanisms is the motivation for this work. In our approach, we focus on a class of compliant mechanisms that can be approximated as spring-loaded rigid-link mechanisms. Instead of developing static balancing techniques directly for the compliant mechanisms, we seek analytical balancing techniques for the simplified spring–loaded rigid–link approximations. Towards that, we first provide new static balancing techniques for a spring-loaded four-bar linkage. We also find relations between static balancing parameters of the cognates of a four-bar linkage. Later, we develop a new perfect static balancing method for a general n-degree-of-freedom revolute and spherical jointed rigid-body linkages. This general method distinguishes itself from the known techniques in the following respects: 1 It adds only springs and not any auxiliary bodies. 2 It is applicable to linkage shaving any number of links connected in any manner. 3 It is applicable to both constant(i.e., gravity type) and linear spring loads. 4 It works both in planar and spatial cases. This analytical method is applied on the approximated compliant mechanisms as well. Expectedly, the compliant mechanisms would only be approximately balanced. We study the effectiveness of this approximate balance through simulations and a prototype. The analytical static balancing technique for rigid-body linkages and the study of its application to approximated compliant mechanisms are among the main contributions of this thesis.

Bei Compliantmechanismen ergibt sich die Bewegungsfreiheit durch die elastische Verformung nachgiebiger Elemente. Durch deren Formgebung und Werkstoffauswahl kann das Verformungsbild unter definierter Belastung theoretisch gezielt eingestellt werden. Die Nachgiebigkeit eines einzelnen Mechanismenelements kann dabei über seine gesamte Länge gleichmäßig verteilt oder aber auf einen bestimmten Bereich konzentriert sein. Ein besonderer Vorteil nachgiebiger Elemente ist dabei die Reduktion der Einzelteile und die hiermit verbundene Verringerung der Systemmasse, des Montageaufwands und der Montagekosten. Für den Einsatz im Maschinenbau wird in auch die Möglichkeit einer spielfreien und somit sehr exakten Führung der Bewegung genannt. Zudem ist es durch die Einsparung reibungsbehafteter Berührungselemente bzw. beweglicher Lagerungen möglich, den Verschleiß innerhalb des Mechanismus zu reduzieren. Somit vereinfacht sich auch die Wartung, was den Einsatz von Compliantmechanismen beispielsweise bei schwerer Zugänglichkeit besonders vorteilhaft erscheinen lässt. Eine Herausforderung bei der Entwicklung von Nachgiebigkeitsmechanismen ist die hinreichend genaue Beschreibung des Verformungsverhaltens ihrer nachgiebigen Glieder. Vereinfachte Modellansätze im Sinne der Biegebalken-Theorie 1. Ordnung sind hier nicht geeignet, die großen Verformungen analytisch zu erfassen. Zwar finden sich heute zahlreiche höherwertige Lösungen zur Theorie 2. und 3. Ordnung in einer fast unüberschaubaren Vielzahl von Publikationen – beispielgebend sei genannt – die verallgemeinert auf Grundlagenarbeiten fußen. Die analytische Beschreibung eines Biegebalkens bei großer Verformung ist jedoch noch immer eine komplexe Aufgabe, die ein hohes Maß an mathematischen Fähigkeiten vom praxisorientierten Ingenieur erfordert. Nur die präzise Beschreibung der nachgiebigen Mechanismenelemente eröffnet aber den Weg für eine Genaulagen-Synthese und somit letztlich den breiten Einsatz von nachgiebigen Elementen in Leichtbau-Mechanismen. Für eine effiziente Synthese sind daher alternative Lösungsansätze notwendig, die dem Ingenieur eine schnelle und hinreichend genaue Vorhersage des komplexen Verformungsverhaltens erlauben. Im Rahmen der Arbeit werden hierfür zunächst die erarbeiteten, neuartigen Methoden des SFB 639 in kompakter Form aufbereitet. Für die Mehrzahl der technischen Probleme soll hierauf aufbauend eine praxisgerechte Methode erarbeitet werden, die es erlaubt mit einfachen Mitteln eine Genaulagen-Synthese von Compliantmechanismen durchzuführen. Hierfür ist die Nachgiebigkeit (Kehrwert von Elastizitätsmodul × Flächenträgheitsmoment) so anzupassen, dass das veränderliche Schnittmoment entlang des Balkens zu einer stets gleichen Krümmung führt. Durch den Einsatz anisotroper Werkstoffe – wie etwa mehrschichtiger, textilverstärkter Faser-Kunststoff-Verbundwerkstoffe (FKV) – kann etwa, durch eine lokale Anpassung der Faserorientierung, der Elastizitätsmodul entlang des Mechanismenelementes gezielt eingestellt werden. Eine Veränderung der Nachgiebigkeit daher nicht nur geometrisch (Variation des Flächenträgheitsmoment) sondern auch werkstofflich induziert werden. Es entstehen Mechanismenelemente mit lokal angepasster Nachgiebigkeit, für die im Rahmen der Arbeit auch die Methoden zur gezielten Einstellung der veränderlichen Faserorientierung entlang der Balkenachse entwickelt werden.:1 Einleitung 1 1.1 Einführung in Nachgiebigkeitsmechanismen . . . . . . . . . . . . . . . . 2 1.2 Literaturschau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Problemstellung und Zielsetzung . . . . . . . . . . . . . . . . . . . . . . 6 2 Verformungsverhalten nachgiebiger Mechanismenelemente 8 2.1 Modellierung biegebeanspruchter brettförmiger Balken . . . . . . . . . 8 2.2 Betrachtungen zum Verformungsverhalten nachgiebiger Strukturen . . . 12 2.3 Krümmungsgleichung für die Analyse großer Verformungen . . . . . . . 15 2.4 Analyse von Compliantelementen mittels Phasenportrait-Methode . . . 18 3 Anpassung der lokalen Nachgiebigkeit 27 3.1 Erzeugung konstanter Krümmung . . . . . . . . . . . . . . . . . . . . . 27 3.2 Variation des Flächenträgheitsmomentes . . . . . . . . . . . . . . . . . 30 3.2.1 Modellanalyse mittels normierter Betrachtung . . . . . . . . . . 31 3.2.2 Technologische Umsetzung . . . . . . . . . . . . . . . . . . . . . 33 3.2.3 Experimentelle Validierung . . . . . . . . . . . . . . . . . . . . . 36 3.3 Variation des Elastizitätsmoduls . . . . . . . . . . . . . . . . . . . . . . 41 3.3.1 Anpassung durch lokale Variation der Faserorientierung . . . . . 42 3.3.2 Technologische Umsetzung . . . . . . . . . . . . . . . . . . . . . 51 3.3.3 Experimentelle Validierung . . . . . . . . . . . . . . . . . . . . . 57 4 Gezielte Synthese von Compliantmechanismen 67 4.1 Genaulagen-Synthese – Burmester-Theorie der bewegten Ebenen . . . . 68 4.1.1 Vorgabe von zwei Ebenenlagen . . . . . . . . . . . . . . . . . . 70 4.1.2 Vorgabe von drei und mehr Ebenenlagen . . . . . . . . . . . . . 73 4.2 Synthese von Mechanismen mit nachgiebigen Elementen . . . . . . . . 75 4.2.1 Polkongruente Synthese für zwei Ebenenlagen . . . . . . . . . . 75 4.2.2 Nicht-polkongruente Synthese für zwei Ebenenlagen . . . . . . . 77 4.2.3 Lösungsansatz zur Synthese von drei Ebenenlagen . . . . . . . . 80 4.3 Experimentelle Validierung . . . . . . . . . . . . . . . . . . . . . . . . . 81 5 Gestaltungshinweise für Compliantmechanismen 84 5.1 Freiheitsgrad von Mechanismen mit nachgiebigen Elementen . . . . . . 84 5.2 Langzeitverhalten von nachgiebigen Elementen . . . . . . . . . . . . . . 90 6 Zusammenfassung 94 Literaturverzeichnis 97 A Anhang 103 A.1 MATLAB R2016 Skript: Berechnung Phasenportrait . . . . . . . . . . 105 A.2 MATLAB R2016 Skript: Faserorientierung bei Vorgabe der Last . . . . 113 A.3 MATLAB R2016 Skript: Faserorientierung bei Vorgabe der Gliedlänge . 117

Mecanismos flexíveis são mecanismos onde o movimento é dado pela flexibilidade da estrutura ao invés da presença de juntas e pinos. Tem grande aplicação em dispositivos de mecânica de precisão, área biomédica, e mais recentemente na construção de microeletromecanismos (“MEMS" em inglês). Várias técnicas são usadas no projeto de mecanismos flexíveis, sendo que entre elas, a Otimização Topológica tem se mostrado a mais genérica e sistemática. O método de Otimização Topológica combina um método de otimização com o método dos elementos finitos (MEF). A utilização da Otimização Topológica permite que um engenheiro ou cientista projete o mecanismo para a sua aplicação específica sem precisar adquirir conhecimentos específicos sobre estruturas e mecanismos flexíveis. Dessa forma, o objetivo desse trabalho é aplicar o método de Otimização Topológica no projeto de mecanismos flexíveis, usando o modelo de material SIMP (método de densidades). O projeto é definido como sendo um problema de otimização de uma estrutura flexível, sujeito à restrição na quantidade de material, onde a função objetivo é maximizar o deslocamento numa dada região do domínio da estrutura quando submetida a um dado carregamento em outra região. Para ilustrar a implementação do método são apresentados resultados de topologias bidimensionais de mecanismos flexíveis. / Compliant Mechanisms consist of mechanisms where the movement is giving by the structural flexibility rather than the presence of joints and pins. They are applied to precision mechanic devices, biomedical field, and more recently to the design of microelectromechanical systems (MEMS). Many techniques has been applied to design compliant mechanisms. Among them, topology optimization method is a generic and systematic method. Topology optimization combines optimization algorithms with finite element method and allows an engineer or a scientist to design a compliant mechanism for its application without having to acquire specific knowledge about structures or compliant mechanisms. Therefore, the objective of this work is to apply topology optimization to design compliant mechanisms. The topology optimization method implemented is based on the SIMP material model. The design is defined as the optimization problem of a flexible structure, subject to an amount of material constraint, where the objective function is to maximize the output displacement in a certain region of the structure domain due to an applied load to other region. To illustrate the implementation of the method, two-dimensional topologies of compliant mechanisms are presented as a result.