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.

Despite many advances in the design methods for compliant mechanisms, it is still not possible to know if a set of user-specifications has a solution. Furthermore, practical considerations such as failure limits and manufacturing limitations cannot be easily incorporated into existing methods. To address these issues, we have recently developed the concept of feasible stiffness and inertia maps. This thesis extends the concept of feasible maps and proposes another kind of maps that comprehensively depict the nonlinear kinetoelastostatic behaviour of compliant mechanisms. Feasible maps drawn as per user-specifications, with compliant mechanisms of the database overlaid on it, instantly inform the reader whether the specifications are feasible; whether the specifications are stringent; whether any mechanisms in the database meet the specifications, and whether any mechanism can be interactively modified to meet the specifications including size, strength and manufacturability. This thesis extends the earlier work on feasible maps by relaxing one condition that all beam segments in a compliant mechanism must retain their relative proportions. This is achieved by using size optimization. Thus, a certain degree of automation is brought into the procedure, which enhances the ease of use of the feasible maps. Illustrative examples are presented and implementation into a software is demonstrated. A major contribution of this work is the development of the concept of kinetoelastostatic maps of compliant mechanisms with fixed topology, shape, and relative proportions of beam segments in them. The map is drawn on a 2D plot using two non-dimensional quantities, one that captures the response of the mechanism and the other that combines the force, geometry, and material parameters. The map encloses a region that indicates the kinetoelastostatic capability of the mechanism. Another contribution of this work is the observation that the enclosed region can be parameterized using average slenderness ratio of the beam segments. The resulting curves help designers in assessing the capability and limits of a mechanism in terms of geometric advantage, mechanical advantage, normalized output displacement, inherent stiffness, etc. Numerous examples are presented to explain various uses of the non-dimensional maps.

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.

The high cost of experimentation and product development in the field of microelectromechanical systems (MEMS) has led to a greater emphasis on simulation-based design for increasing first-pass design success and reliability. The use of compliant or flexible mechanisms can help eliminate friction, wear, and backlash, but compliant MEMS are sensitive to variations in material properties and geometry. This dissertation proposes approaches for design stage uncertainty analysis, model validation, and robust optimization of nonlinear compliant MEMS to account for critical process uncertainties including residual stress, layer thicknesses, edge bias, and material stiffness. Methods for simulating and mitigating the effects of non-idealities such joint clearances, semi-rigid supports, non-ideal loading, and asymmetry are also presented. Approaches are demonstrated and experimentally validated using bistable micromechanisms and thermal microactuators as examples.

In this study analysis and design procedures of partially compliant mechanisms using two degree of freedom mechanism model are developed. The flexible segments are modeled as revolute joints with torsional springs. While one freedom is controlled by the input to the mechanism, the motion of the parts are governed both by the kinematics and the force balance. The procedure developed for the analysis of such mechanisms is shown on two different mechanisms: a five link mechanism with crank input and slider output (five-bar mechanism) / a five link mechanism with crank input and rocker output. Design charts are prepared according to output-link oscillation and dimensionless design parameters

This research presents the initial studies and results on shield design for Shape-Shifting Surfaces (SSSs) seeking maximum compression and maximum expansion of a unit-cell. Shape-Shifting Surfaces (SSSs) are multilayered surfaces that are able to change shape while maintaining their integrity as physical barriers. SSSs are composed of polygonal unit-cells, which can change side lengths and corner angles. These changes are made possible by each side and corner consisting of at least two different shields, or layers of material. As the layers undergo relative motion, the unit-cell changes shape. In order for the SSS to retain its effectiveness as a barrier, no gaps can open between different layers. Also, the layers cannot protrude past the boundaries of the unit-cell. Based on these requirements, using equilateral triangle unit-cells and triangular shields, a design space exploration was performed to determine the maximum deformation range of a unit-cell. It was found that the triangular shield that offered maximum expansion and compression ratio is a right triangle with one angle of 37.5 degrees and its adjacent side equal to 61% of the side of the unit-cell. The key contribution of this paper is a first algorithm for systematic SSS shield design. Possible applications for SSSs include protection, by creating body-armor systems; reconfigurable antennas able to broadcast through different frequencies; recreational uses, and biomedical applications.

Made available in DSpace on 2016-12-12T20:25:11Z (GMT). No. of bitstreams: 1 Luis Reanto Meneghelli.pdf: 5980064 bytes, checksum: 65a0002e42f206e56e3875504a6f0660 (MD5) Previous issue date: 2013-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Compliant mechanisms are mechanical devices that transform or transfer motion, force or energy through a single part. These mechanisms have important applications in micro electromechanical systems (MEMS) as well as systems that require large accuracy in motion and micro scale. In this work the compliant mechanisms design is performed by means of the Topology Optimization Method, and the optimization problem is formulated in order to maximize the strain energy stored inside the mechanism, eliminating the appearance of hinges. The kinematic behavior of the mechanism is imposed through a set of constraints on displacements of a few degrees of freedom of interest. The elastic behavior is imposed by means of a global stress constraint and some issues associated to the stress parametrization in topology optimization are addressed in the context of mechanisms design. The numerical examples shown that the proposed formulation is able to generate clean topologies of feasible compliant mechanisms. Based on the results, it is clear that the stress constraint has a deep impact on the design of compliant mechanisms, since it can constraint the amount of energy used to enforce the displacement constraints. / Mecanismos flexíveis são dispositivos mecânicos que transformam ou transferem movimento, força ou energia, através de uma única peça. Este tipo de mecanismo encontra aplicações importantes em sistemas micro eletromecânicos (MEMS, micro electromechanical systems) e demais sistemas que exijam grandes precisões nos movimentos e escala microscópica. O projeto de mecanismos flexíveis é realizado através do Método de Otimização Topológica e o problema de otimização será formulado tendo em vista a maximização de energia de deformação elástica armazenada pelo mecanismo, eliminando assim a ocorrência de rótulas (hinges). O comportamento cinemático do mecanismo é imposto através de restrições sobre o campo de deslocamentos em alguns graus de liberdade de interesse. O comportamento elástico dos mecanismos flexíveis é imposto usando um critério global de restrição de tensão e algumas questões importantes associadas a parametrização das tensões são discutidas no contexto de projeto de mecanismos. Os exemplos numéricos mostram que é possível obter topologias bem definidas e que satisfaçam as restrições do projeto. Com base nestes exemplos, verifica-se que a restrição de tensão exerce forte influência no resultado, podendo limitar a quantidade de energia necessária para atender às restrições do mecanismo.

Mecanismos flexíveis, nos quais a deformação elástica é aproveitada na atuação cinemática, têm grande empregabilidade em dispositivos de mecânica de precisão, engenharia biomédica, e mais recentemente em microeletromecanismos (MEMS). Entre as diversas técnicas empregadas para o seu projeto, a otimização topológica tem se mostrado a mais genérica e sistemática. A grande dificuldade destes projetos é conciliar os requisitos cinemáticos com a resistência mecânica da estrutura. Neste trabalho, é implementado um critério de resistência dentro da formulação do problema de otimização, com o intuito de gerar mecanismos que cumpram a tarefa cinemática desejada mas ao mesmo tempo não ultrapassem limites de tensão predeterminados. Esta restrição adicional também visa aliviar o problema bastante conhecido do aparecimento de articulações. Não linearidade geométrica e de material (hiperelasticida de compressível) são implementadas na solução das equações através do método dos elementos finitos para levar em conta os grandes deslocamentos do mecanismo. O método das assíntotas móveis é usado para a atualização das variáveis de projeto. As derivadas do problema de otimização são calculadas analiticamente, pelo método adjunto. Técnicas de projeção são aplicadas para a garantia de topologias livres de instabilidades numéricas comuns em otimização topológica, e projetos otimizados mais próximos de um espaço 0/1 para as densidades físicas. / Compliant me hanisms, in whi h the elasti strain is the basis for kinemati a tua- tion are widely used in pre ision me hani s devi es, biomedi al engineering, and re ently in mi roele trome hani al systems (MEMS). Among several te hniques applied in ompliant me hanisms design, topology optimization has been one of the most general and systemati . The great hallenge in these designs is to ouple both the kinemati s and the me hani al strength riteria requirements. In this work, a strength riteria for the optimization problem is applied, with the aim of generating ompliant me hanisms that ful ll the desired kine- mati tasks while omplying with a stress threshold. The addition of a stress onstraint to the formulation for ompliant me hanisms in topology optimization also aims to allevi- ate the appearan e of hinges in the optimized topology, a well known issue in the design of ompliant me hanisms. Geometri al and material ( ompressible hyperelasti ity) nonlin- earities are applied to the nite element equilibrium equations, to take into a ount large displa ements. The method of moving asymptotes is applied for design variables updating. The derivatives are al ulated analyti ally, by the adjoint method. Proje tion ltering te h- niques are applied, in order to guarantee topologies free of ommon numeri al instabilities in topology optimization, and optimized designs near the 0/1 solution for the physi al densities.

Mecanismos flexíveis, nos quais a deformação elástica é aproveitada na atuação cinemática, têm grande empregabilidade em dispositivos de mecânica de precisão, engenharia biomédica, e mais recentemente em microeletromecanismos (MEMS). Entre as diversas técnicas empregadas para o seu projeto, a otimização topológica tem se mostrado a mais genérica e sistemática. A grande dificuldade destes projetos é conciliar os requisitos cinemáticos com a resistência mecânica da estrutura. Neste trabalho, é implementado um critério de resistência dentro da formulação do problema de otimização, com o intuito de gerar mecanismos que cumpram a tarefa cinemática desejada mas ao mesmo tempo não ultrapassem limites de tensão predeterminados. Esta restrição adicional também visa aliviar o problema bastante conhecido do aparecimento de articulações. Não linearidade geométrica e de material (hiperelasticida de compressível) são implementadas na solução das equações através do método dos elementos finitos para levar em conta os grandes deslocamentos do mecanismo. O método das assíntotas móveis é usado para a atualização das variáveis de projeto. As derivadas do problema de otimização são calculadas analiticamente, pelo método adjunto. Técnicas de projeção são aplicadas para a garantia de topologias livres de instabilidades numéricas comuns em otimização topológica, e projetos otimizados mais próximos de um espaço 0/1 para as densidades físicas. / Compliant me hanisms, in whi h the elasti strain is the basis for kinemati a tua- tion are widely used in pre ision me hani s devi es, biomedi al engineering, and re ently in mi roele trome hani al systems (MEMS). Among several te hniques applied in ompliant me hanisms design, topology optimization has been one of the most general and systemati . The great hallenge in these designs is to ouple both the kinemati s and the me hani al strength riteria requirements. In this work, a strength riteria for the optimization problem is applied, with the aim of generating ompliant me hanisms that ful ll the desired kine- mati tasks while omplying with a stress threshold. The addition of a stress onstraint to the formulation for ompliant me hanisms in topology optimization also aims to allevi- ate the appearan e of hinges in the optimized topology, a well known issue in the design of ompliant me hanisms. Geometri al and material ( ompressible hyperelasti ity) nonlin- earities are applied to the nite element equilibrium equations, to take into a ount large displa ements. The method of moving asymptotes is applied for design variables updating. The derivatives are al ulated analyti ally, by the adjoint method. Proje tion ltering te h- niques are applied, in order to guarantee topologies free of ommon numeri al instabilities in topology optimization, and optimized designs near the 0/1 solution for the physi al densities.