This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

Mecanismo Flexível é um dispositivo mecânico utilizado para transformar movimento, força ou energia entre as portas de entrada e saída sem a presença de juntas, pinos baseados em uma estrutura em monolítica, em outras palavras, a transformação do movimento é dada pela flexibilidade de sua estrutura. Deste modo a transformação pode ser direcionada em uma direção em específico, amplificando ou reduzindo o deslocamento ou força aplicados. Por este motivo mecanismos flexíveis tem grandes aplicações em micromanipulação e nano posicionamento. A concepção deste tipo de mecanismo é complexa e uma das possibilidades de elaboração deste dispositivo mecânico é através da distribuição de flexibilidade ou rigidez dentro do domínio de projeto utilizando o Método de Otimização Topológica (MOT), que essencialmente combina algoritmos de otimização numéricos como Método de Elementos Finitos (MEF), por exemplo. A grande maioria das classes de mecanismos flexíveis existentes trabalha sob pequenos deslocamentos, na ordem de micro ou nano metros, no entanto, existe uma classe de mecanismos que utiliza o recurso da flambagem não linear para operar com grandes deslocamentos. O procedimento de concepção desta de classe de mecanismo é complexa e ainda se encontra em estagio inicial, necessitando de aprimoramentos que permitam o seu projeto completo via métodos computacionais. Portanto, esta tese foi desenvolvida como objetivo desenvolver uma metodologia computacional para projetar esta classe de mecanismo flexível inovador que emprega a flambagem não linear na sua estrutura como meio para obter sob grandes deslocamentos na porta de saída. A metodologia desenvolvida se baseia no MOT para obter a topologia da estrutura que satisfaça as restrições de projeto. A modelagem do comportamento físico da estrutura utiliza uma formulação variacional não linear do problema elástico, considerando a cinemática não linear com um modelo constitutivo policonvexo. O modelo de material aplicado para obter a topologia da estrutura do mecanismo foi o Solid IsotropicMaterial with Penalization (SIMP) com um algoritmo de otimização numérico baseado no método de ponto interior, onde foi utilizada a implementação do IpOpt em conjunto com a plataforma Python FEniCS de soluções de Equações Diferenciais Parciais (EDPs). São apresentados resultados bidimensionais de mecanismos considerando algumas configurações de geometria, condições de contorno e restrições de flambagem não-linear, como incremento de carga. / The compliant mechanism is a mechanical device used to transform displacement, force or energy between the input and output ports without joints, pins based on a monolithic structure, in other words, the motion transformation is given by the flexibility of its structure. In this way the movement can be defined to a specific axis direction, amplifying or reducing the applied displacement or force. For this reason, the compliant mechanism has significant applications in micromanipulation and nanopositioning system. The design of this type of device is intricate, and one way to achieve such design is trying to distribution flexibility or rigidity within the design domain using the Topology Optimization Method (TOM), which essentially combines numerical optimization algorithms with Finite ElementMethod (FEM), for example. Most models of existing compliant mechanism work under small displacements, in the order of micro or nanometers, nevertheless, there is a class of such mechanisms that uses the nonlinear buckling behavior to operate under large displacements. The design process of this mechanism type is complicated and is still at early stages, requiring improvements that allow a complete design process via computational methods. Therefore, this thesis goal is to develop a computational methodology to create this class of innovative compliant mechanism that employs nonlinear buckling behavior to work under large displacement at the output port. The approach developed is based on TOM to achieve the optimal structure topology that satisfies the design and optimization constraints. The modeling of the elasticity behavior of the structure relies on the nonlinear variational formulation, applying the nonlinear kinematics with a polyconvex constitutive model. The SIMP is employed as a material model to obtain the optimal topology of the mechanismstructure with a numeric optimization algorithm based on the interior point method, where the IpOpt implementation was used with the high-level Python interfaces to FEniCS to solve the partial differential equations (PDEs) problem. Two-dimensional results ofmechanisms are presented considering some geometric, boundary configuration, and including nonlinear buckling as design constraints.

In this two-part study, developments in finite element technology and the application thereof to topology optimization are investigated. Ultimately, the developed finite elements and corresponding topology optimization procedures are aimed at, but not restricted to, aiding the design of piezoelectrically driven compliant mechanisms for micropositioning applications. The objective is to identify and exploit existing, or to develop new, finite element technologies to alleviate the numerical instabilities encountered in topology optimization. Checkerboarding and one-node connected hinges are two commonly encountered examples which can directly be attributed to inadequacies or deficiencies in the finite element solution of structural problems using 4-node bilinear isoparametric finite elements (denoted Q4). The numerical behaviour leading to checkerboard layouts stems from an over-stiff estimation of a checkerboard patch of Q4 elements. The numerical model of a one-node connected hinge using Q4 elements, on the other hand, possesses no (or very little) stiffness in rotation about the common node. In the first part of the study, planar finite elements with in-plane rotational (drilling) degrees of freedom are investigated. It is shown that the skew-symmetric part of the stress tensor can directly be used to quantitatively assess the validity of the penalty parameter ã, which relates the in-plane translations to the rotations. Thereafter, the variational formulations used to develop these planar finite elements with drilling degrees of freedom are extended to account for the piezoelectric effect. Several new piezoelectric elements that include in-plane rotational degrees of freedom (with and without assumed stress and electric flux density) are implemented, evaluated and shown to be accurate and stable. Furthermore, the application of alternative reduced order integration schemes to quadratic serendipity (Q8) and Lagrangian (Q9) elements is investigated. Reduced or selective reduced integration schemes are often used to enhance element accuracy by `softening' higher order deformation modes. However, application of reduced integration schemes to Q8 and Q9 elements is usually accompanied by element rank deficiencies. It is shown how the application of five and eight point modified integration schemes preserve the accuracy benefits of reduced integration, while preventing element rank deficiencies. In the second part of the investigation, the salient features of elements with drilling degrees are utilized in two schemes to prevent, or improve the modelling of, one-node connected hinges. In principle, the first scheme uses the rotations computed at interior nodes to detect excessive rotations at suspect nodes. The second scheme essentially replaces planar elements forming a one-node hinge, where appropriate, with a more realistic beam model of the material layout while other elements in the mesh are modelled using planar elements as usual. Next, the dependence of optimal topologies on element formulation is demonstrated. Attention is especially paid to plate and shell applications. It is shown that Mindlin-Reissner based elements, which employ selective reduced integration on shear terms, are not reliable in topology optimization problems. Conversely, elements based on an assumed natural strain formulation are shown to be stable and capable of reproducing thin plate topology results computed using shear-rigid elements. Furthermore, it is shown that an ad hoc treatment of rotational degrees of freedom in shell problems is sensitive to the related adjustable parameter, whereas optimal topologies, using a proper treatment of drilling degrees of freedom are not. Finally, the use of reduced order integration schemes as a strategy to reduce the stiffness of a checkerboard patch of elements is considered. It is demonstrated that employing the five and eight point integration schemes, used to enhance the accuracy of Q8 and Q9 elements, also significantly reduce the stiffness of a checkerboard patch of elements, thereby reducing the probability of observing checkerboard layouts in optimal topologies. / Thesis (PhD (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / PhD / unrestricted

This thesis adds to the knowledge base of constant-force mechanisms (CFMs). It begins by reviewing past work done in the area of CFMs and then develops new nondimensionalized parameters that are used to simplify the calculations required to design a CFM. Comparison techniques are then developed that utilize these non-dimensionalized parameters to compare mechanisms based on stiffnesses, percent constant-force, actual lengths, normal displacements, and feasible design orientations. These comparison techniques are then combined with optimization to define new mechanisms with improved performance and range of capabilities. This thesis also outlines a design process, methods to identify mechanisms that are suitable for a given design problem, and relationships and trends between variables. The thesis concludes by discussing the adaptation of CFMs for use in electrical contacts and presenting the results of a design case study which successfully developed a constant-force electrical contact (CFEC).

Microactuators are needed to convert energy into mechanical work at the microscale. Thermal microactuators can be used to produce this needed mechanical work. The purpose of this research was to design, fabricate, and test thermal microactuators for use at the microscale in microelectromechanical systems (MEMS). The microactuators developed were tested to determine the magnitude of their deflection and estimate their force. Five groups of thermal microactuators were designed and tested. All of the groups used the geometrically constrained expansion of various segments to produce their deflection. The first group, Thermal Expansion Devices (TEDs), produced a rotational displacement and had deflections up to 20 µm. The second group, Bi-directional Thermal Expansion Devices (Bi-TEDs) were similar to the TEDs. The difference, as the name implies, was that the Bi-TEDs deflected up to 6 µm in two directions. Thermomechanical In-plane Micromechanisms (TIMs) were the third group tested. They produced a linear motion up to 20 µm. The fourth group was the Rapid Expansion Bi-directional Actuators (REBAs). These microactuators were bi-directional and produced up to 12 µm deflection in each direction. The final group of thermal microactuators was the Joint Actuating Micro-mechanical Expansion Systems (JAMESs). These thermal microactuators rotated pin joints up to 8 degrees. The thermal microactuators studied can be used in a wide variety of applications. They can move ratchets, position valves, move switches, change devices, or make connections. The thermal microactuator groups have their own unique advantages. The TIMS can be tailored for the amount of deflection and output force they produce. This will allow them to replace some microactuator arrays and decrease the space used for actuation. The Bi-TEDs and REBAs are bi-directional and can possibly replace two single direction micro-actuators. The JAMESs can be attached directly to a pin joint of an existing mechanism. These advantages allow these thermal microactuator groups to be used for a wide variety of applications.

This thesis introduces lamina emergent mechanisms (LEMs) and presents components that can be used as building blocks to create LEMs capable of more complex motion. As the name suggests, lamina emergent mechanisms are fabricated out of planar materials (the lamina) but their motion is out of that plane (emergent). Lamina emergent mechanisms can provide benefits that include reduced manufacturing costs and minimal volume when in the planar state. The compact initial state of LEMs is beneficial in reducing shipping costs, especially in volume critical applications. LEMs also exhibit the potential benefits of compliant mechanisms, namely increased precision, reduced weight, reduced wear, and part count reduction. The LEM components presented in this thesis include flexible segments, fundamental mechanisms, and a new complaint joint, the lamina emergent torsional (LET) Joint. The flexible segments are developed through changes in geometry, boundary/loading conditions, and material. The fundamental mechanisms presented have motion similar to planar change-point four-bar and six-bar mechanisms, and spherical change-point mechanisms. The LET Joint is presented as a compliant joint suited for applications where large angular rotation is desired, but high off-axis stiffness is not as critical. The joint is introduced and the equations necessary for determining the force-deflection characteristics and stress are presented. Since the LET Joint can be fabricated from a single planar layer, it is well suited for macro and micro applications. Illustrative examples of the LET Joint are provided with devices fabricated from materials as diverse as steel, polypropylene, and polycrystalline silicon.

In this research a variable-stiffness compliant mechanism was developed to generate variable force-displacement profiles at the mechanisms coupler point. The mechanism is based on a compliant Roberts straight-line mechanism, and the stiffness is varied by changing the effective length of the compliant links with an actuated slider. The variable-stiffness mechanism was used in a one-degree-of-freedom haptic interface to demonstrate the effectiveness of varying the stiffness of a compliant mechanism. Unlike traditional haptic interfaces, in which the force is controlled using motors and rigid links, the haptic interface developed in this work displays haptic stiffness via the variable-stiffness compliant mechanism. The force-deflection behavior of the mechanismwas analyzed using the Pseudo-Rigid Body Model (PRBM), and two key parameters, KQ and g,were optimized using finite element analysis (FEA) to match the model with the behavior of the device. One of the key features of the mechanism is that the inherent return-to-zero behavior of the compliant mechanism was used to provide the stiffness feedback felt by the user. A prototype haptic interface was developed capable of simulating the force-displacement profile of Lachmans Test performed on an injured ACL knee. The compliant haptic interface was capable of displaying stiffnesses between 4200 N/m and 7200 N/m.

The HGR valve, or hot gas recirculation valve, is an essential component of modern internal combustion engines. Its main function is to reduce emissions of nitrous oxide (NOx), which is a harmful pollutant produced during combustion. This research focuses on developing a compliant mechanism for HGR valve activation, in order to minimize wear leakage and reduce the number of parts.However, the project faced challenges, including limitations in steel elasticity, fatigue due to high frequency operation, and high stress due to elastic deformation. In order to achieve the range of motion required for efficient valve operation, additional mechanisms were incorporated, resulting in dimensional limitations beyond those of the current design. 3D modeling of the concepts were constructed with the help of CATIA, and Finite element analysis was carried out on the same. The concepts were assessed based on stresses and the range of motion. A Pugh’s matrix was used to compare various concepts. A concept using Vulcanized silicone rubber was found to be feasible for the application, but further work is required to bring the concept to a usable state. / HGR-ventilen, eller varmgasåtercirkulationsventilen, är en viktig komponent i moderna förbränningsmotorer. Dess huvudsakliga funktion är att minska utsläppen av kväveoxid (NOx),som är ett skadligt förorenande ämne som produceras under förbränning. Denna forskning fokuserar på att utveckla en kompatibel mekanism för aktivering av HGR-ventilen, för att minimera läckage och minska antalet delar. Projektet stötte dock på utmaningar, bland annat begränsningar i stålets elasticitet, utmattning på grund av högfrekvent drift och hög stress på grund av elastisk deformation. För att uppnå det rörelseomfång som krävs för effektiv ventildrift införlivades ytterligare mekanismer, vilket resulterade i dimensionella begränsningar utöver dem i den nuvarande konstruktionen. 3D modellering av koncepten konstruerades med hjälp av CATIA, och Finite element-analys utfördes på samma. Koncepten utvärderades baserat på spänningar och rörelseomfång. En Pughs matris användes för att jämföra de olika koncepten. Ett koncept som använder vulkaniserat silikongummi visade sig vara genomförbart för applikationen, men ytterligare arbete krävs för att föra konceptettill ett användbart tillstånd.

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We have designed and examined a compliant knee mechanism that may offer solutions to problems that exist for infants and toddlers who are just learning to walk. Pediatric prosthetic knees on the market today are not well designed for infants and toddlers for various reasons. Children at this age need a prosthetic that is light in weight, durable, and stable during stance. Of the eleven knees on the market for children, all but three are polycentric or four-bar knees, meaning they have multiple points of movement. Polycentric knees are popular designs because they offer the added benefit of stable stance control and increased toe clearance, unfortunately this type of knee is often too heavy for young children to wear comfortably and is not well suited for harsh environments such as sand or water, common places children like to play. The remaining three knees do not offer a stance control feature and are equally vulnerable to harsh environments due to ball bearing hinges. Compliant mechanisms offer several design advantages that may make them suitable in pediatric prosthetic knees -- light weight, less susceptible to harsh environments, polycentric capable, low part count, etc. Unfortunately, they present new challenges that must be dealt with individually. For example compliant mechanisms are typically not well suited in applications that need adjustability. This problem was solved by mixing compliant mechanism design with traditional mechanism design methods. This paper presents a preliminary design concept for a compliant pediatric prosthetic knee. The carbon fiber composite spring steel design was first built and then evaluated using Finite Element Analysis. The prototype's instant center was plotted using the graphical method. From our analysis position, force and stress information was gathered for a deflection up to 120 degrees. The instant centers that were plotted indicate that the knee has good potential in offering adequate stability during stance.