A mathematical dynamic model is derived for the compliant constant-force mechanism, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force mechanism is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully validated with empirical data from five separate mechanisms, comprising two configurations of compliant constant-force mechanism. The dynamic model is cast in generalized form to represent all possible configurations of compliant constant-force mechanism. Deriving the dynamic equation from the pseudo-rigid-body model is useful because every configuration is represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force mechanism is discovered: there exists a range of frequencies for which the output force of the mechanism accords nearer to constant-force than does the output force at static levels.

The purpose of this research is to identify the configurations of several mechanism classes which result in bistable behavior. Bistable mechanisms have use in many applications, such as switches, clasps, closures, hinges, and so on. A powerful method for the design of such mechanisms would allow the realization of working designs much more easily than has been possible in the past. A method for the design of bistable mechanisms is especially needed for micro-electro-mechanical systems (MEMS) because fabrication and material constraints often prevent the use of simple, well-known bistable mechanism configurations. In addition, this knowledge allows designers to take advantage of the many benefits of compliant echanisms, especially their ability to store and release energy in their moving segments. Therefore, an analysis of a variety of mechanism classes has been performed to determine the configurations of compliant segments or rigid-body springs in a mechanism which result in bistable behavior. The analysis revealed a relationship between the placement of compliant segments and the stability characteristics of the mechanism which allows either analysis or synthesis of bistable mechanisms to be performed very easily. Using this knowledge, a method of type synthesis for bistable mechanisms has been developed which allows bistable mechanisms to be easily synthesized. Several design examples have been presented which demonstrate the method. The theory has also been applied to the design of several bistable micromechanisms. In the process of searching for usable designs for micro-bistable mechanisms, a mechanism class was defined, known as "Young" mechanisms, which represent a feasible and useful way of achieving micro-mechanism motion similar to that of any four-bar mechanism. Based on this class, several bistable micro-mechanisms were designed and fabricated. Testing demonstrated the ability of the mechanisms to snap between the two stable states. In addition, the mechanisms showed a high degree of repeatability in their stable positions.

This thesis introduces two ortho-planar MEMS devices that can be used to position microcomponents: the XZ Micropositioning Mechanism and the XYZ Micromanipulator. The displacement and force relationships are presented. The devices were fabricated using surface micromachining processes and the resulting mechanisms were tested. A compliant XYZ Micromanipulator was also designed to reduce backlash and binding. In addition, several other MEMS positioners were fabricated and tested: the Micropositioning Platform Mechanism (MPM), the Ortho-planar Twisting Micromechanism (OTM), and the Ortho-planar Spring Micromechanism (OSM).

Nanopositioners have been developed with electrostatic, piezoelectric, magnetic, thermal, and electrochemical actuators. They move with as many as six degrees of freedom; some are composed of multiple stages that stack together. Both macro-scale and micro-scale nanopositioners have been fabricated. A summary of recent research in micropositioning and nanopositioning is presented to set the background for this work. This research project demonstrates that a dual-stage nanopositioner can be created with microelectromechanical systems technology such that the two stages are integrated on a single silicon chip. A nanopositioner is presented that has two stages, one for coarse motion and one for fine motion; both are fabricated by surface micromachining. The nanopositioner has one translational degree of freedom. Thermal microactuators operate both stages. The first stage includes a bistable mechanism: it travels 52 micrometers between two discrete positions. The second stage is mounted on the first stage and moves continuously through an additional 8 micrometers in the same direction as the first stage. Two approaches to the control of the second stage are evaluated: first, an electrical input is transmitted to an actuator that moves with the first stage; second, a mechanical input is applied to an amplifier mechanism mounted on the first stage after completing the coarse motion. Four devices were designed and fabricated to test these approaches; the one that performed best was selected to fulfill the objective of this work. Thermal analysis of the actuators was performed with previously developed tools. Pseudo-rigid-body models and finite element models were created to analyze the mechanical behavior of the devices. The nanopositioners were surface micromachined in a two-layer polysilicon process. Experiments were performed to characterize the resolution, repeatability, hysteresis, and drift of the second stages of the nanopositioners with open-loop control. Position measurements were obtained from scanning electron micrographs by a numerical procedure, which is described in detail. The selected nanopositioner demonstrated 170-nanometer resolution and repeatability within 37 nanometers. The hysteresis of the second stage was 6% of its full range. The nanopositioner drifted 25 nanometers in the first 60 minutes of operation with a time constant of about 6 minutes. The dual-stage nanopositioner may be useful for applications such as variable optical attenuators or wavelength-specific add--drop devices.

Linear-motion compliant mechanisms have generally been developed for small displacement applications. The objective of the thesis is to provide a basis for improved large-displacement linear-motion compliant mechanisms (LLCMs). One of the challenges in developing large-displacement compliant mechanisms is the apparent performance tradeoff between displacement and off-axis stiffness. In order to facilitate the evaluation, comparison, and optimization of the performance of LLCMs, this work formulates and presents a set of metrics that evaluates displacement and off-axis stiffness. The metrics are non-dimensionalized and consist of the relevant characteristics that describe mechanism displacement, off-axis stiffness, actuation force, and size. Displacement is normalized by the footprint of the device. Transverse stiffness is normalized by a new performance characteristic called virtual axial stiffness. Torsional stiffness is normalized by a performance characteristic called the characteristic torque. Because large-displacement compliant mechanisms are often characterized by non-constant axial and off-axis stiffnesses, these normalized stiffness metrics are formulated to account for the variation of both axial and off-axis stiffness over the range of displacement. In pursuit of mechanisms with higher performance, this work also investigates the development of a new compliant mechanism element. It presents a pseudo-rigid-body model (PRBM) for rolling-contact compliant beams (RCC beams), a compliant element used in the RCC suspension. The loading conditions and boundary conditions for RCC beams can be simplified to an equivalent cantilever beam that has the same force-deflection characteristics as the RCC beam. Building on the PRBM for cantilever beams, this paper defines a model for the force-deflection relationship for RCC beams. Included in the definition of the RCC PRBM are the pseudo-rigid-body model parameters that determine the shape of the beam, the length of the corresponding pseudo-rigid-body links and the stiffness of the equivalent torsional spring. The behavior of the RCC beam is parameterized in terms of a single parameter defined as clearance, or the distance between the contact surfaces. The RCC beams exhibit a unique force-displacement curve where the force is inversely proportional to the clearance squared. The RCC suspension is modeled using the newly defined PRBM. The suspension exhibits unique performance, generating no resistance to axial motion while providing significant off-axis stiffness. The mechanism has a large range of travel and operates with frictionless motion due to the rolling-contact beams. In addition to functioning as a stand-alone linear-motion mechanism, the RCC suspension can be configured with other linear mechanisms in superposition to improve the off-axis stiffness of other mechanisms without affecting their axial resistance.

Lamina emergent mechanisms (LEMs) are a maturing technology that is prepared for commercial implementation into new products. LEMs are defined by three functional characteristics; they (1) are compliant, (2) are fabricated from planar materials, and (3) emerge from a flat initial state. Advantages, design challenges, and design tools are described for each of the functional characteristics. Opportunities for LEMs are discussed, namely disposable LEMs, novel arrays of LEMs, scaled LEMs, LEMs with surprising motion, shock absorbing LEMs, and deployable LEMs. Technology push product development processes were employed to select applications for LEMs. LEM technology was characterized. In a LEM workshop, eighteen industry professionals then helped identify over 200 potential applications for the technology. The applications were evaluated, and the most promising ideas that were identified for each LEM opportunity are described with graphics of possible product embodiments. Of the various product opportunities enabled by LEMs, deployable mechanisms – particularly in the credit card size – are among the most viable. The compactness and portability of credit-card-sized products create a strong motivation for their development. Expanding the capabilities of credit-card-sized mechanisms to include more sophisticated motions and a broader range of tasks may dramatically increase their market potential. A review of the current state-of-the-art in credit-card-sized mechanisms reveals two primary classes of mechanisms most commonly used in this form factor: rigid-body mechanisms and in-plane compliant mechanisms. The limitations of each and corresponding LEM advantages are described. Criteria for determining whether a product is a suitable candidate for using LEM technology to create or improve a credit-card-sized product are established. The advantages of LEMs in credit-card-sized products are illustrated through an example product: a compact lancing device that could be used as a main component for a highly portable epinephrine syringe.

Origami-based approaches for the folding of thick materials for specific application to large deployable space arrays is explored in this work. The folding approaches presented utilize strain energy, spatial kinematics, membranes, compliant mechanisms, and or in combination together to fold finite-thickness materials viewed through the lens of origami-based engineering. Novel architectures and behaviors of mechanisms are developed to achieve packaging efficiency, deployment, and self-stiffening. A method for the folding of monolithic thick-sheet materials is developed by incorporating compliant mechanisms into the material itself to strategically add degrees of freedom. The design and characterization of the compliant mechanisms with consideration to stress, material selection, and stiffness is given. Other folding approaches developed include a bistable vertex and a double-membrane method.The folding approaches derived are applied to larger tessellations and folding patterns. The fold patterns developed and used lend themselves well to large reconfiguration and the combination of the folding approaches with the patterns create opportunities to fabricate products out of thick, functional materials. Of specific interest is the application of these approaches and patterns to the field of deployable space arrays. Spatial kinematics, computational dynamics, physical tests, and systems engineering are used to develop an array architecture that is self-deployable, self-stiffening, and retractable. This architecture is shown to open the design space of large deployable arrays by increasing packaging efficiency and mass.The method, approaches, and architectures developed by this dissertation contribute to the fields origami-based engineering and deployable space arrays. While a focus of this work is the advancement of space technologies, the depth of the analyses provided are transferable to other origami-based and compliant-mechanism disciplines.

Un manipulateur parallèle à mobilité réduite a moins de six degrés de liberté et présente généralement différents types de mouvement connus sous le nom de modes d'opération. Ainsi, ce type de manipulateur peut être classifié comme reconfigurable selon sa capacité de transition entre les différents modes d'opération. Cette thèse de doctorat s'articule principalement autour de l'analyse cinématique de manipulateurs parallèles à mobilité réduite, de manipulateurs parallèles en série obtenus à partir de leur empilement en série et de mécanismes conformes conçus à partir de leurs configurations singulières à contraintes. La transformation cinématique de Study est utilisée pour dériver les équations algébriques de contraintes. Ensuite, elles sont interprétées à l'aide d'outils de géométrie algébrique pour effectuer des analyses de mobilité, de cinématique et de singularité. Les techniques de ‘‘screw theory’’ et ‘‘line geometry’’ sont utilisées à côté de l'approche algébrique au besoin. / A lower mobility parallel manipulator has less than six degrees of freedom and usually exhibits different motion types known as operation modes. Thus, it can be classified as reconfigurable on account of its ability to transition between different operation modes. This doctoral thesis mainly revolves around the kinematic analysis of some lower-mobility parallel manipulators, series-parallel manipulators obtained from their serial stacking and compliant mechanisms designed using their constraint singular configurations. Study's kinematic mapping is used to derive the algebraic constraint equations. They are further interpreted using algebraic geometry tools to perform mobility, kinematic and singularity analysis. Screw theory and line geometry techniques are used adjacent to algebraic approach wherever necessary.

La robotique chirurgicale vise à rendre les gestes du chirurgien plus précis et moins invasifs. La complexité d’une salle d’opération conduit à rechercher des dispositifs robotiques aussi compacts que possible et pouvant être facilement stérilisés. Une conception robotique basée sur l’emploi de mécanismes compliants à structures monolithiques et d’actionneurs piézoélectriques est particulièrement intéressante sur ce point. Des travaux précédents conduits au laboratoire ont permis de proposer un dispositif robotique pour le pontage coronarien qui facilite la réalisation des gestes minimalement invasifs sur cœur battant. Ce dispositif répond au besoin médical mais manque aujourd’hui de la compacité souhaitée pour une intégration optimale. À partir du cas d’application où nous cherchons à réduire la taille du dispositif de compensation, nous nous intéressons, dans cette thèse, aux problématiques de conception de mécanismes compliants à fortes contraintes d’intégration. Nous étudions d’abord la possibilité d’intégrer le dispositif de compensation directement dans la tige du stabilisateur cardiaque passif. Puis, nous étudions la possibilité de réduire la taille du dispositif de compensation en amont, en explorant les possibilités de réaliser des mécanismes dans un plan. Nous avons notamment proposé une méthode originale de conception de mécanismes compliants plans à partir de l‘analyse des singularités de mécanismes à architectures parallèles en configuration plane. Afin d’optimiser les différents mécanismes très contraints par les volumes imposés, une méthode originale d’optimisation à base d’un algorithme de colonie de fourmis est employée. / Surgical robotics helps to increase the surgeon’s accuracy and limits the invasiveness of the surgery. The complexity of an operation room implies to design surgical devices that are as compact as possible and that can be easily sterilized. One interesting design approach is to combine compliant mechanisms, which have a monolithic structure, and piezoelectric actuators. Based on this approach, a robotic device for minimally invasive coronary artery bypass grafting has been proposed previously in our laboratory. This device successfully helps to increase the stabilization of the heart surface during the surgery but its compactness needs to be increased for an optimal integration in the operation room. Based on the need to reduce the compensation mechanism of this device, the problem of the design of compliant mechanisms with strong integration constrains is studied in this PhD thesis. First, the possibility to integrate the compensation mechanism directly in the shaft is considered. Then, the possibility to reduce the compensation mechanism at the end of the shaft by considering an assembly of planar manufactured structures is considered. Among the contributions, we propose an original design method based on the analysis of singularities of parallel manipulators in planar configuration. We also propose an original optimization method based on ant colony optimization in order to optimize the compliant architectures proposed in this work.

This thesis work provides an insight into the design of Force-amplifying Compliant Mechanisms (FaCMs) that are integrated with micromachined resonant accelerometers to increase their sensitivity. An FaCM, by mechanically amplifying the inertial force, enhances the shift in the resonance frequency of the beams used for sensing the acceleration whose effect causes an axial force on the beams. An extensive study on different configurations of resonators namely, single beam resonator, single-ended tuning fork (SETF), and double-ended tuning fork (DETF), is carried out to gain insights about their resonant behavior. The influence of the boundary conditions on the sensor’s sensitivity emerged from the study. We found that not only the force-amplification factor but also the multi-axial stiffness of the FaCM and proof-mass influence the resonance frequency of the resonator as well as the bandwidth of the modified sensor for certain configurations but not all. Thus, four lumped parameters were identified to quantify the effectiveness of an FaCM. These parameters determine the boundary condition of the sensing beams and also the forces and the moment transmitted to them. Also presented in this work is a computationally efficient model, called the Lumped Parameter Model (LPM) for evaluation of the sensitivity. An analytical expression for the frequency-shift of the sensing resonator beams is obtained by considering the FaCM stiffness parameters as well as the lumped stiffness of the suspension of the inertial mass. Various FaCMs are evaluated and compared to understand how the four lumped parameters influence the sensor’s sensitivity. The FaCMs are synthesized using topology optimization to maximize the net amplification factor with the volume constraint. One of the FaCMs outperforms the lever by a factor of six. Microfabrication of resonant accelerometer coupled with FaCM and comb-drive actuator is carried out using a silicon-on-insulator process. Finally, the selection map technique, a compliant mechanism redesign methodology is used for enhancing the amplification of FaCMs. This technique provides scope for further design improvement in FaCMs for given sensor specifications.