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.

While variation analysis methods for compliant assemblies are not new, little has been done to include the effects of multi-step, fixtured assembly processes. This thesis introduces a new method to statistically analyze compliant part assembly processes using fixtures. This method, consistent with the FASTA method developed at BYU, yields both a mean and a variant solution. The method, called Piecewise-Linear Elastic Analysis, or PLEA, is developed for predicting the residual stress, deformation and springback variation in compliant assemblies. A comprehensive, step-by-step analysis map is provided. PLEA is validated on a simple, laboratory assembly and a more complex, production assembly. Significant modeling findings are reported as well as the comparison of the analytical to physical results.

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.

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.

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.

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.