O presente trabalho dedica-se a uma modelagem da interação entre corpos celestes, em regime Newtoniano, levando-se em consideração as influências que suas deformações e viscosidades internas exercem sobre seus movimentos orbitais e suas velocidades angulares. A abordagem adotada é uma variação do conhecido problema do corpo pseudo-rígido, a qual simplifica drasticamente a determinação dos equilíbrios relativos e torna a questão da dinâmica matematicamente acessível. Com este tratamento, podemos relacionar ou comparar os resultados com aqueles estabelecidos na literatura, dentre eles: formato de equilíbrio de um fluido isolado em rotação, deformação de maré causada pela interação gravitacional e o torque de maré induzido no mesmo. Pela simplicidade do modelo pode-se ainda fazer uma análise qualitativa da dinâmica do sistema e obter estimativas sobre a velocidade com que se aproxima dos equilíbrios. / The present work is devoted to model the interaction among celestial bodies, in a Newtonian regime, but considering the role played by the internal deformation and viscosity on the orbital motion and angular velocities of the components of the system. The work is mainly developed with an alternative approach to the pseudo-rigid body model, which simplifies the determination of the relative equilibria and allows precise conclusions about the dynamics. So, we are able to compare the results of this theory with those established in the literature, namely: the equilibrium shape of an isolated fluid in rotation, the tidal elongation induced by gravitational interaction and the tidal torque. Due to its simplicity, we can further perform a qualitative analysis of the dynamics of the system and estimate the velocity of attraction of the equilibrium states.

Compliant mechanism theory permits a procedure called rigidbody replacement, in which two or more rigid links of the mechanism are replaced by a compliant flexure with equivalent motion. Methods for designing flexure with equivalent motion to replace rigid links are detailed in Pseudo-Rigid-Body Models (PRBMs). Such models have previously been developed for planar mechanisms. This thesis develops the first PRBM for spherical mechanisms. In formulating this PRBM for a spherical mechanism, we begin by applying displacements are applied to a curved beam that cause it todeflect in a manner consistent with spherical kinematics. The motion of the beam is calculated using Finite Element Analysis. These results areanalyzed to give the PRBM parameters. These PRBM parameters vary with the arc length and the aspect ratio of the curved beam.

The aim of this study is to present a design approach for compliant bistable four-link mechanisms. The design constraints are the two positions of the mechanism, the force required to snap between the positions and the fatigue life of the designed mechanism. The theory presented here will be applied to the door lock mechanism used in commercial dishwashers, which is originally designed as a rigid inverted slider crank mechanism snapping between two positions with the force applied by a spring. The mechanism is re-designed as a compliant bistable four-link mechanism and a prototype has been manufactured.

O presente trabalho dedica-se a uma modelagem da interação entre corpos celestes, em regime Newtoniano, levando-se em consideração as influências que suas deformações e viscosidades internas exercem sobre seus movimentos orbitais e suas velocidades angulares. A abordagem adotada é uma variação do conhecido problema do corpo pseudo-rígido, a qual simplifica drasticamente a determinação dos equilíbrios relativos e torna a questão da dinâmica matematicamente acessível. Com este tratamento, podemos relacionar ou comparar os resultados com aqueles estabelecidos na literatura, dentre eles: formato de equilíbrio de um fluido isolado em rotação, deformação de maré causada pela interação gravitacional e o torque de maré induzido no mesmo. Pela simplicidade do modelo pode-se ainda fazer uma análise qualitativa da dinâmica do sistema e obter estimativas sobre a velocidade com que se aproxima dos equilíbrios. / The present work is devoted to model the interaction among celestial bodies, in a Newtonian regime, but considering the role played by the internal deformation and viscosity on the orbital motion and angular velocities of the components of the system. The work is mainly developed with an alternative approach to the pseudo-rigid body model, which simplifies the determination of the relative equilibria and allows precise conclusions about the dynamics. So, we are able to compare the results of this theory with those established in the literature, namely: the equilibrium shape of an isolated fluid in rotation, the tidal elongation induced by gravitational interaction and the tidal torque. Due to its simplicity, we can further perform a qualitative analysis of the dynamics of the system and estimate the velocity of attraction of the equilibrium states.

This dissertation presents new concepts and methodology in designing shape-morphing structures using bistable elements. Developed using the Pseudo-Rigid-Body Model (PRBM), linear bistable compliant mechanism elements produce predictable and controllable length changes. Step-by-step design procedures are developed to guide the design process of these bistable elements. Two different examples of Shape-Morphing Space Frames (SMSFs) were designed and prototyped utilizing the bistable linear elements in a single-layer grid, in addition to flexures and rigid links, to morph a cylindrical space frame into both a hyperbolic and a spherical space frame. Moreover, bistable unit-cell compliant-mechanism elements were also developed to morph a compact structure from a specific initial shape to a final specific shape. The detailed design of those unit cells were done using Computer-aided design (CAD) software following a novel design procedure to transform a one-degree-of-freedom mechanism into a structure with sufficient compliance within its links to toggle between two chosen stable positions. Two different design examples were investigated in this research and prototyped to demonstrate the ability to morph disks into a hemisphere or a sphere with the structure being stable in both states (disk and sphere).

The purpose of this research is to present a class of Self-Retracting Fully-compliant Bistable Micromechanisms (SRFBM). Fully-compliant mechanisms are needed to overcome the inherent limitations of microfabricated pin joints, especially in bistable mechanisms. The elimination of the clearances associated with pin joints will allow more efficient bistable mechanisms with smaller travel. Small travel, in a linear path facilitates integration with efficient on-chip actuators. Tensural pivots are developed and used to deal with the compressive loading to which the mechanism is subject. SRFBM are modeled using the Pseudo-Rigid-Body Model and finite element analysis. Suitable configurations of the SRFBM concept have been identified and fabricated using the MUMPs process. Complete systems, including external actuators and electrical contacts are 1140 μm by 625 μm (individual SRFBM are less than 300 μm by 300 μm). These systems have been tested, demonstrating on-chip actuation of bistable mechanisms. Power requirements for these systems are approximately 150 mW. Testing with manual force testers has also been completed and correlates well with finite element modeling. Actuation force is approximately 500 μN for forward actuation. Return actuation can be achieved either by external actuators or by thermal self-retraction of the mechanism. Thermal self-retraction is more efficient, but can result in damage to the mechanism. Fatigue testing has been completed on a single device, subjecting it to approximately 2 million duty cycles without failure. Based on the SRFBM concept a number of improvements and adaptations are presented, including systems with further power and displacement reductions and a G-switch for LIGA fabrication.

Haptic interfaces are robotic force-feedback devices that give the user a sense of touch as they interact with virtual or remote environments. These interfaces act as input devices, mapping the 3-dimensional (3D) motions of the user's hand into 3D motions in a slave system or simulated virtual world. A major challenge in haptic interfaces is ensuring that the user's experience is a realistic depiction of the simulated environment. This requires the interface's design to be such that it does not hinder the user's ability to feel the forces present in the environment. This "transparency" is achieved by minimizing the device's physical properties (e.g., weight, inertia, friction). The primary objective of the work is to utilize compliant mechanisms as a means to improve transparency of a haptic interface. This thesis presents work toward the design of a fully compliant mechanism that can be utilized in haptic interfaces as a means to reduce parasitic forces. The approach taken in this work is to design a series of mechanisms that when combined act as a statically balanced compliant joint (SBCJ). Simulated and experimental results show that the methods presented here result in a joint that displays a significant decrease in return-to-home behavior typically observed in compliant mechanisms. This reduction in the torque needed to displace the joint and the absence of friction suggest that the joint design is conducive to the methods previously proposed for increasing transparency in haptic interfaces.

The aim of this study is to design a compliant lock mechanism for a dishwasher, using a systematic approach. Functionally binary pinned-pinned segment that exhibits bistable behavior is utilized. Pseudo-rigid-body model of the whole mechanism and the half segment is developed separately and the corresponding calculations are carried out. Among current solutions a different method namely &ldquo / arc fitting method&rdquo / is developed and it is utilized to construct the model. A software code is written to get the exact solutions, which require the evaluation of elliptic integrals. Results are compared with the analytical model and confirmed with physical prototype. Predefined tip forces are seen to provide the transition from one stable position to other. Durability, reliability and compactness characteristics are particularly considered.

This paper presents designs for Multistable Shape-Shifting Surfaces (MSSS) by introducing bistability into the Shape-Shifting Surface (SSS). SSSs are defined as surfaces that retain their effectiveness as a physical barrier while undergoing changes in shape. The addition of bistability to the SSS gives the surface multiple distinct positions in which it remains when shifted to, i.e. by designing bistability into a single SSS link, the SSS unit cell can change into multiple shapes, and stabilize within the resulting shape, while maintaining integrity against various forms of external assaults normal to its surface. Planar stable configurations of the unit cell include, expanded, compressed, sheared, half-compressed, and partially-compressed, resulting in the planar shapes of a large square, small square, rhombus, rectangle, and trapezoid respectively. Tiling methods were introduced which gave the ability to produce out-of-plane assemblies using planar MSSS unit cells. A five-walled rigid storage container prototype was produced that allowed for numerous stable positions and volumes. Applications for MSSSs can include size-changing vehicle beds, expandable laptop screens, deformable walls, and volume-changing rigid-storage containers. Analysis of the MSSS was done using pseudo-rigid-Body Models (PRBMs) and Finite Element Analysis (FEA) which ensured bistable characteristics before prototypes were fabricated.

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).