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.

Origami-based design is increasing in popularity as its benefits and advantages become better understood and explored. However, many opportunities still exist for the application of origami principles to engineered designs, especially in the use of non-paper, thick sheet materials. One specific area utilizing thick sheet materials that is especially promising is origami-based mechanisms that require electrical power transfer applications. Many of these opportunities can be met by the use of surrogate folds. This thesis provides methods and frameworks that can be used by engineers to efficiently select and design surrogate folds for use in origami-based mechanisms and products. Surrogate folds are a means of achieving fold-like behavior, offering a simple method for achieving folding motions in thicker materials. A surrogate fold is a localized reduction in stiffness in a given direction allowing the material to function like a fold. A family of surrogate folds is reviewed, and the respective behaviors of the folds discussed. For a specified fold configuration, the material thickness is varied to yield different sizes of surrogate folds. Constraint assumptions drive the design, and the resultant configurations are compared for bending motions. Finite element and analytical models for the folds are also compared. Prototypes are made from different materials. This work creates a base for creating design guidelines for using surrogate folds in thick sheet materials. As mechanisms with origami-like movement increase in popularity, there is a need for conducting electrical power across folds. Surrogate folds can be used to address this need. Current methods and opportunities for conducting across folds are reviewed. A framework for designing conductive surrogate folds that can be adapted to fit specific applications is presented. Equations for calculating the electrical resistance in single surrogate folds as well as arrays are given. Prototypes of several conductive joints are presented and discussed. The framework is then followed in the design and manufacture of a conductive origami-inspired mechanism.

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.

This work develops and examines design strategies for reducing the stiffness of 3D-printed compliant mechanisms. The three aspects of a flexure that determine its stiffness are well known: material, boundary conditions, and geometry. In a highly constrained design space however, flexure stiffness may remain unacceptably high even while arriving at the limits of design constraints. In this work, changes to geometry and boundary conditions are examined that lead to drastically reduced stiffness behavior without changing flexure thickness, width, or length. Changes to geometry can result in very complex mechanisms. However, 3D printing enables almost arbitrarily complex geometries. This dissertation presents three design strategies for stiffness reduction: static balancing, lattice flexures, and compound joints. Static balancing refers to changes in the boundary conditions that result in a near-zero net change in potential energy storage over the useful deflection of a flexure. In this work, I present a method for static balancing that utilizes non-dimensional parameters to quickly synthesize a joint design with stiffness reduced by nearly 90%. This method is not only simple and straightforward, it is applicable to a wide range of flexure topologies. The only requirements on the joint to be balanced are that it must be approximated as a pin joint and torsion spring, and it must have a well-understood stiffness when subjected to a compressive load. Lattice flexures result from modifications to geometry that reduce cross-sectional area without changing width or thickness. However, the reduction in stiffness is greater than the reduction in cross sectional area. This can occur because the bending load is now carried by beams partially in torsion. Two lattice geometries are proposed and analyzed in detail using analytic and numeric techniques. It is shown that the off-axis stiffness behavior of lattice flexures can be better than that of conventional blade flexures while bending stiffness is reduced >60%. Compound joints are those that consist of arrays of flexures arranged co-axially. This arrangement provides increased range of motion, generally decreased stiffness, and improved stability. Additionally, a method is herein presented to reduce the parasitic center shift of a compound joint to nearly zero at a specified deflection. The penultimate chapter demonstrates how all three strategies can be used together, and includes new results to facilitate their combination.

A compliant mechanism gains its motion from the deflection of flexible members or the deformation of one portion of materials with respect to other portions. Design and operation of compliant mechanisms are very important, as most of the natural objects are made of compliant materials mixed with rigid materials, such as the bird wings. The most serious problem with compliant mechanisms is their fatigue problem due to repeating deformation of materials in compliant mechanisms. This thesis presents a study on the computational framework for designing a compliant mechanism under fatigue strength control. The framework is based on the topology optimization technique especially ground structure approach (GSA) together with the Genetic Algorithm (GA) technique. The study presented in this thesis has led to the following conclusions: (1) It is feasible to incorporate fatigue strength control especially the stress-life method in the computational framework based on the GSA for designing compliant mechanisms and (2) The computer program can well implement the computational framework along with the general optimization model and the GA to solve the model. There are two main contributions resulting from this thesis: First one is provision of a computational model to design compliant mechanisms under fatigue strength control. This model also results in a minimum number of elements of the compliant mechanism in design, which means the least weight of mechanisms and least amount of materials. Second one is an experiment for the feasibility of implementing the model in the MATLAB environment which is widely used for engineering computation, which implies a wide applicability of the design system developed in this thesis.

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.

This dissertation describes the development and effectiveness of a mathematical model used to predict the behavior of cantilever beams whose loading conditions include parallel combinations of evenly distributed loads and endpoint forces. The large deflection of cantilever beams has been widely studied. A number of models and mathematical techniques have been utilized in predicting the endpoint path coordinates and load-deflection relationships of such beams. The Pseudo-Rigid-Body Model (PRBM) is one such method which replaces the elastic beam with rigid links of a parameterized pivot location and torsional spring stiffness. In this paper, the PRBM method is extended to include cases of a constant distributed load combined with a parallel endpoint force. The phase space of the governing differential equations is used to store information relevant to the characterization of the PRBM parameters. Correction factors are also given to decrease the error in the load-deflection relationship and extend the angular range of the model, thereby further aiding compliant mechanism design. The calculations suggest a simple way of representing the effective torque caused by a distributed load in a PRBM as a function of easily calculated model parameters.

This thesis improves a previous kinematic analysis and develops the elastic portion of the analysis of a curved compliant beam. This analysis is used to develop a Pseudo-Rigid-Body Model for the curved compliant beam. The Pseudo-Rigid-Body Model consist of kinematic and elastic parameters which can be used to simplify the computation of the large deflections of the beam as it undergoes spherical motion. The kinematic parameters that are developed are the characteristic radius, Gamma*length, the parametric angle coefficient, c_theta, and the kinematic parametrization limit, Capital_theta_max(Gamma). The elastic parameters developed are the stiffness coefficient, K_theta, and the elastic parameterization limit, Capital_theta_max(K). Additionally, curve fit parameters are developed which enable the calculation of the stress in curved beam as it deflects.

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.