Reconfiguration of a four-bar mechanism using phase space connections

Linkage mechanisms are perhaps the simplest mechanical structures in engineering, but they can exhibit significant nonlinearity which can in principle be exploited. In this paper a simple smart structure model is developed based on such nonlinearity to investigate the reconfiguration of a four-bar mechanism through phase space connections. The central idea is based on heteroclinic connections in the mechanism phase space between equal-energy unstable equilibria. It is proposed that transitions between such equal-energy unstable (but actively controlled) equilibria in principle require zero net energy input, compared to transitions between stable equilibria which require the input and then dissipation of energy. However, it can be difficult to obtain such heteroclinic connections numerically in complex dynamical systems, therefore an objective function approach is used to seek transtions between unstable equilibria which approximate true heteroclinic connections. The instability inherent in the model is therefore actively utilised to provide energy-efficient transitions between configurations of the mechanism. It will be shown that the four-bar mechanism then forms the basis for an elastic model of a smart buckling beam

Development of a novel synthesis method of a rigid-body four-bar linkage into a compliant mechanism

The four-bar linkage mechanism is widely used in various machinery applications. This study presents a synthesis method to transform a rigid-body four-bar mechanism into a compliant mechanism using four leaf-type hinges based on linear theory and Castigliano's Theorem. The objective is to determine the dimensions and configuration of a flexible four-bar mechanism that replicates the behavior of the initial rigid-body mechanism. The meeting point between the two mechanisms is the flexure hinge of the compliant mechanism, which is determined using the Pseudo-Rigid-Body model (PRBM). To validate the proposed method, a program based on non-linear theory is employed. The results confirm that the dimensional differences between the two are minimal, ranging from 0% to 0.13%. This study demonstrates the feasibility of synthesizing a Rigid-Body Four-Bar Mechanism into a compliant mechanism using the PRBM, as long as the deformations are within the linear domain

Mechatronic Model of a Compliant 3PRS Parallel Manipulator

Compliant mechanisms are widely used for instrumentation and measuring devices for their precision and high bandwidth. In this paper, the mechatronic model of a compliant 3PRS parallel manipulator is developed, integrating the inverse and direct kinematics, the inverse dynamic problem of the manipulator and the dynamics of the actuators and the control. The kinematic problem is solved, assuming a pseudo-rigid model for the deflection in the compliant revolute and spherical joints. The inverse dynamic problem is solved, using the Principle of Energy Equivalence. The mechatronic model allows the prediction of the bandwidth of the manipulator motion in the 3 degrees of freedom for a given control and set of actuators, helping in the design of the optimum solution. A prototype is built and validated, comparing experimental signals with the ones from the model.Authors would like to thank the Ministerio de Ciencia e Innovación of the Spanish government for funding the project PID2019-105262RB-I00

A generalized approach for compliant mechanism design using the synthesis with compliance method, with experimental validation

Compliant mechanisms offer numerous advantages over their rigid-body counterparts. The synthesis with compliance technique synthesizes compliant mechanisms for conventional rigid-body synthesis tasks with energy/torque specifications at precision positions. In spite of its usefulness, the method suffers from some limitations/problems. The purpose of this work is to investigate these sensitivities with the synthesis with compliance technique and improve upon existing method. A new, simple but efficient, method for synthesis with compliance using an optimization approach is proposed, and its usefulness and simplicity demonstrated over the existing method. The strongly and weakly coupled system of kinematic and energy/torque equations in the existing method has been studied, and the new method is made simple by removing the strong coupling between these sets of equations. All synthesis cases are solved by treating them as though they are governed by weakly coupled systems of equations. Representative examples of different synthesis tasks are presented. The results are verified with finite element analysis software ABAQUS® and ANSYS® by means of coupler curve/precision position comparisons, and stored energy comparisons. An experimental setup has been devised to perform experiments on compliant mechanisms for validation purposes. The results obtained using the Pseudo-Rigid-Body Model (PRBM) for compliant mechanism synthesis match closely with experimental and finite element analysis (FEA) results, and hence reinforce the utility of the synthesis with compliance method using the PRBM in compliant mechanism synthesis --Abstract, page iii

Development of methods for the synthesis of compliant mechanisms

Einer der am häufigsten verwendeten Mechanismen in Geräten und Maschinen ist die Viergelenkkette. Dieses Getriebe hat viele Verwendungsmöglichkeiten: Verriegelungszangen, Hebebühnen, Frontlader, Aufhängung von Fahrrädern usw. Alle diese Beispiele sind Starrkörpersysteme, jedoch gibt es heutzutage auch nachgiebige Mechanismen, die Festkörpergelenke statt der konventionellen Kopplungen (Stifte, Gleitgelenke, Schubgelenke usw.) verwenden. Diese nachgiebigen Mechanismen werden aufgrund ihres reproduzierbaren Bewegungsverhaltens meistens in der Präzisionstechnik eingesetzt. Sie erlauben nur kleine Verschiebungen, sind aber sehr genau. Außerdem bieten nachgiebige Mechanismen viele weitere Vorteile. Aus diesem Grund wird in dieser Masterarbeit die Entwicklung einer neuen Synthesemethode vorgestellt, um ausgehend von einem viergliedrigen Starrkörpermechanismus mit gegebenen Gliedlängen einen nachgiebigen Mechanismus mit vier blattfederartigen Festkörpergelenken mit variabler Gelenklänge zu erzeugen. Diese Methode basiert auf der linearen Theorie nach Castigliano, wobei auch die Maximalspannung berücksichtigt wird. Es wird ein Algorithmus entwickelt und die numerische Implementierung erfolgt in MATLAB mit einer grafischen Benutzeroberfläche (GUI). Zu Beginn werden grundlegende Definitionen und der Ausgangszustand von Entwicklungen, die für diese Arbeit hilfreich sein können, vorgestellt. Daraufhin wird die Entwicklung der theoretischen Grundlage der Synthese basierend auf der linearen Theorie erläutert. In diesem Abschnitt werden die verschiedenen untersuchten Fälle mit ihren jeweiligen Gleichungen dargestellt. Abschließend wird ein Vergleich zwischen der entwickelten Synthesemethode basierend auf der linearen Theorie und einem existierenden nichtlinearen Analyseansatz vorgestellt, um eine Verifikation für Beispielvarianten zu erhalten. Der Unterschied zwischen diesen beiden Ansätzen beträgt weniger als 0,5 %, wenn sich beide Modelle im Bereich kleiner Verformungen befinden. Daher kann das Modell in der Präzisionstechnik verwendet werden. Für zukünftige Forschungen kann der Algorithmus verbessert werden, um mehr Mechanismenmodelle zu entwickeln. Außerdem kann das Verfahren zum Lösen des Gleichungssystems verbessert werden, da die durchschnittliche Berechnungszeit einer Simulation im Bereich mehrerer Minuten liegt und damit vergleichsweise lang ist.One of the most used mechanism in devices and machines is the four-bar linkage mechanism. This mechanism can be presented in different ways and has many uses: locking pliers, pumpjacks, lift platforms, front loaders, suspension of bikes, etc. All these examples are rigid-body systems, but nowadays there are also compliant mechanisms which use flexure hinges instead of conventional couplings (pins, sliding joints, prismatic joints, etc.). These compliant mechanisms are used mostly in precision engineering because of their reproducible motion behavior. However, they only allow small displacements, but they are highly precise. Also, the compliant mechanisms have many further advantages. This is the reason why in this Master thesis the development of a novel synthesis method of a rigid-body four-bar linkage with given link lengths into a compliant mechanism with four leaf-type flexure hinges with varying hinge lengths is presented. This method is based on the linear theory according to Castigliano's Theorem, while the maximum stress is considered, too. An algorithm is developed and numerically implemented in MATLAB in combination with a graphical user interface (GUI). First basic definitions and the state of developments that may help in this work are presented. Thereon the development of the theoretical basis of the synthesis based on the linear theory will be provided, while in this section the different considered cases are explained, each with their respective equations. Finally, a comparation between the developed synthesis method based on the linear theory and an existing non-linear analysis approach is presented in order to get a verification for example designs. The difference between these two approaches is less than 0.5 % when both models undergo small deflections. This can approve the model to be used in precision engineering. For future research, the algorithm can be improved to investigate more models of mechanisms. Also, the method to solve the system of equations could have improvements because the average calculation time of one simulation is in the range of several minutes and is therefore comparatively long.Tesi

On the design and analysis of compliant mechanisms using the pseudo-rigid-body model concept

The pseudo-rigid-body model (PRBM) concept, developed for the analysis and design of large-deflection flexible members, has proved over time to be a simple, efficient and accurate tool for the synthesis, analysis and design of compliant mechanisms. This dissertation investigates a variety of compliant mechanism analysis and design problems using the PRBM concept and assists in further advancement of the implementation of the PRBMs. The dissertation begins with the development of a PRBM for a fixed-guided compliant beam with one inflection point in the deformed state. This research investigation advances the concept of characteristic deflection domain to a new synthesis framework for the design of fully-compliant mechanisms containing fixed-guided segments with an inflection point. The dissertation then formalizes a new approach for the evaluation of mechanical advantage of compliant mechanisms. In order to extend the approach towards synthesis and design of compliant mechanisms with higher mechanical advantage, the dissertation revisits the synthesis with compliance method of compliant mechanism design and provides an implementation strategy. A new method to determine an appropriate PRBM is presented. The method also allows determination of the expected static mode shape(s) of a given compliant mechanism structural configuration. Finally, the dissertation provides experimental results to validate the simplicity, accuracy, efficiency and applicability of the PRBM concept towards the synthesis, analysis and design of compliant segments and compliant mechanisms. The test setup design utilized for the experimental investigations may be found in the addendum to this dissertation. --Abstract, page iii

Optimal Design of Beam-Based Compliant Mechanisms via Integrated Modeling Frameworks

Beam-based Compliant Mechanisms (CMs) are increasingly studied and implemented in precision engineering due to their advantages over the classic rigid-body mechanisms, such as scalability and reduced need for maintenance. Straight beams with uniform cross section are the basic modules in several concepts, and can be analyzed with a large variety of techniques, such as Euler-Bernoulli beam theory, Pseudo-Rigid Body (PRB) method, chain algorithms (e.g.~the Chained Beam-Constraint Model, CBCM) and Finite Element Analysis (FEA). This variety is unquestionably reduced for problems involving special geometries, such as curved or spline beams, variable section beams, nontrivial shapes and, eventually, contacts between bodies. 3D FEA (solid elements) can provide excellent results but the solutions require high computational times. This work compares the characteristics of modern and computationally efficient modeling techniques (1D FEA, PRB method and CBCM), focusing on their applicability in nonstandard problems. In parallel, as an attempt to provide an easy-to-use environment for CM analysis and design, a multi-purpose tool comprising Matlab and modern Computer-Aided Design/Engineering (CAD/CAE) packages is presented. The framework can implement different solvers depending on the adopted behavioral models. Summary tables are reported to guide the designers in the selection of the most appropriate technique and software architecture. The second part of this work reports demonstrative case studies involving either complex shapes of the flexible members or contacts between the members. To improve the clarity, each example has been accurately defined so as to present a specific set of features, which leads in the choice of a technique rather than others. When available, theoretical models are provided for supporting the design studies, which are solved using optimization approaches. Software implementations are discussed throughout the thesis. Starting from previous works found in the literature, this research introduces novel concepts in the fields of constant force CMs and statically balanced CMs. Finally, it provides a first formulation for modeling mutual contacts with the CBCM. For validation purposes, the majority of the computed behaviors are compared with experimental data, obtained from purposely designed test rigs

Development of a methodology for pseudo-rigid-body models of compliant segments with inserts, and experimental validation

Compliant mechanisms have shown a great deal of potential in the last few decades in providing better solutions to design problems with numerous benefits; however, their use has been limited due to current challenges in the material selection. With ever increasing focus on the applications of compliant mechanisms, it is necessary to find alternatives to the existing materials and methods of prototyping. The purpose of this work is to develop a methodology for pseudo-rigid-body models of compliant segments with compliant inserts, comprised of a resilient material placed between the layers of a softer material, to alleviate any creep and strength issues associated with the softer material. The pseudo-rigid-body models (PRBMs) for such beams subjected to various boundary conditions are presented and validated by means of analytical and experimental methods. Pseudo-rigid-body models are used to devise simple methods of large deflection analysis, and help expedite the compliant mechanism design process. A method to improve the accuracy of the PRBM of a fixed-free beam by evaluating more accurate values of the stiffness coefficient is also presented --Abstract, Page iii

Virtual-work-based optimization design on compliant transmission mechanism for flapping-wing aerial vehicles

This paper presents a method for analyzing and optimizing the design of a compliant transmission mechanism for a flapping-wing aerial vehicle. Its purpose is of minimizing the peak input torque required from a driving motor. In order to maintain the stability of flight, minimizing the peak input torque is necessary. To this purpose, first, a pseudo-rigid-body model was built and a kinematic analysis of the model was carried out. Next, the aerodynamic torque generated by flapping wings was calculated. Then, the input torque required to keep the flight of the vehicle was solved by using the principle of virtual work. The values of the primary attributes at compliant joints (i.e., the torsional stiffness of virtual spring and the initial neutral angular position) were optimized. By comparing to a full rigid-body mechanism, the compliant transmission mechanism with well-optimized parameters can reduce the peak input torque up to 66.0%