A proposição desta tese consiste na aplicação da técnica de Sistemas Multicorpos, na dinâmica de veículos guiados em trajetória variável. Foi apresentada uma visão geral do formalismo matemático, baseado nos métodos de Lagrange e Kane, utilizados nos programas de multicorpos, para geração automática das equações de movimento. A teoria de mecânica de contato, fundamental para o cálculo das forças de contato, entre o veículo e a guia, foi exposta detalhadamente. Sua validação, foi realizada, através de ensaios de laboratório, realizados no INRETS (França). A técnica de modelagem de Sistemas Multicorpos, foi aplicada, na previsão do comportamento dinâmico de veículos guiados. Neste sentido, a elaboração do modelo, através da descrição topológica, obtenção das equações de movimentos, análise e simulação do comportamento, foram realizadas. Foram selecionados na literatura internacional, os estudos de caso propostos pela International Association of Vehicle System Dynamics (IAVSD), para avaliação de veículos guiados. Foram modelados, o rodeiro ferroviário, submetido a força lateral, truque trafegando por um desvio e um veículo completo inscrevendo uma curva. O veículo modelado com 35 graus de liberdade, produziu mais de 1100 equações algébrico/diferenciais (DAE). As simulações do comportamento dinâmico dos sistemas, foram realizadas e os resultados apresentados em gráficos temporais. Os modos de movimento foram quantificados, através da analise modal, realizada no sistema linearização em torno de um ponto de operação. Os valores obtidos, foram comparados com números publicados e algumas discrepâncias, foram encontradas e justificadas. Pode-se observar nitidamente, o movimento de lacet, a partir dos auto-vetores complexos da matriz dinâmica do sistema. De forma geral, os resultados obtidos tanto na análise temporal, como no domínio da freqüência, apresentaram boa concordância, com os resultados publicados por outros autores. Estes resultados encorajadores, promovem a confiança na aplicação da técnica de Multicorpos em veículos guiados, sendo estímulo, para aplicação no desenvolvimento de novos projetos. / The subject of this thesis is the application of multibody system modelling techniques for dynamic behaviour investigation on guided vehicle on variable track trajectories. Analysis of existing techniques for generating vehicle motion equations, using multibody systems (MBS), is also carried out. Rolling contact theory, fundamental for vehicle/track forces calculations, are extensively reviewed. Validation have been carried out with laboratorial experiments. Multibody system modelling techniques have been used to predict, guided vehicle behaviour. Topological model description, have been used to generate equation of motion for simulation purposes. It has been chosen the railway vehicle, proposed by the International Association of Vehicle System Dynamics (IAVSD), as evaluation benchmark. The solution of wheelset benchmark proposition is presented. A two wheelset bogie model in a deviation, is also solved. A complete railway vehicle, with 35 degrees of freedom model, producing more than 1100 differential/algebraic equations (DAE), is performed and analysed. Time result simulation have been presented. Modal analysis have been performed around an operation point. Results have been compare with numbers published and discrepancy founded have been justified. Hunting movement have been obtained with the complex eigen-vector from system dynamic matrix. In general, results obtained from time and frequency domain, agreed with available results published from other authors. This encouraging results, promote credibility to Multibody System technique application to guided vehicle, stimulating new developing applications.

Recentemente, uma mudança de paradigma vem impactando toda a engenharia e manufatura na forma de se planejar, projetar, testar e construir produtos. A forma mais tradicional de desenvolvimento, que se caracterizava pelo processo seriado de múltiplos ciclos de design-construção-teste, vem sendo substituída gradativamente por processos de desenvolvimento guiados por simulação computacional. Decorrentes disso, os primeiros protótipos físicos são freqüentemente capazes de atingir os objetivos quando testados. Esta mudança, chamada também de projeto baseado em simulação, permite reduzir drasticamente o tempo de desenvolvimento de produtos e trazer a inovação para o mercado. Este trabalho apresenta uma forma computacional, via técnica de multicorpos, para se analisar a dinâmica de uma lavadora de eixo vertical. É proposto um protótipo virtual no software ADAMS, para estudo dinâmico de uma lavadora durante o processo crítico de centrifugação. O modelo virtual é posteriormente confrontado com dados experimentais, para sua validação. Uma extensa pesquisa bibliográfica foi realizada, com a intenção de capturar as técnicas mais usuais de modelamento e estudo dinâmico em lavadoras, bem como de compreender melhor o papel de seus componentes durante o processo crítico de centrifugação. / Recently a paradigm shift has impacted the engineering and manufacturing in the way of planning, designing, testing and building products. The most traditional way of product development, characterized by multiple cycles of design-build-test, has been substituted by a process based on computational simulation, where the first physical prototypes are capable of delivering the desired performance. This new way of developing products is called simulation based design and allows organizations to reduce drastically the product lead time and bring innovation to the market. This work presents a computational way to analyze the dynamic behavior of a top load washing machine using multibody system (MBS). It\'s proposed a virtual prototype developed in the ADAMS software, for dynamic study of a commercial washing machine during spin cycle. The virtual model is compared to experimental data for validation. An extensive research in the literature has been done in order to find the most usual ways of modeling and analyzing washing machine dynamics during spin.

In computer simulation the term \"multibody system\" is usually employed to describe a system of interconnected bodies. Several examples of multibody systems can be found in railway engineering. A wheelset interacting with a track through a contact interface is just one example of practical interest. Modelling mechanical systems in a virtual environment contributes to the understanding of subjects such as dynamic behaviour, stability, durability, wear, fatigue, etc. In the context of a rigid-flexible multibody system mathematically described by a weak-form, the purpose of the present work is to evaluate the contributions due to rigid bodies considering their contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. Then, the so-called master-surface to master-surface contact formulation is adapted to be used in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are proposed to establish contact pairs, permitting pointwise interaction in a frictional scenario. The proposed formulation is used to represent mechanical systems from different contexts, including a numerical example of the wheel-rail contact interface. The obtained results show the robustness and applicability of the methods. / Em simulação computacional o termo \"sistema multicorpos\" é usualmente empregado para descrever um sistema de corpos interconectados. Diversos exemplos de sistemas multicorpos podem ser encontrados no campo da engenharia ferroviária. Um rodeiro interagindo com a via através de uma interface de contato é apenas um dos exemplos de interesse prático. A modelagem de sistemas mecânicos em um ambiente virtual contribui para o entendimento de assuntos como comportamento dinâmico, estabilidade, durabilidade, desgaste, fadiga, etc. No contexto de um sistema multicorpos rígido-flexível descrito matematicamente por uma forma fraca, o propósito do presente trabalho é avaliar as contribuições devido à presença de corpos rígidos considerando interações de contato. Contribuições inerciais devido à distribuição de massa do corpo rígido são desenvolvidas e apresentadas em totalidade, considerando um polo genérico associado a um único nó, representando o corpo rígido. Parâmetros de rotação de Rodrigues são usados para descrever rotações finitas em uma descrição Lagrangiana atualizada. A formulação de contato master-surface to master-surface é adaptada para ser usada em conjunto com o elemento de corpo rígido e corpos flexíveis, estabelecendo a interação entre esses corpos em um ambiente de simulação multicorpos. Novas parametrizações de superfícies de contato são desenvolvidas para estabelecer os pares de contato, assumindo-se interações pontuais, em um cenário de contato com atrito. A formulação proposta é usada para representar sistemas mecânicos em diferentes contextos, incluindo um exemplo numérico do caso de contato roda-trilho. Os resultados obtidos mostram a robustez e a aplicabilidade dos métodos.

Recentemente, uma mudança de paradigma vem impactando toda a engenharia e manufatura na forma de se planejar, projetar, testar e construir produtos. A forma mais tradicional de desenvolvimento, que se caracterizava pelo processo seriado de múltiplos ciclos de design-construção-teste, vem sendo substituída gradativamente por processos de desenvolvimento guiados por simulação computacional. Decorrentes disso, os primeiros protótipos físicos são freqüentemente capazes de atingir os objetivos quando testados. Esta mudança, chamada também de projeto baseado em simulação, permite reduzir drasticamente o tempo de desenvolvimento de produtos e trazer a inovação para o mercado. Este trabalho apresenta uma forma computacional, via técnica de multicorpos, para se analisar a dinâmica de uma lavadora de eixo vertical. É proposto um protótipo virtual no software ADAMS, para estudo dinâmico de uma lavadora durante o processo crítico de centrifugação. O modelo virtual é posteriormente confrontado com dados experimentais, para sua validação. Uma extensa pesquisa bibliográfica foi realizada, com a intenção de capturar as técnicas mais usuais de modelamento e estudo dinâmico em lavadoras, bem como de compreender melhor o papel de seus componentes durante o processo crítico de centrifugação. / Recently a paradigm shift has impacted the engineering and manufacturing in the way of planning, designing, testing and building products. The most traditional way of product development, characterized by multiple cycles of design-build-test, has been substituted by a process based on computational simulation, where the first physical prototypes are capable of delivering the desired performance. This new way of developing products is called simulation based design and allows organizations to reduce drastically the product lead time and bring innovation to the market. This work presents a computational way to analyze the dynamic behavior of a top load washing machine using multibody system (MBS). It\'s proposed a virtual prototype developed in the ADAMS software, for dynamic study of a commercial washing machine during spin cycle. The virtual model is compared to experimental data for validation. An extensive research in the literature has been done in order to find the most usual ways of modeling and analyzing washing machine dynamics during spin.

Multibody System Dynamics has been responsible for revolutionizing Mechanical Engineering Design by using mathematical models to simulate and optimize the dynamic behavior of a wide range of mechanical systems. These mathematical models not only can provide valuable informations about a system that could otherwise be obtained only by experiments with prototypes, but also have been responsible for the development of many model-based control systems. This work represents a contribution for dynamic modeling of multibody mechanical systems by developing a novel recursive modular methodology that unifies the main contributions of several Classical Mechanics formalisms. The reason for proposing such a methodology is to motivate the implementation of computational routines for modeling complex multibody mechanical systems without being dependent on closed source software and, consequently, to contribute for the teaching of Multibody System Dynamics in undergraduate and graduate levels. All the theoretical developments are based on and motivated by a critical literature review, leading to a general matrix form of the dynamic equations of motion of a multibody mechanical system (that can be expressed in terms of any set of variables adopted for the description of motions performed by the system, even if such a set includes redundant variables) and to a general recursive methodology for obtaining mathematical models of complex systems given a set of equations describing the dynamics of each of its uncoupled subsystems and another set describing the constraints among these subsystems in the assembled system. This work also includes some discussions on the description of motion (using any possible set of motion variables and admitting any kind of constraint that can be expressed by an invariant), and on the conditions for solving forward and inverse dynamics problems given a mathematical model of a multibody system. Finally, some examples of computational packages based on the novel methodology, along with some case studies, are presented, highlighting the contributions that can be achieved by using the proposed methodology. / A Dinâmica de Sistemas Multicorpos tem sido responsável por revolucionar projetos de Engenharia Mecânica pela utilização de modelos matemáticos para simulação e otimização do comportamento dinâmico de uma ampla gama de sistemas mecânicos. Estes modelos matemáticos não somente podem fornecer valiosas informações acerca de um sistema que caso contrário poderiam ser obtidas somente através de experimentos com protótipos, como também têm sido responsável pelo desenvolvimento de diversos sistemas de controle baseados em modelo. Este trabalho representa uma contribuição para a modelagem dinâmica de sistemas mecânicos multicorpos por meio do desenvolvimento de uma nova metodologia modular e recursiva que unifica as principais contribuições de diversos formalismos da Mecânica Clássica. A razão para propor tal metodologia é motivar a implementação de rotinas computacionais para a modelagem de sistemas mecânicos multicorpos complexos sem depender de pacotes de software de código fechado e, consequentemente, contribuir para o ensino de Dinâmica de Sistemas Multicorpos nos níveis de graduação e pós-graduação. Todos os desenvolvimentos teóricos são baseados em e motivados por uma revisão crítica da literatura, conduzindo a uma forma matricial geral das equações dinâmicas de movimento de um sistema mecânico multicorpos (que podem ser expressas em termos de qualquer conjunto de variáveis adotado para a descrição dos movimentos realizados pelo sistema, ainda que tal conjunto inclua variáveis redundantes) e a uma metodologia recursiva geral para a obtenção de modelos matemáticos de sistemas complexos, dado um conjunto de equações descrevendo a dinâmica de cada um de seus subsistemas desacoplados e outro descrevendo os vínculos entre estes subsistemas (no sistema) quando acoplado. Este trabalho também inclui algumas discussões acerca da descrição de movimentos (utilizando qualquer conjunto admissível de variáveis de movimento e admitindo qualquer tipo de vínculo que seja passível de descrição por invariantes), e das condições para a solução dos problemas de dinâmica direta e inversa dado um modelo matemático de um sistema multicorpos. Finalmente, alguns exemplos de pacotes computationais baseados na nova metodologia, juntamente com alguns estudos de caso, são apresentados, ressaltando as contribuições que podem ser alcançadas por meio do uso da metodologia proposta.

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

Large displacement and large strain problems of mechanical systems can be solved mainly by four methods. These are Floating Frame of Reference, Incremental Finite Element, Large Rotation Vector and Absolute Nodal Coordinate Formulations (ANCF). Due to exact rigid body representation, simple mass matrix structure and non-incremental formulation, ANCF is more convenient in analyzing flexible multibody systems. However, it is limited to problems with regular boundaries, currently. The aim of the thesis is to improve the current ANCF in order to handle various problems with irregular boundaries. For this purpose, firstly meshfree ANCF has been developed to analyze flexible multibody systems. Verification of the developed meshfree formulation has been performed for beam type structures and accurate results have been obtained. Then, &ldquo / ANCF with Virtual Element Mapping Method&rdquo / has been proposed to overcome the boundary problems of the current formulations. The proposed method has been implemented to plane stress, plane strain, plate/shell and 3D solid finite elements. Verification of the proposed method has been performed by using the patch test problems available in the literature. Besides, it has been verified by various flexible multibody problems with large deformations. Additionally, shape function polynomials for thin plate assumption have been derived. It is observed that developed formulations and methods can be useful not only for flexible multibody systems but also for structural mechanics problems subjected to large deformations and/or rotations. The proposed methods and formulations are more efficient than the current formulations in the literature due to extended shape limits of finite elements.

There is a need for smaller and more economic transportation systems. Two-wheeled inverted-pendulum machines, such as the Segway, have been proposed to address this need. However, the Segway places the operator on top of a naturally unstable platform that is stabilized by means of a control system. The control stability of the Segway can be severely affected when minor disturbances or unanticipated conditions arise. In this thesis, a dynamic model of a Segway is developed and used in simulations of various conditions that can arise during normal use. The dynamic model of a general two-wheeled inverted pendulum and human rider is presented. Initial estimates of the parameters were calculated or obtained from other references. The results from numerous experiments are presented and used to develop a better understanding of the dynamics of the vehicle. The experimental data was then used to adjust the model parameters to match the dynamics of a real Segway Human Transporter. Finally, the model was used to simulate various failure conditions. The simulations provide a better understanding of how these conditions arise, and help identify which parameters play an important role in their outcome.

This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

Rigid multibody systems have been studied extensivley due to its direct application in design and analysis of various mechanical systems such as robots and spacecraft structures. The dynamics of multibody system is governed by its equations of motion and various terms associated with it, such as the mass matrix, the generalized force vector, are well known..Forward dynamics algorithms play an important role in the simulation of multibody systems and the recursive forward dynamics algorithm for branched multibody systems is very popular. The recursive forward dynamic algorithm is highly efficient algorithm with O(n) computational complexity and scores over other algorithms when number of rigid bodies n in the system is very large. The algorithm involves finding an important mass matrix, which has been popularly termed as articulated body inertia (AB inertia). To find ijth term of any general mass matrix, we separately give virtual change to ith and jth generalized coordinates. At each point of the multibody system, the dot product of the resulting virtual displacements are taken with each other and eventually integrated over the entire multibody system, weighted by the mass. This quantity divided by the virtual changes in ith and jth coordinates gives the ijth element of the mass matrix. This is one of the fundamental ways of looking at the mass matrix. However, in literature, the AB inertia is obtained as a result of mathematical manipulation and its physical or geometrical significance from the above view point is not clear. In this thesis we present a more geometric and physical explanation for the AB inertia. The main step is to obtain a new set of generalized coordinates which relate directly to the AB inertia. We have also shown the equivalence of our method with existing methods. A comprehensive treatement on change of generalized coordinates and its effect on equations of motion has also been presented as preliminaries. The second part of the thesis deals with closed loop multibody systems.A few years ago an iterative algorithm called the sequential regularization method (SRM) was proposed for simulation of closed loop multibody systems with attractive claims on its efficiency. In literature we find that this algorithm has been implemented and studied only for planar multibody systems. As a part of the thesis work, we have developed a C-programming language code which can simulate 3-dimensional spatial multibody systems using the SRM algorithm. The programme can also perform simulation using a relatively efficient Conventional algorithm having O(n+m3) complexity, where m denotes number of closed loop constraints. Simulation studies have been carried out on a few multibody systems using the two algorithms. Some of the results have been also been validated using the commercial simulation package -ADAMS. As a result of our simulation studies, we have detected certain points, after which the solution from SRM loses it convergence. More study is required to understand this lack of convergence.