Vinkelväxlar och slutväxlar spelar en viktig roll för kraftöverföringen mellan motor och hjuli fyrhjulsdrivna bilar. Med en ökande konkurrens finns en efterfrågan för att ständigt förbättraeffektivitet, ljudgenereringegenskaper och hållfasthet. För att uppnå detta krävs en bättreförståelse av systemets dynamiska egenskaper. En detaljerad numerisk dynamisk modell ärdock ofta beräkningsmässigt tung och tidskrävande. Verktygen för den dynamiska modelleringenbehöver bli mer effektiva och i vissa fall kan en kombinationen av två verktyg vara ett bättrealternativ. Denna integrerade plattform kan användas för att effektivt modellera dynamiken ochfå en bättre inblick i systemts beteende.Vinkelväxlen är en enhet vars funktion är att fördela kraften mellan fram- och bakaxel. De viktigastekomponenterna i vinkelväxeln är en hypoid-drevsats och en klokoppling, som aktiveras närkraft ska överföras till bakaxeln via kardanaxeln. Detta arbete modellerar dynamiskt beteendei vinkelväxeln och har sytftet att beräkna transmissionsfelet i systemet och dess effekt somexciteringskälla av ljud och vibrationer i systemet. MSC ADAMS har använts för Multi-Bodyberäkningsverktyg för modelleringen.Det beräknade transmissionsfelet har jämfört med testresultat. Dessutom har en co-simuleringmed både ADAMS och SIMULINK genomförts för att skapa en bas för tillämpa optimeringsalgoritmer.Bultarna i bultförbandet samt deras styvhet och förspänning har inkluderats i modellenoch studerats med avseende på effekten på vibrationer i kopplingspunkter, samt algoritmerför optimering har föreslagits. Korrelationen mellan test och beräkning var mycket god, ochdessutom har förslag på hur denna typ av beräkning kan förbättras ytterligare givits. / Automotive drive units play an important role in transmitting power from an engine to the wheels.In today’s competitive world, there is an increasing demand for these devices to be more efficient,quiet, and reliable at the same time. In order to achieve this, a better understanding of system’sdynamic behavior is necessary. A detailed dynamic model of a system is often computationallyintense to solve and time consuming. This demands more efficient tools to be developed and insome cases integrating two or more tools would be a better option. The integrated platform can beused to effectively model the dynamic behavior of a system and get better insights on the systembehavior.Power Transfer Unit (PTU) is a device whose function is to distribute power between a front axleand rear axle. This unit basically includes hypoid gear set and a dog clutch that is engaged whenthere is a requirement to transfer power to the Rear Drive Unit (RDU) through prop shaft. Thismaster thesis describes modeling the dynamic behavior of a PTU with a goal of predicting thetransmission error in the system and its effect as a source of excitation on the entire unit followedby studying system response to this type of excitation. MSC ADAMS was used as a Multi-BodySimulation tool to model the dynamic behavior of the PTU.The transmission error predicted by the simulation was compared with the test results, a cosimulationbetween SIMULINK and ADAMS was established in order to create a platform toapply optimization algorithms. The bolt and bearing stiffness were incorporated in the model andtheir effect on the mounting point accelerations and bearing point accelerations were studied. Itwas found that the bolt stiffness affects the acceleration levels at the coupling points and suitablealgorithms could be applied in order to find an optimum value. As a result of the good correlationbetween test and simulation data, some other useful conclusions have been derived in order todevelop this approach of modeling.

This thesis highlights one of the most significant concerns that has preoccupied drivetrain engineers in recent times, namely drivetrain clonk. Clonk is an unacceptable audible sound, which is accompanied by a tactile drivetrain response. This may occur under several different driving conditions. Many drivetrain NVH concerns are related to impact loading of subsystems down-line of engine. These concerns are induced by power torque surge through engagement and disengagement processes, which may propagate through various transmission paths as structural waves. The coincidence of these waves with the acoustic modes of sub-system components leads to audible responses, referred to as clonk. The approach usually undertaken and reported in literature is either purely theoretical or constitutes experimental observation of vehicle conditions. A few research workers have reported rig-based investigations, but not under fully dynamic conditions with controlled and reproducible impulsive action. The research reported in this thesis combines experimental and numerical investigation of high frequency behaviour of light truck drivetrain systems, when subjected to sudden impulsive action, due to driver behaviour. The problem is treated as a multi-physics interactive phenomenon under transient conditions. The devised numerical method combines multi-body dynamics, structural modal analysis, impact dynamics in lash zones and acoustic analysis within an overall investigation framework. A representative drivetrain system rig is designed and implemented, and controlled tests simulating driver behaviour undertaken. The combined numerical predictions and experimental noise and vibration monitoring has highlighted the fundamental aspects of drivetrain behaviour. Good agreement is' also found between the detailed numerical approach and the experimental findings. Novel methods of measurement such as Laser Doppler Vibrometery have been employed. Simultaneous measurements of vibration and noise radiation confirm significant elasto-acoustic coupling at high impact energy levels. One of the major finds of the thesis is the complex nature of the clonk signal, being a combination of accelerative and ringing noise, with the latter also comprising of many other lower energy content as observed in the case of transmission rattle and bearing-induced responses. Therefore, the link between rattle and clonk, long suspected, but not hitherto shown has been confirmed in the thesis. Another major find of particular commercial interest is the insignificant contribution of torsional damping devices such as dual mass flywheels upon the accelerative component of the clonk response.

The thesis presents an intermediate modelling approach to study transient behaviour of vehicle systems, with emphasis put on simplified yet accurate representation of important system elements. A representative non-linear vehicle model is developed in MA TLAB/Simulink environment, where non-linear characteristics of tyre, suspension and braking system are included to capture the dynamic behaviour of a vehicle under transient conditions. The novel aspect of this work is the application of a representative full vehicle-tyre-ABS integrated set-up to study the complicated interaction between tyre and anti-lock braking, under a range of demanding operating conditions, including combined cornering and braking. The modelling methodology involves development of low end vehicle models, based on the Newton-Euler formulation. Subsequently, an intermediate vehicle model is devised, where more details are incorporated such as additional DOF to capture the sprung mass motion in space, along with its non-linear interactions with the un-sprung masses, large angle effects, kinematics of steering/wheels and an appropriate tyre model suitable for transient manoeuvres. Particular attention is paid to the suspension system modelling, through inclusion of non-linear effects in springs, dampers, bump-stops, and anti-roll bars, along with the jacking and anti-dive effects using the virtual work method. The model also incorporates a hydraulic brake model, based on the reduced order brake system dynamics for realistic simulation of the braking manoeuvres. A complex multi-body ADAMS/Chassis model, with much greater level of detail, has also been established to extensively compare and enhance the realistic behaviour of the intermediate vehicle model. During the simulation exercise, the intermediate vehicle model has shown good agreement with the complex ADAMS model, thus justifying the accurate representation of vehicle.non-linear characteristics, particularly the suspension system. The realistic behaviour of the vehicle model is further ascertained with a reliable GPS enabled test vehicle, by performing number of manoeuvres on test tracks, including combined cornering and braking. A representative 4-channel conventional ABS system is modelled and integrated in the intermediate vehicle model. The ABS adopts generic peak seeking approach, employing wheel deceleration and brake slip as control variables. External braking inputs, in form of stepped pressure pulses, are also separately used to represent the transient braking system dynamics. In the current work, different transient tyre models based on the single point contact approach and using Magic Formula steady-state characteristics are applied, while studying the influence of their dynamic behaviour on the ABS system. By employing a representative ABS system in a multi-body vehicle model and considering the particularly demanding situation of combined braking I cornering, it is shown that the models which are adequate for pure braking might struggle when the complicated full vehicle dynamics are excited. It is shown that the first order relaxation length approach may not be sufficient to fully satisfy the requirements of an ABS braking, especially if the relaxation length is not modelled as a variable dependent on tyre slip. In comparison, the modelling approach, where the carcass compliances and contact patch properties are explicitly represented, can handle the oscillatory tyre behaviour associated with ABS braking, in a far more accurate manner. In comparison to the earlier studies, which were mostly conducted for straight-line braking, this thesis stresses the fact that the tyre behaviour can be influenced by the complex interaction of handling and braking, and hence the effect should be captured while investigating or evaluating the performance of a tyre model in relation with ABS simulation.

Esta tese apresenta o desenvolvimento de um método de elementos de contorno (BEM) no domínio do tempo baseado em fontes de Rankine para analise linear de comportamento no mar de sistemas oceânicos. O método e formulado por dois problemas de valor inicial de contorno definidos para os potenciais de velocidade e aceleração, sendo este ultimo utilizado para calcular de maneira acurada a derivada temporal do potencial de velocidades. Testes de verificação são realizados para a solução dos problemas de difração, radiação e de corpo livre para flutuar. Uma vez verificada, a ferramenta e aplicada em dois problemas multicorpos considerados no estado-da-arte em termos de modelagem hidrodinâmica utilizando BEM. O primeiro trata do problema envolvendo duas embarcações atracadas a contrabordo. Este é um caso no qual os códigos baseados na teoria de escoamento potencial são conhecidos por apresentarem dificuldades na determinação das soluções, tendendo a superestimar as elevações de onda no vão entre as embarcações e a apresentar problemas de convergência numérica associados a efeitos ressonantes de onda. O problema e tratado por meio do método de damping lid e a convergência das series temporais e investigada avaliando diferentes níveis de amortecimento. Os resultados são comparados com dados experimentais. O segundo problema se refere a analise de sistemas multicorpos com grandes deslocamentos relativos. Neste problema, ferramentas no domínio da frequência nao podem ser utilizadas, por considerarem apenas malhas fixas. Deste modo, o presente método e estendido para considerar um gerador de malhas de paineis e um algoritmo de interpolação de ordem alta no laco de tempo do código, possibilitando a mudança de posições relativas entre os corpos durante a simulação. Os resultados são comparados com dados de experimentos executados especificamente para fins de verificação do código, apresentando uma boa concordância. De acordo com o conhecimento do autor, esta e a primeira vez que certas questões relativas a modelagem numérica destes dois problemas multicorpos são relatadas na literatura especializada em hidrodinâmica computacional. / The development of a time domain boundary elements method (BEM) based on Rankine\'s sources for linear seakeeping analysis of offshore systems is here addressed. The method is formulated by means of two Initial Boundary Value Problems defined for the velocity and acceleration potentials, the latter being used to ensure an accurate calculation of the time derivatives of the velocity potential. Verification tests for solving the difraction, radiation and free floating problems are presented. Once verified, the code is applied for two complex multi-body problems considered to be in the state-of-the-art for hydrodynamic modelling using BEM. The first is the seakeeping problem of two ships arranged in side-by-side, a problem in which all potential flow codes are known to have a poor performance, tending to provide unrealistic high wave elevations in the gap between the vessels and to present numerical convergence problems associated to resonant effects. The problem is here addressed by means of a damping lid method and the convergence of the time series with different damping levels is investigated. Results are compared to data measured in an experimental campaign. The second problem refers to the analysis of multi-body systems composed of bodies undergoing large relative displacements. This is a case that cannot be properly analyzed by frequency domain codes, since they only consider fixed meshes. For this application, the present numerical method is extended to consider a panel mesh generator in the time loop of the code, enabling the change of body relative positions during the computations. Furthermore, a higher order interpolation algorithm designed to recover the solutions of a previous time-step was also implemented, enabling the calculations to progress with reasonable accuracy in time. The numerical results are compared to data of experimental tests designed and executed for verification of the code, and presented a very good agreement. To the author\'s knowledge, this is the first time that certain issues concerning the numerical modelling of these two complex multi-body problems are reported in the literature specialized in hydrodynamic computations.

The objective of this study is to develop an integrated multibody dynamics computational framework for the deterministic and reliability-based design optimization of wind turbine drivetrains to obtain an optimal wind turbine gear design that ensures a target reliability under wind load and gear manufacturing uncertainties. Gears in wind turbine drivetrains are subjected to severe cyclic loading due to variable wind loads that are stochastic in nature. Thus, the failure rate of drivetrain systems is reported to be relatively higher than the other wind turbine components. It is known in wind energy industry that improving reliability of drivetrain designs is one of the key issues to make wind energy competitive as compared to fossil fuels. Furthermore, a wind turbine is a multi-physics system involving random wind loads, rotor blade aerodynamics, gear dynamics, electromagnetic generator and control systems. This makes an accurate prediction of product life of drivetrains challenging and very limited studies have been carried out regarding design optimization including the reliability-based design optimization (RBDO) of geared systems considering wind load and manufacturing uncertainties. In order to address these essential and challenging issues on design optimization of wind turbine drivetrains under wind load and gear manufacturing uncertainties, the following issues are discussed in this study: (1) development of an efficient numerical procedure for gear dynamics simulation of complex multibody geared systems based on the multi-variable tabular contact search algorithm to account for detailed gear tooth contact geometry with profile modifications or surface imperfections; (2) development of an integrated multibody dynamics computational framework for deterministic and reliability-based design optimization of wind turbine drivetrains using the gear dynamics simulation software developed in (1) and RAMDO software by incorporating wide spatiotemporal wind load uncertainty model, pitting gear tooth contact fatigue model, and rotor blade aerodynamics model using NREL AeroDyn/FAST; and (3) deterministic and reliability-based design optimization of wind turbine drivetrain to minimize total weight of a drivetrain system while ensuring 20-year reliable service life with wind load and gear manufacturing uncertainties using the numerical procedure developed in this study. To account for the wind load uncertainty, the joint probability density function (PDF) of 10-minute mean wind speed (V₁₀) and 10-minute turbulence intensity (I₁₀) is introduced for wind turbine drivetrain dynamics simulation. To consider wide spatiotemporal wind uncertainty (i.e., wind load uncertainty for different locations and in different years), uncertainties of all the joint PDF parameters of V₁₀, I₁₀ and copula are considered, and PDF for each parameter is identified using 249 sets of wind data. This wind uncertainty model allows for the consideration of a wide range of probabilistic wind loads in the contact fatigue life prediction. For a given V₁₀ and I₁₀ obtained from the stochastic wind model, the random time-domain wind speed data is generated using NREL TurbSim, and then inputted into NREL FAST to perform the aerodynamic simulation of rotor blades to predict the transmitted torque and speed of the main shaft of the drivetrain that are sent to the multibody gear dynamics simulation as an input. In order to predict gear contact fatigue life, a high-fidelity gear dynamics simulation model that considers the detailed gear contact geometry as well as the mesh stiffness variation needs to be developed to find the variability of maximum contact stresses under wind load uncertainty. This, however, leads to a computationally intensive procedure. To eliminate the computationally intensive iterative online collision detection algorithm, a numerical procedure for the multibody gear dynamics simulation based on the tabular contact search algorithm is proposed. Look-up contact tables are generated for a pair of gear tooth profiles by the contact geometry analysis prior to the dynamics simulation and the contact points that fulfill the non-conformal contact condition and mesh stiffness at each contact point are calculated for all pairs of gears in the drivetrain model. This procedure allows for the detection of gear tooth contact in an efficient manner while retaining the precise contact geometry and mesh stiffness variation in the evaluation of mesh forces, thereby leading to a computationally efficient gear dynamics simulation suited for the design optimization procedure considering wind load uncertainty. Furthermore, the accuracy of mesh stiffness model introduced in this study and transmission error of gear tooth with tip relief are discussed, and a wind turbine drivetrain model developed using this approach is validated against test data provided in the literature. The gear contact fatigue life is predicted based on the gear tooth pitting fatigue criteria and is defined by the sum of the number of stress cycles required for the fatigue crack initiation and the number required for the crack to propagate from the initial to the critical crack length based on Paris-Erdogan equation for Mode II fracture. All the above procedures are integrated into the reliability-based design optimization software RAMDO for design optimization and reliability analysis of wind turbine drivetrains under wind load and manufacturing uncertainties. A 750kW GRC wind turbine gearbox model is used to perform the design optimization and the reliability analysis. A deterministic design optimization (DDO) is performed first using an averaged joint PDF of wind load to ensure a 20-year service life. To this end, gear face width and tip relief (profile modification) are selected as design variables and optimized such that 20-year fatigue life is ensured while minimizing the total weight of drivetrains. It is important to notice here that an increase in face width leads to a decrease in the fatigue damage, but an increase in total weight. On the other hand, the tip relief has almost no effect on the total weight, but it has a major impact on the fatigue damage. It is shown in this study that the optimum tip relief allows for lowering the greatest maximum shear stresses on the tooth surface without relying heavily on face width widening to meet the 20-year fatigue life constraint and it leads to reduction of total drivetrain weight by 8.4%. However, if only face width is considered as design variable, total weight needs to be increased by 4.7% to meet the 20-year fatigue life constraint. Furthermore, the reliability analysis at the DDO optimum design is carried out considering the large spatiotemporal wind load uncertainty and gear manufacturing uncertainty. Local surrogate models at DDO optimum design are generated using Dynamic Kriging method in RAMDO software to evaluate the gear contact fatigue damage. 49.5% reliability is obtained at the DDO optimum design, indicating that the probability of failure is 50.5%, which is as expected for the DDO design. RBDO is, therefore, necessary to further improve the reliability of the wind turbine drivetrain. To this end, the sampling-based reliability analysis is carried out to evaluate the probability of failure for each design using the Monte Carlo Simulation (MCS) method. However, the use of a large number of MCS sample points leads to a large number of contact fatigue damage evaluation time using the 10-minute multibody drivetrain dynamics simulation, resulting in the RBDO calculation process being computational very intensive. In order to overcome the computational difficulty resulting from the use of high-fidelity wind turbine drivetrain dynamics simulation, intermediate surrogate models are created prior to the RBDO process using the Dynamic Kriging method in RAMDO and used throughout the entire RBDO iteration process. It is demonstrated that the RBDO optimum obtained ensures the target 97.725 % reliability (two sigma quality level) with only 1.4 % increase in the total weight from the baseline design with 8.3 % reliability. This result clearly indicates the importance of incorporating the tip relief as a design variable that prevents larger increase in the face width causing an increase in weight. This, however, does not mean that a larger tip relief is always preferred since an optimum tip relief amount depends on stochastic wind loads and an optimum tip relief cannot be found deterministically. Furthermore, accuracy of the RBDO optimum obtained using the intermediate surrogate models is verified by the reliability analysis at the RBDO optimum using the local surrogate models. It is demonstrated that the integrated design optimization procedure developed in this study enables the cost effective and reliable design of wind turbine drivetrains.

One way to make rail vehicles a competitive means of transportation is to increase running speed. However, higher speeds usually generate increased forces and accelerations on the vehicle, which have a negative effect on ride comfort. With conventional passive suspension, it may be difficult to maintain acceptable passenger comfort. Therefore, active technology in the secondary suspension can be implemented to improve, or at least maintain, ride comfort at increased vehicle speeds or when track conditions are unfavourable. This thesis describes the development of an active secondary suspension concept to improve ride comfort in a high-speed train. Firstly, an active lateral secondary suspension system (ALS) was developed, including dynamic control of the lateral and yaw modes of the carbody. Furthermore, quasi-static lateral carbody control was included in the suspension system in order to laterally centre the carbody above the bogies in curves at high track plane acceleration and hence to avoid bumpstop contact. By means of simulations and on-track tests, it is shown that the ALS system can offer significant lateral ride comfort improvements compared to a passive system. Two different control strategies have been studied—the relatively simple sky-hook damping and the multi-variable H∞ control—using first a quarter-car and then a full-scale vehicle model. Simulation results show that significant ride comfort improvements can be achieved with both strategies compared to a passive system. Moreover, H∞ control in combination with the carbody centring device is better at reducing the relative lateral displacement in transition curves compared to sky-hook damping. Secondly, an active vertical secondary suspension system (AVS) was developed, using simulations. Dynamic control of the vertical and roll modes of the carbody, together with quasi-static roll control of the carbody, show significant vertical ride comfort improvements and allow higher speeds in curves. Further, the AVS system compensates for negative ride comfort effects if the structural stiffness of the carbody is reduced and if the vertical air spring stiffness is increased. Finally, the two active suspension systems (ALS and AVS) were combined in simulations. The results show that both lateral and vertical ride comfort is improved with the active suspension concept at a vehicle speed of 250 km/h, compared to the passive system at 200 km/h. Further, active suspension in one direction does not affect the other direction. The ALS system has been included in two recent orders comprising more than 800 cars. / QC 20111205 / Gröna Tåget

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.

The thesis outlines a hierarchical modelling methodology for investigation in vehicle dynamics, in particular for combined ride and handling manoeuvres. The methodology involves the use of detailed multi-degrees of freedom models of vehicles with the inclusion of sources of non-linearity, using a multi-body approach, based on Lagrangian dynamics for constrained systems. It also includes the use of simpler and task-specific models, formulated in Newton-Euler approach. These simpler models with lower degrees of freedom, but with appropriate level of detail are more efficient in the study of specific, but non-trivial problems such as transient behaviour of vehicles in combined ride and handling, as encountered in many routine daily manoeuvres. The modelling methodology is supported by careful vehicle testing, both for validation of the proposed approach, and assessment of the extent of applicability of simple, intermediate and multi-degrees of freedom full-vehicle models. Certain important vehicle handling and ride characteristics in pitch plane dynamics, roll behaviour, vehicle body bounce and combination of these have been studied, as well as the effectiveness of restraining action of chassis elements, such as the semileading and trailing arms for passive control of vehicle squat and dive motions, arising from acceleration from coast to drive and deceleration/brake of vehicle from drive to coast. Combined pitch and bounce motions have been studied when negotiating speed traps such as bumps, which also combine with significant body roll when single event obstacles of this kind are introduced. The novelty of the research is in the detailed integrative numerical-experimental approach, and the development of intermediate models that adequately predict vehicle behaviour under steady and non-steady conditions for a wide range of ride and handling manoeuvres. The investigations have culminated in a significant number of findings of practical use, particularly the ineffectiveness of anti-squat and dive features when combined pitch and bounce motions limit the usefulness of these devices. On the contrary, excessive roll dynamic behaviour of the vehicle is effectively palliated by the anti-roll bar, even under complex combined pitch, roll and body bounce such as those experienced in negotiating single event speed bumps. Good agreement is found between the predictions of the intermediate model and those of the multi-body model and the actual vehicle tests, particularly for pitch and bounce dynamics.

A falta de um membro, devido a doenças, más-formações ou traumas, impacta enormemente na vida de um indivíduo. Para que o mesmo possa realizar Atividades de Vida Diária (AVD), sem drásticas limitações, faz-se necessário o desenvolvimento de próteses e cientes. Para auxiliar no projeto de tais produtos, este trabalho visa criar e solucionar um modelo de sistema dinâmico capaz de simular o comportamento de joelhos prostéticos. A m de alcançar tal objetivo, foi estudada a biomecânica da marcha humana, além dos tipos de amputações existentes e seus impactos na mesma. Buscou-se também estudar os principais componentes de próteses existentes atualmente no mercado, além de suas geometrias básicas. Após de nir-se um modelo simpli cado que representasse os componentes protéticos e as partes remanescentes do corpo, foram buscadas métodos de solução disponíveis para tal sistema. Baseado nos estudos encontrados em uma revisão bibliográ ca, foi de nida uma metodologia de solução numérica de sistemas multi-corpos. Durante o trabalho, surgiu a necessidade de representar forças de contato entre corpos rígidos, e foram incluídas soluções de atuais teorias do assunto. Essas metodologias foram então empregadas para a construção de um algoritmo capaz de solucionar o sistema proposto. Depois de resolvido o sistema, os valores encontrados para as variáveis cinéticas foram comparados com valores obtidos por uma simulação numérica utilizando dois programas computacionais comercias, cujas fundamentações teóricas utilizam diferentes métodos de solução. A comparação das diferenças entre os resultados apontou similaridade entre o algoritmo e os programas utilizados, mas com a necessidade de validação do método através de ensaio mecânico. Ao nal foram sugeridas ideias para trabalhos futuros. / The lack of a member due to diseases, malformations or trauma, greatly impacts the life of an individual. In order to perform Activities of Daily Living (ADL) without drastic limitations, it is necessary to develop e cient prosthetic devices. To assist the design of such products, this work aims to create and solve a dynamic system model to simulate the behavior of prosthetic knees. In order to achieve this goal, the biomechanics of human gait was studied, as well as the existing types of amputation and their impact on human gait. The main components of existing prosthetic devices, currently on the market, were identi ed, as well as its basic geometries. After de ning a simpli ed model able to incorporate the prosthetic components and the individual remaining body parts, an available methodology for the solution of such a system was prospected. Based on the studies found in the currently literature of multibodysystems, a numerical solution methodology for has been set. During the work, the need to represent contact between parts occurred, leading to the implementation of currently theories of contact forces for rigid bodies. These methodologies were then used to construct an algorithm for solving the proposed system. After the system has been solve, the values found for the kinetic variables were compared with those obtained by numerical simulations using two commercial softwares, whose theoretical foundation used di erent solution methodology. Comparing the di erences in results of these simulations, it was revealed a similar behavior between the algorithm and the commercial programs, but with the need of an experimental test, for truly validation of the method. At the end of this work, ideas for future improvement were suggested.

A falta de um membro, devido a doenças, más-formações ou traumas, impacta enormemente na vida de um indivíduo. Para que o mesmo possa realizar Atividades de Vida Diária (AVD), sem drásticas limitações, faz-se necessário o desenvolvimento de próteses e cientes. Para auxiliar no projeto de tais produtos, este trabalho visa criar e solucionar um modelo de sistema dinâmico capaz de simular o comportamento de joelhos prostéticos. A m de alcançar tal objetivo, foi estudada a biomecânica da marcha humana, além dos tipos de amputações existentes e seus impactos na mesma. Buscou-se também estudar os principais componentes de próteses existentes atualmente no mercado, além de suas geometrias básicas. Após de nir-se um modelo simpli cado que representasse os componentes protéticos e as partes remanescentes do corpo, foram buscadas métodos de solução disponíveis para tal sistema. Baseado nos estudos encontrados em uma revisão bibliográ ca, foi de nida uma metodologia de solução numérica de sistemas multi-corpos. Durante o trabalho, surgiu a necessidade de representar forças de contato entre corpos rígidos, e foram incluídas soluções de atuais teorias do assunto. Essas metodologias foram então empregadas para a construção de um algoritmo capaz de solucionar o sistema proposto. Depois de resolvido o sistema, os valores encontrados para as variáveis cinéticas foram comparados com valores obtidos por uma simulação numérica utilizando dois programas computacionais comercias, cujas fundamentações teóricas utilizam diferentes métodos de solução. A comparação das diferenças entre os resultados apontou similaridade entre o algoritmo e os programas utilizados, mas com a necessidade de validação do método através de ensaio mecânico. Ao nal foram sugeridas ideias para trabalhos futuros. / The lack of a member due to diseases, malformations or trauma, greatly impacts the life of an individual. In order to perform Activities of Daily Living (ADL) without drastic limitations, it is necessary to develop e cient prosthetic devices. To assist the design of such products, this work aims to create and solve a dynamic system model to simulate the behavior of prosthetic knees. In order to achieve this goal, the biomechanics of human gait was studied, as well as the existing types of amputation and their impact on human gait. The main components of existing prosthetic devices, currently on the market, were identi ed, as well as its basic geometries. After de ning a simpli ed model able to incorporate the prosthetic components and the individual remaining body parts, an available methodology for the solution of such a system was prospected. Based on the studies found in the currently literature of multibodysystems, a numerical solution methodology for has been set. During the work, the need to represent contact between parts occurred, leading to the implementation of currently theories of contact forces for rigid bodies. These methodologies were then used to construct an algorithm for solving the proposed system. After the system has been solve, the values found for the kinetic variables were compared with those obtained by numerical simulations using two commercial softwares, whose theoretical foundation used di erent solution methodology. Comparing the di erences in results of these simulations, it was revealed a similar behavior between the algorithm and the commercial programs, but with the need of an experimental test, for truly validation of the method. At the end of this work, ideas for future improvement were suggested.