Rigid body modeling has historically been used to study various features of the elbow joint including both physical and computational models. Computational modeling provides an inexpensive, easily customizable, and effective method by which to predict and investigate the response of a physiological system to in vivo stresses and applied perturbations. Utilizing computer topography scans of a cadaveric elbow, a virtual representation of the joint was created using the commercially available MIMICS(TM) and SolidWorks(TM) software packages. Accurate 3D articular surfaces, ligamentous constraints, and joint contact parameters dictated motion. The model was validated against two cadaveric studies performed by Chanlalit et al. (2011, 2012) considering monopolar and bipolar circular radial head replacements in their effects on radiocapitellar stability and respective reliance upon lateral soft tissues, as well as a comparison of these with a novel anatomic radial head replacement system in an elbow afflicted with the “terrible triad” injury. Rigid body simulations indicated that the computational model was able to accurately recreate the translation of forces in the joint and demonstrate results similar to those presented in the cadaveric data in both the intact elbow and in unstable injury states. Trends in the resulting data were reflective of the average behavior of the cadaveric specimens while percent changes between states correlated closely with the experimental data. Information on the transposition of forces within the joint and ligament tensions gleaned from the computational model provided further insight into the stability of the elbow with a compromised radial head.

The use of computational modeling is an effective and inexpensive way to predict the response of complex systems to various perturbations. However, not until the early 1990s had this technology been used to predict the behavior of physiological systems, specifically the human skeletal system. To that end, a computational model of the human elbow joint was developed using computed topography (CT) scans of cadaveric donor tissue, as well as the commercially available software package SolidWorks™. The kinematic function of the joint model was then defined through 3D reconstructions of the osteoarticular surfaces and various soft-tissue constraints. The model was validated against cadaveric experiments performed by Hull et al and Fern et al that measured the significance of coronoid process fractures, lateral ulnar collateral ligament ruptures, and radial head resection in elbow joint resistance to varus displacement of the forearm. Kinematic simulations showed that the computational model was able to mimic the physiological movements of the joint throughout various ranges of motion including flexion/extension and pronation/supination. Quantitatively, the model was able to accurately reproduce the trends, as well as the magnitudes, of varus resistance observed in the cadaveric specimens. Additionally, magnitudes of ligament tension and joint contact force predicted by the model were able to further elucidate the complex soft-tissue and osseous contributions to varus elbow stability.

Analisa o comportamento tribológico do pneumático. Discute o coeficiente de atrito do pneu, a influência do pavimento e os avanços na modelagem. Apresenta uma metodologia para estimativa do desgaste de pneus pelo método dos elementos finitos. Usa o conceito de trabalho de abrasão. Considera nas condições de contorno do modelo de pneu o efeito do camber e do ângulo de deriva. Investiga a interação vibracional entre o pneu e a suspensão como causa de desgaste irregular. Utiliza modelagem de ônibus rodoviário por multicorpos com eixo flexível. Emprega técnica tempo-freqüência para análise do acoplamento modal entre pneu e suspensão. Propõe novos modelos para estudo do desgaste em pneus analisando-se um modelo completo de veículo pelo método dos elementos finitos. Sugere análises de sensibilidade considerando os parâmetros de regulagem da suspensão e condições operacionais dos componentes. Propõe análises estocásticas da especificação do pneu para otimização do sistema pneu-suspensão. / The tire tribological behavior is analyzed. The friction coefficient of rubbers is presented, and its inherent modeling difficulties regarding the operational condition dependence during measurements are discussed. The influence of the pavement roughness and the advances in friction modeling are presented. A predictive methodology to evaluate the tread wear using finite element method and the concept of frictional energy was used. Camber, lateral forces and slip angles are taken into account as boundary conditions for the tire simulations in steady state. The vibrational interaction between tire and suspension concerning irregular wear on front axle truck tires was investigated. A multibody bus model with flexible front axle was used for modal analysis purposes. A time-frequency methodology was applied to identify modal vibrations of the tire and suspension assemblage. A new simulation model for the tire wear was proposed intending to analyze the whole vehicle with under the finite element method. Sensitivity analysis of the vehicle suspension setup and operational conditions of components was suggested. Stochastic analysis of tire specification is recommended to optimize the tire-suspension system.

Analisa o comportamento tribológico do pneumático. Discute o coeficiente de atrito do pneu, a influência do pavimento e os avanços na modelagem. Apresenta uma metodologia para estimativa do desgaste de pneus pelo método dos elementos finitos. Usa o conceito de trabalho de abrasão. Considera nas condições de contorno do modelo de pneu o efeito do camber e do ângulo de deriva. Investiga a interação vibracional entre o pneu e a suspensão como causa de desgaste irregular. Utiliza modelagem de ônibus rodoviário por multicorpos com eixo flexível. Emprega técnica tempo-freqüência para análise do acoplamento modal entre pneu e suspensão. Propõe novos modelos para estudo do desgaste em pneus analisando-se um modelo completo de veículo pelo método dos elementos finitos. Sugere análises de sensibilidade considerando os parâmetros de regulagem da suspensão e condições operacionais dos componentes. Propõe análises estocásticas da especificação do pneu para otimização do sistema pneu-suspensão. / The tire tribological behavior is analyzed. The friction coefficient of rubbers is presented, and its inherent modeling difficulties regarding the operational condition dependence during measurements are discussed. The influence of the pavement roughness and the advances in friction modeling are presented. A predictive methodology to evaluate the tread wear using finite element method and the concept of frictional energy was used. Camber, lateral forces and slip angles are taken into account as boundary conditions for the tire simulations in steady state. The vibrational interaction between tire and suspension concerning irregular wear on front axle truck tires was investigated. A multibody bus model with flexible front axle was used for modal analysis purposes. A time-frequency methodology was applied to identify modal vibrations of the tire and suspension assemblage. A new simulation model for the tire wear was proposed intending to analyze the whole vehicle with under the finite element method. Sensitivity analysis of the vehicle suspension setup and operational conditions of components was suggested. Stochastic analysis of tire specification is recommended to optimize the tire-suspension system.

A mechatronic system is an assembly of technological components, such as a mechanism, sensors, actuators, and a control unit. Recently, a number of researchers and industrial manufacturers have highlighted the potential advantages of lightweight parallel mechanisms with respect to the accuracy, dynamic performances, construction cost, and transportability issues. The design of a mechatronic system with such a mechanism requires a multidisciplinary approach, where the mechanical deformations have to be considered. This thesis proposes two original contributions in this framework. (i) First, a modular and systematic method is developed for the integrated simulation of mechatronic systems, which accounts for the strongly coupled dynamics of the mechanical and non-mechanical components. The equations of motion are formulated using the nonlinear Finite Element approach for the mechanism, and the block diagram language for the control system. The time integration algorithm relies on the generalized-alpha method, known in structural dynamics. Hence, well-defined concepts from mechanics and from system dynamics are combined in a unified formulation, with guaranteed convergence and stability properties. Several applications are treated in the fields of robotics and vehicle dynamics. (ii) Usual methods in flexible multibody dynamics lead to complex nonlinear models, not really suitable for control design. Therefore, a systematic nonlinear model reduction technique is presented, which transforms an initial high-order Finite Element model into a low-order and explicit model. The order reduction is obtained using the original concept of Global Modal Parameterization: the motion of the assembled mechanism is described in terms of rigid and flexible modes, which have a global physical interpretation in the configuration space. The reduction procedure involves the component-mode technique and an approximation strategy in the configuration space. Two examples are presented: a four-bar mechanism, and a parallel kinematic machine-tool. Finally, both simulation and modeling tools are exploited for the dynamic analysis and the control design of an experimental lightweight manipulator with hydraulic actuators. A Finite Element model is first constructed and validated with experimental data. A reduced model is derived, and an active vibration controller is designed on this basis. The simulation of the closed-loop mechatronic system predicts remarkable performances. The model-based controller is also implemented on the test-bed, and the experimental results agree with the simulation results. The performances and the other advantages of the control strategy demonstrate the relevance of our developments in mechatronics.

The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators.

The main objective of this work is to demonstrate some new computational methods for estimation, optimization and modeling of dynamical systems that use automatic differentiation. Particular focus will be upon dynamical systems arising in Aerospace Engineering. Automatic differentiation is a recursive computational algorithm, which enables computation of analytically rigorous partial derivatives of any user-specified function. All associated computations occur, in the background without user intervention, as the name implies. The computational methods of this dissertation are enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate Embedding Method). OCEA has been recently developed and makes possible efficient computation and evaluation of partial derivatives with minimal user coding. The key results in this dissertation details the use of OCEA through a number of computational studies in estimation and dynamical modeling. Several prototype problems are studied in order to evaluate judicious ways to use OCEA. Additionally, new solution methods are introduced in order to ascertain the extended capability of this new computational tool. Computational tradeoffs are studied in detail by looking at a number of different applications in the areas of estimation, dynamical system modeling, and validation of solution accuracy for complex dynamical systems. The results of these computational studies provide new insights and indicate the future potential of OCEA in its further development.

The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators.

This thesis is concerned with the efficient numerical simulation of finite element based flexible multibody systems. Scaling operations are systematically applied to the governing index-3 differential algebraic equations in order to solve the problem of ill conditioning for small time step sizes. The importance of augmented Lagrangian terms is demonstrated. The use of fast sparse solvers is justified for the solution of the linearized equations of motion resulting in significant savings of computational costs. Three time stepping schemes for the integration of the governing equations of flexible multibody systems are discussed in detail. These schemes are the two-stage Radau IIA scheme, the energy decaying scheme, and the generalized-α method. Their formulations are adapted to the specific structure of the governing equations of flexible multibody systems. The efficiency of the time integration schemes is comprehensively evaluated on a series of test problems. Formulations for structural and constraint elements are reviewed and the problem of interpolation of finite rotations in geometrically exact structural elements is revisited. This results in the development of a new improved interpolation algorithm, which preserves the objectivity of the strain field and guarantees stable simulations in the presence of arbitrarily large rotations. Finally, strategies for the spatial discretization of beams in the presence of steep variations in cross-sectional properties are developed. These strategies reduce the number of degrees of freedom needed to accurately analyze beams with discontinuous properties, resulting in improved computational efficiency.

The area of powertrain dynamics has received considerable attention over a number of years. The recent introduction of more stringent emission requirements together with economic pressure has led to a particular focus on increasing powertrain efficiency. This has seen the incorporation of on-board, real-time measurements to predict system behaviour and engine condition. In this domain, accurate models for all powertrain components are important. One strategy to improve accuracy is to evaluate the assumptions made when deriving each model and then to address the simplifications that may introduce large errors. To this end, the aim of the work presented in this dissertation was to investigate the consequences of some of the more common assumptions and simplifications made in low frequency torsional powertrain models, and to propose improved models where appropriate. In particular, the effects of piston-tocylinder friction, crank/gudgeon pin offset, and the torsional behaviour of tyres were studied. Frequency and time domain models were used to investigate system behaviour and model predictions were compared with measurements on a small single cylinder engine. All time domain engine and powertrain models also include a variable inertia function for each reciprocating mechanism. It was found that piston-to-cylinder friction can increase the apparent inertia variation of a single reciprocating engine mechanism. This has implications for the nonlinear behaviour of engines and the drivetrains they are connected to. The effect of crank/gudgeon pin offset also modified the nonlinear behaviour of the mechanism. Though, for typical (small) gudgeon offset values these effects are small. However, for large offset values, achievable practically with crank offset, the modification to the nonlinear behaviour should not be ignored. The low frequency torsional damping properties of a small pneumatic tyre were found to be more accurately represented as hysteretic rather than viscous. Time domain modelling was then used to extend the results to a multi-cylinder engine powertrain and was achieved using the Time Domain Receptance (TDR) method. Various powertrain component TDRs were developed using Laplacians. Powertrain simulations showed that piston-to-cylinder friction can provide additional excitation to the system.