Flexible Multibody Simulation Approach in the Dynamic Analysis of Bone Strains Activity

The objective of this study is to show that bone strains due to dynamic mechanical loading during physical activity can be analysed using the flexible multibody simulation approach. Strains within the bone tissue play a major role in bone (re)modeling. Based on previous studies, it has been shown that dynamic loading seems to be more important for bone (re)modeling than static loading. The finite element method has been used previously to assess bone strains. However, the finite element method may be limited to static analysis of bone strains due to the expensive computation required for dynamic analysis, especially for a biomechanical system consisting of several bodies. Further, in vivo implementation of strain gauges on the surfaces of bone has been used previously in order to quantify the mechanical loading environment of the skeleton. However, in vivo strain measurement requires invasive methodology, which is challenging and limited to certain regions of superficial bones only, such as the anterior surface of the tibia. In this study, an alternative numerical approach to analyzing in vivo strains, based on the flexible multibody simulation approach, is proposed. In order to investigate the reliability of the proposed approach, three 3-dimensional musculoskeletal models where the right tibia is assumed to be flexible, are used as demonstration examples. The models are employed in a forward dynamics simulation in order to predict the tibial strains during walking on a level exercise. The flexible tibial model is developed using the actual geometry of the subject’s tibia, which is obtained from 3 dimensional reconstruction of Magnetic Resonance Images. Inverse dynamics simulation based on motion capture data obtained from walking at a constant velocity is used to calculate the desired contraction trajectory for each muscle. In the forward dynamics simulation, a proportional derivative servo controller is used to calculate each muscle force required to reproduce the motion, based on the desired muscle contraction trajectory obtained from the inverse dynamics simulation. Experimental measurements are used to verify the models and check the accuracy of the models in replicating the realistic mechanical loading environment measured from the walking test. The predicted strain results by the models show consistency with literature-based in vivo strain measurements. In conclusion, the non-invasive flexible multibody simulation approach may be used as a surrogate for experimental bone strain measurement, and thus be of use in detailed strain estimation of bones in different applications. Consequently, the information obtained from the present approach might be useful in clinical applications, including optimizing implant design and devising exercises to prevent bone fragility, accelerate fracture healing and reduce osteoporotic bone loss.

The Dynamic Analysis of a Human Skeleton Using the Flexile Multibody Simulation Approach

The human motion study, which relies on mathematical and computational models ingeneral, and multibody dynamic biomechanical models in particular, has become asubject of many recent researches. The human body model can be applied to different physical exercises and many important results such as muscle forces, which are difficult to be measured through practical experiments, can be obtained easily. In the work, human skeletal lower limb model consisting of three bodies in build using the flexible multibody dynamics simulation approach. The floating frame of reference formulation is used to account for the flexibility in the bones of the human lower limb model. The main reason of considering the flexibility inthe human bones is to measure the strains in the bone result from different physical exercises. It has been perceived the bone under strain will become stronger in order to cope with the exercise. On the other hand, the bone strength is considered and important factors in reducing the bone fractures. The simulation approach and model developed in this work are used to measure the bone strain results from applying raising the sole of the foot exercise. The simulation results are compared to the results available in literature. The comparison shows goof agreement. This study sheds the light on the importance of using the flexible multibody dynamic simulation approach to build human biomechanical models, which can be used in developing some exercises to achieve the optimalbone strength.

Flexible multibody approach in bone strain estimation during physical activity:

Bone strain plays a major role as the activation signal for the bone (re)modeling process, which is vital for keeping bones healthy. Maintaining high bone mineral density reduces the chances of fracture in the event of an accident. Numerous studies have shown that bones can be strengthened with physical exercise. Several hypotheses have asserted that a stronger osteogenic (bone producing) effect results from dynamic exercise than from static exercise. These previous studies are based on short-term empirical research, which provide the motivation for justifying the experimental results with a solid mathematical background. The computer simulation techniques utilized in this work allow for non-invasive bone strain estimation during physical activity at any bone site within the human skeleton. All models presented in the study are threedimensional and actuated by muscle models to replicate the real conditions accurately. The objective of this work is to determine and present loading-induced bone strain values resulting from physical activity. It includes a comparison of strain resulting from four different gym exercises (knee flexion, knee extension, leg press, and squat) and walking, with the results reported for walking and jogging obtained from in-vivo measurements described in the literature. The objective is realized primarily by carrying out flexible multibody dynamics computer simulations. The dissertation combines the knowledge of finite element analysis and multibody simulations with experimental data and information available from medical field literature. Measured subject-specific motion data was coupled with forward dynamics simulation to provide natural skeletal movement. Bone geometries were defined using a reverse engineering approach based on medical imaging techniques. Both computed tomography and magnetic resonance imaging were utilized to explore modeling differences. The predicted tibia bone strains during walking show good agreement with invivo studies found in the literature. Strain measurements were not available for gym exercises; therefore, the strain results could not be validated. However, the values seem reasonable when compared to available walking and running invivo strain measurements. The results can be used for exercise equipment design aimed at strengthening the bones as well as the muscles during workout. Clinical applications in post fracture recovery exercising programs could also be the target. In addition, the methodology introduced in this study, can be applied to investigate the effect of weightlessness on astronauts, who often suffer bone loss after long time spent in the outer space.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Model reduction techniques in flexible multibody dynamics with application to engine cranktrain simulation

The development of a multibody model of a motorbike engine cranktrain is presented in this work, with an emphasis on flexible component model reduction. A modelling methodology based upon the adoption of non-ideal joints at interface locations, and the inclusion of component flexibility, is developed: both are necessary tasks if one wants to capture dynamic effects which arise in lightweight, high-speed applications. With regard to the first topic, both a ball bearing model and a journal bearing model are implemented, in order to properly capture the dynamic effects of the main connections in the system: angular contact ball bearings are modelled according to a five-DOF nonlinear scheme in order to grasp the crankshaft main bearings behaviour, while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at the conrod big end locations. Concerning the second matter, flexible models of the crankshaft and the connecting rod are produced. The well-established Craig-Bampton reduction technique is adopted as a general framework to obtain reduced model representations which are suitable for the subsequent multibody analyses. A particular component mode selection procedure is implemented, based on the concept of Effective Interface Mass, allowing an assessment of the accuracy of the reduced models prior to the nonlinear simulation phase. In addition, a procedure to alleviate the effects of modal truncation, based on the Modal Truncation Augmentation approach, is developed. In order to assess the performances of the proposed modal reduction schemes, numerical tests are performed onto the crankshaft and the conrod models in both frequency and modal domains. A multibody model of the cranktrain is eventually assembled and simulated using a commercial software. Numerical results are presented, demonstrating the effectiveness of the implemented flexible model reduction techniques. The advantages over the conventional frequency-based truncation approach are discussed.

Towards a flexible and dynamic replication control for distributed real-time embedded systems with QoS interdependencies

Replication is a proven concept for increasing the availability of distributed systems. However, actively replicating every software component in distributed embedded systems may not be a feasible approach. Not only the available resources are often limited, but also the imposed overhead could significantly degrade the system's performance. The paper proposes heuristics to dynamically determine which components to replicate based on their significance to the system as a whole, its consequent number of passive replicas, and where to place those replicas in the network. The results show that the proposed heuristics achieve a reasonably higher system's availability than static offline decisions when lower replication ratios are imposed due to resource or cost limitations. The paper introduces a novel approach to coordinate the activation of passive replicas in interdependent distributed environments. The proposed distributed coordination model reduces the complexity of the needed interactions among nodes and is faster to converge to a globally acceptable solution than a traditional centralised approach.

Flexible and dynamic replication control for interdependent distributed real-time embedded systems

Replication is a proven concept for increasing the availability of distributed systems. However, actively replicating every software component in distributed embedded systems may not be a feasible approach. Not only the available resources are often limited, but also the imposed overhead could significantly degrade the system’s performance. This paper proposes heuristics to dynamically determine which components to replicate based on their significance to the system as a whole, its consequent number of passive replicas, and where to place those replicas in the network. The activation of passive replicas is coordinated through a fast convergence protocol that reduces the complexity of the needed interactions among nodes until a new collective global service solution is determined.

A multibody dynamic model of the cross-country ski-skating technique

The objective of this thesis is the development of a multibody dynamic model matching the observed movements of the lower limb of a skier performing the skating technique in cross-country style. During the construction of this model, the formulation of the equation of motion was made using the Euler - Lagrange approach with multipliers applied to a multibody system in three dimensions. The description of the lower limb of the skate skier and the ski was completed by employing three bodies, one representing the ski, and two representing the natural movements of the leg of the skier. The resultant system has 13 joint constraints due to the interconnection of the bodies, and four prescribed kinematic constraints to account for the movements of the leg, leaving the amount of degrees of freedom equal to one. The push-off force exerted by the skate skier was taken directly from measurements made on-site in the ski tunnel at the Vuokatti facilities (Finland) and was input into the model as a continuous function. Then, the resultant velocities and movement of the ski, center of mass of the skier, and variation of the skating angle were studied to understand the response of the model to the variation of important parameters of the skate technique. This allowed a comparison of the model results with the real movement of the skier. Further developments can be made to this model to better approximate the results to the real movement of the leg. One can achieve this by changing the constraints to include the behavior of the real leg joints and muscle actuation. As mentioned in the introduction of this thesis, a multibody dynamic model can be used to provide relevant information to ski designers and to obtain optimized results of the given variables, which athletes can use to improve their performance.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Real-Time Simulation of Mobile and Industrial Machines Using the Multibody Simulation Approach

This thesis introduces a real-time simulation environment based on the multibody simulation approach. The environment consists of components that are used in conventional product development, including computer aided drawing, visualization, dynamic simulation and finite element software architecture, data transfer and haptics. These components are combined to perform as a coupled system on one platform. The environment is used to simulate mobile and industrial machines at different stages of a product life time. Consequently, the demands of the simulated scenarios vary. In this thesis, a real-time simulation environment based on the multibody approach is used to study a reel mechanism of a paper machine and a gantry crane. These case systems are used to demonstrate the usability of the real-time simulation environment for fault detection purposes and in the context of a training simulator. In order to describe the dynamical performance of a mobile or industrial machine, the nonlinear equations of motion must be defined. In this thesis, the dynamical behaviour of machines is modelled using the multibody simulation approach. A multibody system may consist of rigid and flexible bodies which are joined using kinematic joint constraints while force components are used to describe the actuators. The strength of multibody dynamics relies upon its ability to describe nonlinearities arising from wearing of the components, friction, large rotations or contact forces in a systematic manner. For this reason, the interfaces between subsystems such as mechanics, hydraulics and control systems of the mechatronic machine can be defined and analyzed in a straightforward manner.

Simulation of structural stress history based on dynamic analysis

Modern machine structures are often fabricated by welding. From a fatigue point of view, the structural details and especially, the welded details are the most prone to fatigue damage and failure. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the stress loads that act on each detail. Even though, dynamic simulation of flexible bodies is already current method for analyzing structures, obtaining the stress history of a structural detail during dynamic simulation is a challenging task; especially when the detail has a complex geometry. In particular, analyzing the stress history of every structural detail within a single finite element model can be overwhelming since the amount of nodal degrees of freedom needed in the model may require an impractical amount of computational effort. The purpose of computer simulation is to reduce amount of prototypes and speed up the product development process. Also, to take operator influence into account, real time models, i.e. simplified and computationally efficient models are required. This in turn, requires stress computation to be efficient if it will be performed during dynamic simulation. The research looks back at the theoretical background of multibody dynamic simulation and finite element method to find suitable parts to form a new approach for efficient stress calculation. This study proposes that, the problem of stress calculation during dynamic simulation can be greatly simplified by using a combination of floating frame of reference formulation with modal superposition and a sub-modeling approach. In practice, the proposed approach can be used to efficiently generate the relevant fatigue assessment stress history for a structural detail during or after dynamic simulation. In this work numerical examples are presented to demonstrate the proposed approach in practice. The results show that approach is applicable and can be used as proposed.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Integrating structural and input design of a 2-DOF high-speed parallel manipulator: A flexible model-based approach

This paper discusses the integrated design of parallel manipulators, which exhibit varying dynamics. This characteristic affects the machine stability and performance. The design methodology consists of four main steps: (i) the system modeling using flexible multibody technique, (ii) the synthesis of reduced-order models suitable for control design, (iii) the systematic flexible model-based input signal design, and (iv) the evaluation of some possible machine designs. The novelty in this methodology is to take structural flexibilities into consideration during the input signal design; therefore, enhancing the standard design process which mainly considers rigid bodies dynamics. The potential of the proposed strategy is exploited for the design evaluation of a two degree-of-freedom high-speed parallel manipulator. The results are experimentally validated. (C) 2010 Elsevier Ltd. All rights reserved.