Universität Stuttgart
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Item Open Access Dynamics and energetics of walking with prostheses(2007) Ackermann, Marko; Schiehlen, Werner (Prof. Dr.-Ing.)In Biomechanics musculoskeletal models have been proposed and increasingly used to investigate human walking by means of computational simulations. The skeletal system is often modeled by multibody systems composed of rigid bodies, while the biological actuator is almost exclusively modeled by Hill-type muscle models due to its suitability to computational investigations. The study of normal and pathological walking necessarily involves the consideration of the energetic demand, since it was shown that the energetic demand per unit of distance traveled is the primary performance criterion during walking. These models are used to investigate walking, for instance, by computing moments at the joints required to perform an observed motion using inverse dynamics, by estimating muscle forces from joint moments using optimization techniques, and by generating optimal normal and pathological walking patterns. In spite of the increasing use of computational simulation of gait, the large-scale musculoskeletal models required lead frequently to a prohibitive computational effort, in particular when optimization procedures are involved, preventing its wider use in clinical applications. This dissertation covers part of this wide spectrum of problems in biomechanics focusing on the investigation of normal and pathological walking, in particular prosthetic walking, and on the development of methods that offer alternatives to conventional approaches that either require overwhelming computational effort or deliver unrealistic estimations. In order to investigate the burden caused by lower limb assistive devices experiments are designed to emulate typical deviations of the mechanical properties of the lower limbs caused by prosthetic and orthotic devices. The experiments are performed in a gait analysis laboratory, and the kinematics is reconstructed from markers attached on anatomical landmarks of two subjects. The reconstructed kinematics and measured ground reaction forces are then used to estimate joint moments by inverse dynamics. The results for the kinematics and joint moments for all experiments and subjects are compared and discussed concerning possible contributions to the understanding of prosthetic and orthotic walking. The determination of individual muscle forces has many applications including the assessment of muscle coordination and internal loads on joints and bones, useful for instance, for the design of endoprostheses. Because muscle forces cannot be directly measured without invasive techniques, they are often estimated from joint moments by means of optimization procedures that search for a unique solution among the infinite muscle forces that generate the same joint moments. The conventional method to solve this problem, the static optimization, is computationally efficient but neglects the dynamics involved in muscle force generation and requires the use of an instantaneous cost function, leading often to unrealistic estimations of muscle forces. An alternative is using dynamic optimization associated with a motion tracking, which is, however, computationally very costly. Two alternative approaches are proposed to overcome the limitations of static optimization delivering more realistic estimations of muscle forces while being computationally less expensive than dynamic optimization. One of the great challenges in biomechanics of human walking is the use of the complex, large-scale models of the musculoskeletal system in predictive investigations of pathological gait, for instance, to help on the design of assistive devices, therapies or surgical interventions. The prohibitive computational effort required by dynamic optimization, the conventional approach used to generate optimal walking patterns, prevents a wider use of dynamic simulation of gait for clinical applications. An alternative to avoid the several integrations of the state equations, the major cause for the high computational effort, is the use of inverse dynamics-based methods. Such methods have been used, for instance, in robotics and character animation, but have been poorly explored in biomechanics. Therefore, an inverse dynamics-based approach to simulate human motion that deals with the overdeterminacy of muscle actuation and uses Hill-type muscle models is proposed, too. This approach is applied to generate normal walking patterns, to investigate the gait with a bilateral 2 kg-increase in feet mass, and to predict skeleton motion, muscle coordination and metabolic cost of walking with three different bilateral transtibial prostheses, characterized by their ankle moment versus ankle angle curves. Furthermore, improved parameters describing the prosthetic ankle stiffness curve are determined by incorporating them to the optimization variables.Item Open Access Contact investigations of granular mechanical media in a tumbling sorting machine(2007) Alkhaldi, Hashem; Eberhard, Peter (Prof. Dr. -Ing.)Chapter 1 briefly introduced some contact problems in granular media with some computational procedures used in sequential and parallel computations. In Chapter 2, a general description of the molecular dynamic problems and clarification of the basics of the granular media are presented. Some of the frequently-used algorithms and models, e.g. Discrete Element Method (DEM) and penalty method of the spring-dashpot model are involved in this chapter.Some basic techniques for speeding up simulations of particulate systems by using some proper sorting algorithms and neighbor list computations, e.g. the Verlet approach and the linked linear list method, are used and compared. Different integration approaches was also discussed. It was found that Verlet integrators are efficient, accurate and appropriate to solve the equations of motion of the granular systems. In Chapter 3, the spatial decomposition method is basically used in building the parallel programing codes. This method allows scalability and good results especially when load balancing is done. Needless to say that the important factor which affects the success of the numerical procedure is how much one has access to a computer system which is powerful enough to handle the problem of interest. In this chapter, existing sequential algorithms are extended and modified in such a way that modern high performance computers can be utilized for their parallel evaluation. The library functions of the Parallel Virtual Machine (PVM) are used to handle communication between processors in a distributed memory environment. This chapter also underlined the relation between the speedup, which is the usually used measure of the program scalability, and the size of the system. It was found that the performance improves with increasing the number of particles. The reason is due to the communication and data flow which become more efficient between the different tasks as the number of particles increases and therefore, the communication cost will directly decrease and accordingly, the computational speedup will increase. In some cases, a superlinear behavior is recorded when using different computers with many processors due to the individual cache memory effect of each of the machines used in the network. As a practical industrial application of granular studies, particle screening, which is considered as an essential technology of particle separation in many industrial fields, is selected to be investigated in Chapter 4. This chapter presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shaped particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level oblique vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle-particle and particle-boundary collisions will appear under the tumbling motion of the rotating structure. Herein, the penalty method, which employs spring-damper models, is applied to calculate the normal and frictional forces. For specific geometrical and contact parameters particle transportation, sifting rates and machine efficiency are recorded. Particles are simulated in uniform and stepped models of tumbling cylinders. For both continuous screening and batch sieving, it was found that the segregation process is very sensitive to the rotational speed of the machine. Furthermore, the particle feeding rates, inclination angles and shaft eccentricity have a great influence on the machine efficiency. Small angles between 0.5 degree to 1 degree and eccentricities between 25 to 50mm are recommended. The sieve roughness has also an influence on the number of particles that stay or leave the machine. An optimal value of relatively medium friction coefficient is recommended. Moreover, the barrel oscillation has a significant influence on the sorting process. Oscillatory motion of the barrel shows better performance relative to the non-rotating or even continuous-rotating motion. Finally, the thesis ends in Chapter 5 with a general summary of the presented work and a short overview of the proposed work in the future.Item Open Access Modellierung, Simulation und experimentelle Untersuchung miniaturisierter Schaltventile mit Stoßantrieb(2015) Fischer, Christian; Eberhard, Peter (Prof. Dr.-Ing.)In dieser Arbeit wird eine systematische Methodik zur grundlegenden Untersuchung von Stößen mit und ohne Fluid und zur Simulation stoßbetriebener Schaltventile vorgestellt. Der Kerngedanke eines stoßbetriebenen Schaltventils besteht darin, mit einem Aktor eine hohe Kraft in kurzer Zeit zu erzeugen, die eine dünne Gehäusewand bzw. eine fest eingespannte Platte verformt und eine Kugel im Ventil bzw. auf der anderen Plattenseite durch einen Stoß beschleunigt. Diese Kugel wechselt dann im Ventil ihre Position. Dabei ist der Wirkungsgrad der Energieübertragung, welcher die kinetische Energie der inneren Kugel nach dem Stoß bestimmt, besonders wichtig, um robustes Umschalten zu ermöglichen. Es wird in einem mehrstufigen Prozess die Simulation des Stoßvorgangs ermöglicht. Zunächst wird anhand eines vereinfachten, vergrößerten Modells durch Experimente der Wirkungsgrad der Stoßübertragung unterschiedlicher Materialkombinationen und Geometrien bestimmt. Mit diesen Ergebnissen werden nichtlineare Finite-Elemente-Modelle desselben Modells unter Verwendung nichtlinearer Materialmodelle verglichen und validiert. In einem dritten Schritt wird ein elastisches Mehrkörpermodell erstellt und mit Hilfe der Simulationsergebnisse der Finite-Elemente-Simulation validiert. Dieses Modell dient dann der Simulation der Stoßvorgänge und auf Grund der extrem geringen Rechenzeiten der Durchführung von Parameterstudien und der Optimierung des Wirkungsgrades. Dadurch können viele Erkenntnisse gewonnen werden, die der Entwicklung neuer Ventilvarianten dienen. Beispielsweise wird sich herausstellen, dass die Periodendauer der ersten Eigenfrequenz der Platte mindestens halb so groß wie die Stoßdauer sein sollte, dass die Elastizitätsmodule der Kugeln möglichst hoch sein sollten und der E-Modul der Platte möglichst gering. Außerdem sollte die Platte möglichst dünn und die Oberfläche der Stoßkörper möglichst wenig gekrümmt sein. Für die Untersuchung des Fluideinflusses auf den Stoß wurde das Finite-Elemente-Modell der Platte im elastischen Mehrkörpermodell durch ein Modell ersetzt, welches die Wechselwirkung der Platte mit einem umgebenden Fluid beschreibt. Damit können dann die Experimente, die mit Fluid durchgeführt wurden, verglichen werden. Dabei ist die Auswertung der Ergebnisse mit Fluid nicht direkt möglich, denn es müssen einige Effekte kompensiert werden, die der Brechungsindex des Fluids direkt auf die Messung hat. Es zeigt sich dann aber, dass die Ergebnisse gut überein stimmen. Des Weiteren zeigt sich, dass der Stoß nicht von der Viskosität des Fluids, sondern lediglich von dessen Dichte abhängt. Der Einfluss der Viskosität spielt jedoch eine Rolle, wenn zu Beginn des Stoßes ein kleiner Spalt zwischen der Platte und der Kugel ist und unmittelbar nach dem Stoß, wenn sich die Kugel von der Platte entfernt und Fluid nachströmen muss. Dazu wurde ein Simulationsmodell zur Berechnung des Squeeze-Film-Effekts entwickelt und in das elastische Mehrkörpermodell integriert. Für die Bewegung der Kugel während des Umschaltvorgangs im Ventil wurden CFD-Simulationen mit der ALE-Erweiterung zur Beschreibung der Netzverformungen unter mehreren Methoden als beste befunden und verwendet. Damit stellt man fest, dass der Einfluss von Wasser auf die Kugelbewegung recht gering ist und das Umschalten kaum behindert. Öl hingegen bremst die Kugel stark ab, so dass robustes Umschalten nicht mehr sichergestellt werden kann. Durch Messungen mit einer Hochgeschwindigkeitskamera kann außerdem das Verhalten eines Prototypen beobachtet und es können Vermutungen aus der Simulation bestätigt werden. Darauf aufbauend wurde ein verbessertes Konzept dieses Prototyps vorgeschlagen.Item Open Access A contribution to computational contact procedures in flexible multibody systems(2007) Ebrahimi, Saeed; Eberhard, Peter (Prof. Dr.-Ing.)This thesis is devoted to computational contact procedures in flexible multibody systems. For this purpose, first in Chapter 1 contact problems in multibody systems together with some computational procedures were briefly introduced. Then, in Chapter 2 starting from kinematics and kinetics of rigid bodies, some basic concepts of flexible multibody dynamics including solution algorithms were explained. In this context, some common modeling strategies were briefly explained. Among all, the floating frame of reference has been used in this work to generate equations of motion. This approach is a widely-used method which introduces two kinds of variables for body reference motion and elastic deformations. Chapter 2 ended with giving some notes regarding symbolic and numerical derivation of equations of motion together with numerical integration methods. Some of the most frequently-used formulations for incorporating the contact constraints into the governing equations of motion were introduced briefly in Chapter 3. Among them, the penalty approach, the Lagrange multipliers approach, linear complementarity problem formulations and proximal point approach were mentioned. Contact and impact problem of planar flexible bodies in multibody systems were formulated in Chapters 4 and 5, respectively, yielding the linear complementarity problems. In Chapter 4, the available approach for planar rigid bodies was extended for planar flexible bodies. The major difference between both approaches was in the formulation of contact kinematics. It was also shown that our formulation approaches the LCP formulation developed for rigid bodies when the effect of deformations is ignored. Impact analysis was followed in Chapter 5 by formulating some other LCPs on position and velocity level. The formulations on position level for normal direction was done by imposing non-penetrability conditions through complementarity relations between normal gaps and normal impact forces. In doing so, at first kinematics of impacting bodies was described in terms of generalized coordinates. Some common integration approaches have been further used to find the required relations which represent generalized coordinates as functions of impact forces. Then, this formulation was appended to the formulation of tangential contact forces which was developed for continual contact in Chapter 4. For the velocity level formulation of normal impact, one deals with velocity of normal gaps and the generalized velocities instead of normal gaps and the generalized coordinates. In the case of impact, examples for both short and long impacts were considered. The results showed a good agreement between the results of our approach based on the formulations from the explicit Runge-Kutta approach on position and velocity level and also the RADAU5 approach with the results of FEM. It was shown that the formulations on both position and velocity level approach the precise results of FEM even for stiff planar deformable bodies provided that a proper number of eigenmodes of the FEM model is chosen for building the reduced model of deformable bodies. We also observed that selection of higher number of eigenmodes leads to the lower energy dissipation. Selection of higher eigenmodes allows a better adjustment of the shape of deformable bodies during impact which consequently leads to lower normal impact forces. As a result, the amount of released energy during the expansion phase of impact increases as a higher number of eigenmodes is considered. Then, the modeling of contact and impact of spatial flexible bodies using the Polygonal Contact Model (PCM) approach was explained in Chapter 6. PCM was originally an algorithm of contact of spatial rigid bodies based on the surface compliance approach. In Chapter 6 the extension of PCM as a general algorithm for contact of flexible bodies which establishes a more realistic modeling of many contact problems in multibody systems was explained. It can be summarized that with the extended PCM, contacts between elastic bodies can be considered at only moderate additional costs. As an application of contact modeling in multibody systems, Chapter 7 was devoted to the subject of contact in geared systems. First, the approach for contact modeling of meshing rigid gear wheels was briefly explained. Furthermore, it was extended by introducing some elastic elements between the teeth and the gear body of each gear wheel to consider partially elasticities.Item Open Access Distributed control and organization of communicating mobile robots : design, simulation, and experimentation(2021) Ebel, Henrik; Eberhard, Peter (Prof. Dr.-Ing. Prof. E.h.)Leveraging the communication-based cooperation of multiple robotic systems has the potential to significantly further the state of the art of what is achievable with robotic automation. Therefore, beyond solely improving the capabilities of individual robotic agents, reconfigurable robotic networks have come to the attention of research and industry. However, despite the potential to increase flexibility, robustness, and performance, robotic networks are not yet in widespread application, with many research challenges remaining. After all, developing a reliable, reconfigurable distributed system is very difficult, adding to the manifold, interdisciplinary challenges posed by robotics in general. Hence, to better understand and subsequently overcome these challenges, distributed robotics is still in a state where it can benefit significantly from research that tackles well-defined benchmark problems. Consequently, this thesis faces the challenges of distributed robotics at the example of a cooperative transportation task. In the task, omnidirectional mobile robots cooperate to maneuver polygonal objects purely by pushing forces and in a completely self-reliant manner. The task is found to be a formidable benchmark problem since it raises all major challenges of the field while still being easily graspable, intuitively making evident the qualities of the control and organization schemes employed. The thesis discusses all aspects of the task in an encompassing manner, not only including the design of the employed control and organization methods, but also the software architecture and even the custom robotic hardware employed. Results from simulations and real-world hardware experiments show that the proposed scheme is of unprecedented versatility, putting into practice all major promises of distributed robotics, including plug-and-play control for online reconfigurations of the robotic network. This is achieved by relying, at heart, on optimization-based schemes. The task is decomposed into a formation control task and the organizational task of inferring formations useful for manipulation, allowing the usage of distributed model predictive control for formation control and of distributed optimization for organization. Further challenges dealt with include self-reliant task allocation as well as local and global navigation. However, the contributions of the thesis extend beyond the immediate needs of the benchmark problem. A component that may prove helpful in other research endeavors in the field includes the devised distributed software architecture, which greatly facilitates the transition from simulations to experiments. Similarly, the custom mobile robot and different proposed setups of the formation controller are also suited to other tasks and projects. Due to formation control’s universal appeal, the proposed approach based on distributed predictive control is analyzed separately from the transportation task. In experiments, the predictive control-based approach confirms its theory-rooted advantages in comparison to a more traditional approach, despite the latter being modified to also respect input constraints. Finally, a proposed distributed version of an augmented Lagrangian particle swarm optimization algorithm, which is used to devise formations in the thesis, may even prove useful far beyond robotics.Item Open Access Simulation of a novel restraint safety concept for motorcycles(2023) Maier, Steffen; Fehr, Jörg (apl. Prof. Dr.-Ing.)Item Open Access Dynamic simulation and control of optical systems(2018) Störkle, Johannes; Eberhard, Peter (Prof. Dr.-Ing. Prof. E.h.)This thesis deals with the simulation-based investigation and control of optical systems that are mechanically influenced. Here, the focus is on the dynamic-optical modeling of vibration-sensitive mirror systems, which are utilized, e.g., in large astronomy telescopes or high-precision lithography optics. The large-area primary mirrors of telescopes typically consist of many individual hexagonal mirror segments, which are positioned with precise sensors and actuators. Furthermore, an adaptive optical unit usually compensates for the optical aberrations due to atmospheric disturbances. In practice, these aberrations are detected, and corrected, within a few seconds using deformable mirrors. However, to further improve the performance of these optical systems, dynamical disturbances in the mechanics, i.e., small movements and deformations of the optical surfaces, must also be taken into account. Therefore, multidisciplinary simulation methods are developed and presented. Based on this, the dynamical-optical system behavior is modeled using model-order-reduced, flexible multibody systems. Hence, the dynamical analysis of the mechanical-optical system can be performed at low computation costs. Thanks to the optical analysis in the time domain and using Fourier-optical concepts, one can also simulate exposure processes. To actively compensate for aberrations due to mechanical vibrations, model-based control strategies are also designed. They are not only demonstrated by means of simulation examples, but also illustrated through a laboratory experiment. The latter is realized with a low-cost test setup for student training using Arduino microcontrollers, position and force sensors, as well as high-speed cameras.