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A Contribution to the Development of a Specialpurpose Mohamed Abdelrahman A contribution to the development of a special- purpose vehicle for handicapped persons A contribution to the development of a special-purpose vehicle for handicapped persons Dynamic simulations of mechanical concepts and the biomechanical interaction between wheelchair and user Mohamed Abdelrahman Universitätsverlag Ilmenau 2014 Impressum Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Angaben sind im Internet über http://dnb.d-nb.de abrufbar. Diese Arbeit hat der Fakultät für Maschinenbau der Technischen Universität Ilmenau als Dissertation vorgelegen. Tag der Einreichung: 3. März 2014 1. Gutachter: Univ.- Prof. Dr.-Ing. habil. Klaus Zimmermann (Technische Universität Ilmenau) 2. Gutachter: Prof. Dr.-Ing. habil. Emil Kolev (Fachhochschule Schmalkalden) 3. Gutachter: Prof. Dr. Nikolai Bolotnik (Russian Academy of Sciences, Moscow) Tag der Verteidigung: 20. Juni 2014 „Gedruckt mit Unterstützung des Deutschen Akademischen Austauschdienstes“ Technische Universität Ilmenau/Universitätsbibliothek Universitätsverlag Ilmenau Postfach 10 05 65 98684 Ilmenau www.tu-ilmenau.de/universitaetsverlag Herstellung und Auslieferung Verlagshaus Monsenstein und Vannerdat OHG Am Hawerkamp 31 48155 Münster www.mv-verlag.de ISBN 978-3-86360-103-4 (Druckausgabe) URN urn:nbn:de:gbv:ilm1-2014000123 Titelfoto: Veit Henkel | Fakultät für Maschinenbau, TU Ilmenau Abstract This thesis discusses the mathematical modeling of wheeled locomotion systems. More precisely, the kinematics and the dynamics of a Mecanum wheeled vehicle are studied. The dynamic and kinematic models are introduced for the practical and industrial applications. Also, the motion behavior of the handicapped is captured and analyzed during the propulsion of the wheelchair for different operation conditions. The motivations of this study are introduced in the beginning of the thesis. The state of the art, in the field of Mecanum wheels based vehicles, is presented. A general overview for nowadays aspects in the field of locomotion systems for handicapped and their advantages has been discussed. Chapter 2 discusses the mathematical basics, which are deployed in this thesis. Different theories and principles of the kinematics and dynamics are summarized and presented. The transformation matrices, types of the kinematic constraints, the dynamics of rigid multibody systems with a special focus on the LAGRANGE’s equation of the second kind are presented. The locomotion systems are analyzed analytically from the kinematic and dynamic point of views. It focuses mainly on two important designs, which are commonly used in our everyday life. The first is a model for the two wheels locomotion system such as wheelchairs and similar systems. The second type is a model for the four wheeled Mecanum vehicle. A detailed derivation for the kinematic and dynamic models for both locomotion systems is introduced. Two different ways have been used to model the four wheels Mecanum vehicle. The first method is called the suggested method and the second is the approximation method. In the suggested method, the LAGRANGE’s equation of the second kind is used to introduce a precise dynamic model, which can model all kinds of motion trajectories for the discussed system. The approximation method is estimated using the pseudo inverse matrix and can be used for simulating the standard motion trajectories. The simulation results for different motion trajectories are presented in chapter 4. The second order differential equations of the dynamic models, for both the suggested and approximation models, are numerically integrated and the resulted motion trajectories for predefined driving v moments are presented. A 3D Virtual model for the four wheeled Mecanum vehicle is programmed using MATLAB®, SIMULINK® and the VIRTUAL REALITY TOOLBOX®, that to show the combination between the translational and rotational motion in 3D environment. Two different experimental platforms were constructed for realizing the special-purpose vehicle for the handicapped. The platforms move typical to the simulation results. Finally, the characteristics of the wheelchair propulsion for two test volunteers have been discussed. The motion of the human body has been captured using special experimental setup and has implemented and analyzed using ALASKA® and ERGO TOOL® software. vi Kurzfassung Die Arbeit diskutiert die mathematische Modellbildung von ausgewählten Fortbewegungssystemen mit Rädern. Die Kinematik und Dynamik eines radgetriebenen Fahrzeuges mit Mecanum-Rädern wird beschrieben. Die dynamischen und kinematischen Modelle sind die Voraussetzung für Simulationsrechnungen und gleichzeitig für die praktische Anwendung beim Betrieb der Systeme. Außerdem wird das Bewegungsverhalten von Behinderten während der Fahrt im Rollstuhl für verschiedene Umgebungsbedingungen analysiert. Nach der Darlegung der Motivation der Arbeit wird eine Analyse des Standes der Technik auf dem Gebiet der Fahrzeuge mit Mecanum-Rädern vorgestellt. Eine Übersicht über aktuelle Aspekte der Fortbewegungssysteme für Behinderte und ihre Vor- und Nachteile ist ein weiterer Gegenstand der Arbeit. Im Kapitel 2 sind die mathematischen Grundlagen, die in dieser Arbeit verwendet werden, zusammengefasst. Es handelt sich um die Kinematik der starren Körper und ausgewählte Prinzipien und Gleichungen der analytischen Mechanik. Die Transformationsmatrizen für ebene Drehungen, die Arten der kinematischen Zwangsbedingungen, die Dynamik der starren Körper mit einem speziellen Fokus auf die LAGRANGE Gleichung 2. Art mit Multiplikatoren werden vorgestellt. Die Fortbewegungssysteme sind vor allem mit analytischen Methoden in der Kinematik und Dynamik beschrieben worden. Der Fokus liegt auf 2 Grundmodellen, die auch aktuell technisch genutzt werden. Das erste Modell gilt für zweirädrige Bewegungssysteme, wie zum Beispiel für einen Rollstuhl. Das zweite Modell wurde für ein vierrädriges Fahrzeug mit Mecanum-Rädern entwickelt. Detaillierte Herleitungen für die kinematischen und dynamischen Modelle sind für beide Fortbewegungssysteme dargestellt. Für die Dynamik des Fahrzeuges mit Mecanum-Rädern wird eine exakte Methode, basierend auf den Grundlagen der nichtholonomen Mechanik mit einer zweiten, häufig in der Literatur angeführten, Näherungsmethode verglichen. Aus der nichtholonomen Mechanik werden die LAGRANGE Gleichungen mit Multiplikatoren als effizientes Verfahren eingesetzt, um ein exaktes Modell zu generieren. Diese Modellgleichungen können alle möglichen Bewegungsbahnen des Fahrzeuges mit vier Mecanum-Rädern erfassen. Das Approximationsverfahren aus der Literatur nutzt eine Pseudoinverse Matrix und kann nur ausgewählte Standardtrajektorien abbilden. Simulationsergebnisse, basierend auf der numerischen Integration der Dynamikgleichungen aus beiden Verfahren werden in Kapitel 4 vorgestellt. vii Die resultierenden Bewegungsbahnen sind für vorgegebene Antriebsmomente dargestellt. Ein virtuelles 3D-Modell des vierrädriges Mecanum-Fahrzeuges ist mit Hilfe von MATLAB®, SIMULINK® und VIRTUAL REALITY TOOLBOX® erstellt worden. Ein Vorteil der 3D- Umgebung ist die anschauliche Darstellung komplexer Bewegungsbahnen bei kombinierten Translations- und Rotationsbewegungen des Systems. Zwei Experimentalfahrzeuge, eines mit klassischer Vierradstruktur inklusive Vorderachslenkung und ein weiteres mit vier omnidirektionalen Rädern vom Typ Mecanum, wurden aufgebaut. Sie dienen als Demonstratoren eines möglichen Plattformkonzeptes für Behindertenfahrzeuge. In der Arbeit werden die aus Simulationsrechnungen gewonnenen Trajektorien mit den tatsächlichen Bahnen des Prototyps verglichen. In einem abschließenden Kapitel wird für ausgewählte Szenarien mittels Motion Capturing Verfahren die Mensch-Maschine- Interaktion am Beispiel von Rollstuhlfahrern untersucht. Die Bewegung des menschlichen Körpers und des Rollstuhls wurde in ihren kinematischen Daten erfasst und mit den Werkzeugen ALASKA-DYNAMICUS® und ERGO TOOL® analysiert. viii Acknowledgment First, I would like to thank my direct supervisor, Univ.-Prof. Dr.-Ing. habil. Klaus Zimmermann (Head of Department of Technical Mechanics, Technische Universität Ilmenau, Faculty of Mechanical Engineering). He was generous by his effort and time and showed real willingness to assist me socially and scientifically. He arranged the suitable environment for enhancing the productivity and increasing the motivation for the work. His advices were the guide and the base for all what I achieved in this thesis. I am thankful for his contributions in issuing this thesis. Dr. rer. nat. Igor Zeidis, I am astonishing from his mathematical capabilities and thankful for his efforts. He helped me in the estimation and reviewing of the big number of equations of this work. I have to thank also Dipl.-Ing. Felix Becker for his help finding the correct words in the field of biomechanics in chapter 5. I want to thank all my other colleagues in the Department of Technical Mechanics for the support, fruitful discussions and the friendly spirit: Dr.-Ing. Bernd Fiedler, Dr.-Ing. Erik Gerlach, PD Dr.- Ing. habil. Dipl.-Math. Carsten Behn, Dr.-Ing. Valter Böhm, Dipl.-Ing. Isabel Husung, Dr.-Ing. Jana Popp, M.Sc. Tobias Kaufhold, M.Sc. Christoph Will. I am grateful to , PD Dr.-Ing. habil. A. Möckel (TU Ilmenau, Faculty of Electrical Engineering and Information Technology), Dipl.-Ing (FH) Tobias Kästner (“Mr. K”) and Dipl.-Ing. S. Oberthür
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