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Application of Multibody Dynamics Techniques to the Analysis of Human Gait

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Application of Multibody Dynamics Techniques to the Analysis of Human Gait PhD Thesis Application of Multibody Dynamics Techniques to the Analysis of Human Gait Rosa Pàmies i Vilà Universitat Politècnica de Catalunya Departament d’Enginyeria Mecànica UNIVERSITAT POLITÈCNICA DE CATALUNYA Biomedical Engineering Doctoral Programme APPLICATION OF MULTIBODY DYNAMICS TECHNIQUES TO THE ANALYSIS OF HUMAN GAIT by Rosa Pàmies Vilà A thesis submitted for the degree of Doctor for the Universitat Politècnica de Catalunya Supervised by Dr. Josep Maria Font Llagunes Department of Mechanical Engineering (DEM) Barcelona, December 2012 A tu, pare. Agraïments Han sigut moltes les persones que m’han ajudat i recolzat perquè aquesta tesi hagi tirat endavant. Per això, m’agradaria especialment donar les gràcies Al director, Dr. Josep Maria Font Llagunes, per haver confiat sempre amb mi, per haver-me esperonat en els moments més difícils i foscos i haver-me ajudat a créixer, donant-me sempre la mà, en el fascinant món científic. Pels reptes que hem compartit i per l’amistat que des del respecte sempre ens quedarà. Als companys del Departament d’Enginyeria Mecànica de l’Escola Tècnica Superior d’Enginyeria Industrial de Barcelona: Daniel, Quim, Lluïsa, Joan, Miquel, Jordi, Salvador, Enrique, Pau, Ana, Joaquim, Tània, Laia, Ayoub, Matteo i Bruno, pel seu recolzament i pels molt bons moments que ens han anat portant aquests quatre anys. Als investigadors del Laboratorio de Ingeniería Mecánica (LIM) de la Coruña: Amelia, Roland, Fran, Alberto, Daniel, Emilio, Javier, Jairo i Miguel, per no fer-me sentir gens estranya a Ferrol. En especial al Dr. Javier Cuadrado, per introduir-me al món de la dinàmica multisòlid i posar-me totes les facilitats per l’estada a Galícia. I un agraïment especial perquè el model biomecànic no hagués estat possible sense les llibreries del Daniel ni el treball que hem compartit amb l’Urbano, qui sempre ha estat disposat a ajudar-me i a respondre qualsevol pregunta que li he fet sobre programació i sobre el funcionament del laboratori. Als companys del Departamento de Ingeniería Mecánica, Energética y de los Materiales de la Universidad de Extremadura, al Javier Alonso i al Francisco Romero, per poder compartir juntament amb els companys del LIM l’aventura de participar en un projecte nacional coordinat entre les tres universitats. Als revisors externs, pels seus comentaris i suggeriments. Finalment, també vull agrair el suport d’aquells que han estat al meu costat: A la mare, per ser-hi sempre; al pare, per fer-me costat de lluny estant; a la Montserrat per posar-se fins i tot a entendre la formulació Lagrangiana i pels seus retocs montserratins; a la meva família, per preguntar-me si ja teníem l’ortesi a punt; als amics que han fet l’esforç d’entendre que la tesis no em deixava temps lliure, i al Cesc, per aguantar les llargues nits al departament sense queixar-se mai i per la il·lusió que sempre ha mostrat en aquesta tesi. I a totes aquelles persones que m’heu encoratjat a seguir endavant donant-me suport durant aquests últims anys: “...Sempre hi ha Algú que em crida fort des de la sorra, és una veu que em parla al cor quan tot s’enfonsa i em diu que tiri mar endins... Torna-ho a intentar!” CTF Acknowledgements There have been many people who have helped me during this enjoyable experience. I would like to give my sincerely thanks to them, to only some of whom it is possible to give particular mention here. First of all, I would like to thank to my PhD advisor, Dr. Josep Maria Font Llagunes for the good advice, support and friendship that has been invaluable on both academic and personal level. He has been very patiently supervising me and always guiding me in the right direction. I have learned a lot from him, without his help this thesis would not have met an end. I would like to acknowledge my colleagues in the Departament d’Enginyeria Mecànica in ETSEIB: Daniel, Quim, Lluïsa, Joan, Miquel, Jordi, Salvador, Enrique, Pau, Ana, Joaquim, Tània, Laia, Ayoub, Matteo and Bruno, for their support and for the great time we have shared these four years. I acknowledge with gratitude the support from the researchers of the Laboratorio de Ingenieria Mecánica (LIM) in La Coruña: Amelia, Roland, Urbano, Fran, Alberto, Daniel, Emilio, Javier, Jairo and Miguel, for offering me an ideal work environment in Ferrol. Special thanks go to Dr. Javier Cuadrado, for introducing me the multibody dynamic’s world and offering all the facilities for my research visiting in Galicia. Very particular thanks go to Daniel, the biomechanical model would not have been possible without his libraries, and to Urbano, I know that I could always ask him for advice and opinions on lab related issues. I would also like to express my gratitude to the colleagues Francisco Javier Alonso and Francisco Romero from the Departamento de Ingeniería Mecánica, Energética y de los Materiales at Universidad de Extremadura. We have shared, also with colleagues of the LIM, the adventure of participating in a spanish national research project. I would like to thank the reviewers for their comments which have been very useful to improve the quality of the thesis. Finally, I owe my heartfelt thanks to my close people. I am very grateful for my mother, her understanding encouraged me to work hard. I specially appreciate knowing that my father is near, I miss him. Special thanks go to my sister Montserrat, for transmiting me her happiness and for trying to understand even the Lagrangian formulation. Thanks to my family who always ask for the state of the orthosis, and also thanks to my friends, who have made the effort to understand that PhD does not let me have so much free time. Last but not least, I want to thank Cesc, his love and support without any complaint or regret have enabled me to complete this PhD project. Contents Abstract ........................................................................................................................................ v Resum ......................................................................................................................................... vii List of Tables .............................................................................................................................. ix List of Figures ............................................................................................................................. xi List of Symbols .......................................................................................................................... xv Acronyms ................................................................................................................................ xxiii 1 Introduction ............................................................................................................................. 1 1.1 Motivation ........................................................................................................................ 1 1.2 Gait Analysis .................................................................................................................... 2 1.3 Scope and Objectives ....................................................................................................... 5 1.4 Thesis contents ................................................................................................................. 6 2 State of the Art ...................................................................................................................... 13 2.1 Biomechanical Models for Gait Analysis ...................................................................... 15 2.2 Inverse Dynamic Analysis ............................................................................................. 18 2.3 Forward Dynamic Analysis ............................................................................................ 20 2.4 Motion Reconstruction and Data Filtering ..................................................................... 22 2.5 Foot-Ground Contact Models ........................................................................................ 24 3 Dynamic Modelling of the Human Body ............................................................................. 27 3.1 Biomechanical Models ................................................................................................... 27 3.1.1 Three-Dimensional Model ................................................................................. 28 3.1.2 Two-Dimensional Model ................................................................................... 30 3.2 Motion Reconstruction ................................................................................................... 31 3.3 Body Segment Parameters ............................................................................................. 34 3.4 Multibody Formulation. Kinematic Analysis ................................................................. 36 3.4.1 Constraint Equations ......................................................................................... 38 3.5 Multibody Formulation. Dynamic Analysis ................................................................... 44 3.5.1 Mass Matrices .................................................................................................... 45 3.5.2 Generalized Force Vectors ................................................................................ 49 3.5.3 Solution of the Equations of Motion ................................................................. 50 3.5.4 Integration of the Equations of Motion ............................................................
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