The Master thesis is focused on the influence of procedural parameters on the properties of heterogeneous weld in laser welding. The literature review section offers an overview of the industrial application of the laser welding technology as well as it explains the issue of heterogeneous weld creation. The experimental part of the thesis aims to describe how six carbon steel samples have been welded together with ferritic stainless steel by usage of several different beam oscillation configurations. Tested samples have been used to create trial ensembles that were subjected for a tension testing, Vickers hardness testing, metallographic testing and corrosive resistant testing. As a result of the experiment, there is a suggestion of the study that could be used for an industrial using of a combination of these materials.

This thesis deals with the topic of procedural parameters influence on the properties of welded joint in zinc-coated deep-drawing steels in laser welding with wobbling. First part of the thesis serves as an overview of laser welding technology, welding of steel with protective zinc layer and weld quality testing. Second part is dedicated to a proposal, process flow and evaluation of an experiment. Seven trial lap welding joints of DC04+ZE steel have been welded using different welding parameters. Specimens from these trial welds were used for metallurgical testing by macro-etch examination and for tensile strength break testing to get mechanical properties of welded joints.

O estudo de agregados anfifílicos é de extrema importância devido à sua mimetização de membranas celulares, que são essenciais para a vida da célula. Sabe-se que os fosfolipídios não possuem estruturas moleculares bem definidas nas membranas, porém exercem um papel essencial na manutenção da sua integridade. Fosfolipídios zwitteriônicos são um dos principais componentes estruturais das membranas celulares, e um modelo simplificado destas membranas são as bicamadas que estes fosfolipídios podem formar em meio aquoso. A principal característica destas bicamadas lipídicas é a auto-organização dos lipídios, fazendo-se necessário o estudo de processos naturais e espontâneos, como suas propriedades estruturais e dinâmicas. A espectroscopia de fluorescência tem sido utilizada no estudo de diversos processos e sistemas de interesse biológico, principalmente por medidas de anisotropia de fluorescência, que fornece informações sobre a dinâmica rotacional das sondas fluorescentes inseridas nos sistemas de interesse, refletindo efeitos combinados de flexibilidade, fluidez e interações estáticas com moléculas circundantes. Neste trabalho examinamos as propriedades estruturais e dinâmicas de membranas modelo fosfolipídicas formadas de 1,2-dipalmitoil-sn-glicero-3-fosfocolina (DPPC) por técnicas relacionadas à espectroscopia de fluorescência, principalmente por medidas de anisotropia do estado estacionário e resolvida no tempo, das sondas fluorescentes 1,6-diphenil-1,3,5-hexatrieno (DPH), 7-nitrobenz-2-oxa-1,3-diazol-il (NBD) ligado em diferentes regiões das moléculas fosfolipídicas e também da sonda lipofílica 2-amino-N-hexadecil-benzamida (Ahba). As medidas foram realizadas tanto acima como abaixo da temperatura de transição de fase das bicamadas fosfolipídicas de DPPC, na fase gel e líquido-cristalina, devido à diferença da organização lateral das cadeias de hidrocarboneto nestas duas fases. Medidas de espalhamento dinâmico de luz foram realizadas para confirmar a formação das vesículas unilamelares pelo processo de extrusão da suspensão lipídica contendo vesículas multilamelares, e a técnica de calorimetria diferencial de varredura foi empregada para verificar se baixa concentração das sondas fluorescentes nas vesículas afetam seu empacotamento lipídico. Pelos resultados obtidos, constatamos que os comportamentos das três sondas fluorescentes diferem em ambas as fases das bicamadas fosfolipídicas, revelando suas propriedades estruturais e dinâmicas, principalmente pelas diferentes localizações dos fluoróforos. Verificamos que, devido à afinidade pela região hidrofóbica, o movimento do DPH é restrito ao movimento \"wobbling\", limitado pelas cadeias alifáticas. Para o NBD em lipídios marcados, o movimento do análogo fluorescente como um todo depende da localização do fluoróforo e de sua conformação em ambas as fases das bicamadas lipídicas. Devido à localização do grupo fluorescente da sonda Ahba na interface das bicamadas lipídicas, verificamos que seu movimento rotacional aumenta à medida que a bicamada torna-se mais fluida, mostrando uma dependência deste movimento com a microviscosidade destas bicamadas. / The study of amphiphilic aggregates is extremely important due to their cell membrane mimic, which are essential for the life of the cell. It is known that phospholipids do not have molecular structure well defined in membranes, but play an essential role in maintaining of their integrity. Zwitterionic phospholipids are one of the main components of cell membranes, and a simplified model for the membranes are the bilayers they can form in aqueous medium. The main characteristic of lipid bilayers is the self-organization of lipids, making it necessary to study natural and spontaneous process, as their structural and dynamical properties. The fluorescence spectroscopy has been used to study many processes and systems of biological interest, especially by measurement of fluorescence anisotropy, which gives information about the rotational dynamics of the fluorescent probe inserted in the systems of interest, reflecting the combined effects of flexibility, fluidity and static interactions with surrounding molecules. In this work we examined the structural and dynamic properties of phospholipid model membranes formed of 1,2-dipalmitoyl-sn-glycero-3-phosphocoline DPPC by techniques related to fluorescence spectroscopy, mainly by measurements of steady-state and time resolved anisotropy of the probes 1,6-diphenyl-1,3,5-hexatriene (DPH), 7-nitrobenz-2-oxa-1,3-diazol-yl (NBD) attached to different regions of phospholipid molecules and also the lipophilic probe 2-amino-N-hexadecyl-benzamide (Ahba). The measurements were perfomed above and below of the phase transition temperature of the phospholipid bilayers of DPPC, gel and liquid-crystalline phase, due to the difference in the lateral organization of hydrocarbon chains in these two phases. Measures of dynamic light scattering (DLS) was performed to confirm the formation of the unilamellar vesicles by extrusion of lipid suspension containing multilamellar vesicles, and the technique of differential scanning calorimetry (DSC) was used to verify if the low concentration of fluorescent probes in lipid vesicles affect its packing. From the results, we found that the behavior of the three different fluorescent probes differ in both phases of phospholipid bilayers, revealing their structural and dynamic properties, mainly because to specific locations of the fluorophores. We verify that, due to the affinity for the hydrophobic region, the motion of the DPH is restricted to the \"wobbling\" motion, limited by hydrocarbon chains. For the NBD labeled in lipids, the motion of the fluorescent analogues as a whole depends on the location of the fluorophore and on the lipid conformation in both phases of lipid bilayers. Because of the location of the fluorescent group of the probe Ahba in the interface of lipid bilayers, we found that its rotational motion increases as the bilayers becomes more fluid, showing a dependency of the motion with the microviscosity of these bilayers.

O estudo de agregados anfifílicos é de extrema importância devido à sua mimetização de membranas celulares, que são essenciais para a vida da célula. Sabe-se que os fosfolipídios não possuem estruturas moleculares bem definidas nas membranas, porém exercem um papel essencial na manutenção da sua integridade. Fosfolipídios zwitteriônicos são um dos principais componentes estruturais das membranas celulares, e um modelo simplificado destas membranas são as bicamadas que estes fosfolipídios podem formar em meio aquoso. A principal característica destas bicamadas lipídicas é a auto-organização dos lipídios, fazendo-se necessário o estudo de processos naturais e espontâneos, como suas propriedades estruturais e dinâmicas. A espectroscopia de fluorescência tem sido utilizada no estudo de diversos processos e sistemas de interesse biológico, principalmente por medidas de anisotropia de fluorescência, que fornece informações sobre a dinâmica rotacional das sondas fluorescentes inseridas nos sistemas de interesse, refletindo efeitos combinados de flexibilidade, fluidez e interações estáticas com moléculas circundantes. Neste trabalho examinamos as propriedades estruturais e dinâmicas de membranas modelo fosfolipídicas formadas de 1,2-dipalmitoil-sn-glicero-3-fosfocolina (DPPC) por técnicas relacionadas à espectroscopia de fluorescência, principalmente por medidas de anisotropia do estado estacionário e resolvida no tempo, das sondas fluorescentes 1,6-diphenil-1,3,5-hexatrieno (DPH), 7-nitrobenz-2-oxa-1,3-diazol-il (NBD) ligado em diferentes regiões das moléculas fosfolipídicas e também da sonda lipofílica 2-amino-N-hexadecil-benzamida (Ahba). As medidas foram realizadas tanto acima como abaixo da temperatura de transição de fase das bicamadas fosfolipídicas de DPPC, na fase gel e líquido-cristalina, devido à diferença da organização lateral das cadeias de hidrocarboneto nestas duas fases. Medidas de espalhamento dinâmico de luz foram realizadas para confirmar a formação das vesículas unilamelares pelo processo de extrusão da suspensão lipídica contendo vesículas multilamelares, e a técnica de calorimetria diferencial de varredura foi empregada para verificar se baixa concentração das sondas fluorescentes nas vesículas afetam seu empacotamento lipídico. Pelos resultados obtidos, constatamos que os comportamentos das três sondas fluorescentes diferem em ambas as fases das bicamadas fosfolipídicas, revelando suas propriedades estruturais e dinâmicas, principalmente pelas diferentes localizações dos fluoróforos. Verificamos que, devido à afinidade pela região hidrofóbica, o movimento do DPH é restrito ao movimento \"wobbling\", limitado pelas cadeias alifáticas. Para o NBD em lipídios marcados, o movimento do análogo fluorescente como um todo depende da localização do fluoróforo e de sua conformação em ambas as fases das bicamadas lipídicas. Devido à localização do grupo fluorescente da sonda Ahba na interface das bicamadas lipídicas, verificamos que seu movimento rotacional aumenta à medida que a bicamada torna-se mais fluida, mostrando uma dependência deste movimento com a microviscosidade destas bicamadas. / The study of amphiphilic aggregates is extremely important due to their cell membrane mimic, which are essential for the life of the cell. It is known that phospholipids do not have molecular structure well defined in membranes, but play an essential role in maintaining of their integrity. Zwitterionic phospholipids are one of the main components of cell membranes, and a simplified model for the membranes are the bilayers they can form in aqueous medium. The main characteristic of lipid bilayers is the self-organization of lipids, making it necessary to study natural and spontaneous process, as their structural and dynamical properties. The fluorescence spectroscopy has been used to study many processes and systems of biological interest, especially by measurement of fluorescence anisotropy, which gives information about the rotational dynamics of the fluorescent probe inserted in the systems of interest, reflecting the combined effects of flexibility, fluidity and static interactions with surrounding molecules. In this work we examined the structural and dynamic properties of phospholipid model membranes formed of 1,2-dipalmitoyl-sn-glycero-3-phosphocoline DPPC by techniques related to fluorescence spectroscopy, mainly by measurements of steady-state and time resolved anisotropy of the probes 1,6-diphenyl-1,3,5-hexatriene (DPH), 7-nitrobenz-2-oxa-1,3-diazol-yl (NBD) attached to different regions of phospholipid molecules and also the lipophilic probe 2-amino-N-hexadecyl-benzamide (Ahba). The measurements were perfomed above and below of the phase transition temperature of the phospholipid bilayers of DPPC, gel and liquid-crystalline phase, due to the difference in the lateral organization of hydrocarbon chains in these two phases. Measures of dynamic light scattering (DLS) was performed to confirm the formation of the unilamellar vesicles by extrusion of lipid suspension containing multilamellar vesicles, and the technique of differential scanning calorimetry (DSC) was used to verify if the low concentration of fluorescent probes in lipid vesicles affect its packing. From the results, we found that the behavior of the three different fluorescent probes differ in both phases of phospholipid bilayers, revealing their structural and dynamic properties, mainly because to specific locations of the fluorophores. We verify that, due to the affinity for the hydrophobic region, the motion of the DPH is restricted to the \"wobbling\" motion, limited by hydrocarbon chains. For the NBD labeled in lipids, the motion of the fluorescent analogues as a whole depends on the location of the fluorophore and on the lipid conformation in both phases of lipid bilayers. Because of the location of the fluorescent group of the probe Ahba in the interface of lipid bilayers, we found that its rotational motion increases as the bilayers becomes more fluid, showing a dependency of the motion with the microviscosity of these bilayers.

Le mouvement des masses molles est à la fois une source d'erreur en analyse cinématique et une source d'information en analyse de la dynamique articulaire. Leur effet sur la cinématique peut être numériquement minimisé et leur dynamique estimée seulement par la simulation car aucune méthode numérique ne permet de distinguer la cinématique des masses molles de celle de l'os. Le travail présenté dans ce mémoire propose de développer une méthode numérique pour distinguer ces deux cinématiques. Une méthode d'optimisation locale a d'abord été utilisée pour évaluer le mouvement des masses molles et comparée à l'os pour valider celle-ci. Les résultats ont montré une inadaptation de la méthode locale à évaluer quantitativement et analyser le mouvement des masses molles. L'incapacité de cette méthode vient du fait qu'elle ne prend pas en compte l'ensemble des composantes du mouvement des masses molles. Un modèle numérique du membre inférieur a été développé dans la seconde étude pour considérer l'ensemble de ces composantes. Ce modèle assure le calcul de la cinématique articulaire du membre inférieur et estime un plus grand mouvement des masses molles à partir du déplacement total des marqueurs. Ce déplacement de marqueur est plus le fait d'une composante à l'unisson que d'une composante propre du mouvement des masses molles. Cette composante à l'unisson induit un mouvement commun des marqueurs par rapport à l'os. Ce mouvement commun permet ainsi de déduire la cinématique des masses molles autour des axes anatomiques des os modélisés. Cette méthode numérique permet ainsi de distinguer la cinématique de l'os de celle des masses molles offre une perspective d'étudier leur dynamique. / The movement of wobbling mass is the major source of error in kinematic analysis and a source of information in joint kinetic analysis. The effect on joint kinematic can numerically be minimized and their kinetic estimated using numerical model because there is no numerical method able to distinguish the wobbling masses kinematic from bones kinematic. The work presented in this thesis aims to develop a numerical method to distinguish those two kinematics. Firstly, a local optimisation method was used to assess the movement of wobbling mass and was compared to the bone in order to validate this numerical method. Results show maladjustment of the local method to assess quantitavely and analyze the movement of wobbling mass. The inability of this method is caused by the fact it cannot take in account all component of the movement of wobbling mass. A numerical model has been developing in the second part in order to consider all these components. This model insure similar joint kinematics, provides a bigger estimate of the movement of wobbling mass from marker displacements. This marker displacements is more induced by an unison component rather a own component of the movement of wobbling mass. The in unison component induce a common displacement of markers relative to the bones. This common movement allows to infer the kinematic of the wobbling mass in regard to anatomical axes of the modelled bones” This numerical method allows to distinguish the kinematic of bones and the kinematic of wobbling mass, and offers a perspective to investigate their kinetic.

The aim of this work was to carry out an experiment to assess the influence of the individual welding parameters in the laser welding method with the beam wobbling on the made weld, respectively. welds. The material which was welded was ferritic stainless steel with the designation 1.4016, which, like all ferritic steels, is susceptible to coarse grains and the resulting brittleness which leads to degradation of the mechanical properties of the weld. The welds were compared to a sample welded without wobbling an between themselves. Unfortunately, however, the evaluation of the test samples did not bring significant differences from laser welding without wobbling, however some changes are evident, such as grain orientation, weld defects, or uniformity of mechanical properties over the weld length, where wobbling frequency is most important. Further research should focus on limiting the porosity at higher wobbling frequencies in the shape of a circle or ellipse.

In the thesis, the influence of the shape of the beam wobbling geometry and the spot vibration frequency on the properties of the heterogeneous weld of X12Cr13 martensitic stainless steel with carbon steel S355MC in laser oscillation welding is investigated. Macroscopic control was performed on the samples, which were focused on weld size and heat affected areas, weld defects, weld shape and cant / drop face and weld joint root. Subsequent microscopic inspection determined both the weld metal structure and the heat affected area and base material. The last was a Vickers microhardness test. Based on the experiment, it was found that the spot process frequency is an important process parameter.

L’analyse biomécanique du mouvement humain en utilisant des systèmes optoélectroniques et des marqueurs cutanés considère les segments du corps comme des corps rigides. Cependant, le mouvement des tissus mous par rapport à l'os, c’est à dire les muscles et le tissu adipeux, provoque le déplacement des marqueurs. Ce déplacement est le fait de deux composantes, une composante propre correspondant au mouvement aléatoire de chaque marqueur et une composante à l’unisson provoquant le déplacement commun des marqueurs cutanés lié au mouvement des masses sous-jacentes. Si nombre d’études visent à minimiser ces déplacements, des simulations ont montré que le mouvement des masses molles réduit la dynamique articulaire. Cette observation est faite uniquement par la simulation, car il n'existe pas de méthodes capables de dissocier la cinématique des masses molles de celle de l’os. L’objectif principal de cette thèse consiste à développer une méthode numérique capable de distinguer ces deux cinématiques. Le premier objectif était d'évaluer une méthode d'optimisation locale pour estimer le mouvement des masses molles par rapport à l’humérus obtenu avec une tige intra-corticale vissée chez trois sujets. Les résultats montrent que l'optimisation locale sous-estime de 50% le déplacement des marqueurs et qu’elle conduit à un classement de marqueurs différents en fonction de leur déplacement. La limite de cette méthode vient du fait qu'elle ne tient pas compte de l’ensemble des composantes du mouvement des tissus mous, notamment la composante en unisson. Le second objectif était de développer une méthode numérique qui considère toutes les composantes du mouvement des tissus mous. Plus précisément, cette méthode devait fournir une cinématique similaire et une plus grande estimation du déplacement des marqueurs par rapport aux méthodes classiques et dissocier ces composantes. Le membre inférieur est modélisé avec une chaine cinématique de 10 degrés de liberté reconstruite par optimisation globale en utilisant seulement les marqueurs placés sur le pelvis et la face médiale du tibia. L’estimation de la cinématique sans considérer les marqueurs placés sur la cuisse et le mollet permet d'éviter l’influence de leur déplacement sur la reconstruction du modèle cinématique. Cette méthode testée sur 13 sujets lors de sauts a obtenu jusqu’à 2,1 fois plus de déplacement des marqueurs en fonction de la méthode considérée en assurant des cinématiques similaires. Une approche vectorielle a montré que le déplacement des marqueurs est surtout dû à la composante à l’unisson. Une approche matricielle associant l’optimisation locale à la chaine cinématique a montré que les masses molles se déplacent principalement autour de l'axe longitudinal et le long de l'axe antéro-postérieur de l'os. L'originalité de cette thèse est de dissocier numériquement la cinématique os de celle des masses molles et les composantes de ce mouvement. Les méthodes développées dans cette thèse augmentent les connaissances sur le mouvement des masses molles et permettent d’envisager l’étude de leur effet sur la dynamique articulaire. / Biomechanical analysis of human movement using optoelectronic system and skin markers considers body segments as rigid bodies. However the soft tissue motion relative to the bone, including muscles, fat mass, results in relative displacement of markers. This displacement is the results of two components, an own component which corresponds to a random motion of each marker and an in-unison component corresponding to the common movement of skin markers resulting from the movement of the underlying wobbling mass. While most studies aim to minimize these displacements, computer simulation models have shown that the movement of the soft tissue motion relative to the bones reduces the joint kinetics. This observation is only available using computer simulations because there are no methods able to distinguish the kinematics of wobbling mass of the bones kinematics. The main objective of this thesis is to develop a numerical method able to distinguish this different kinematics. The first aim of this thesis was to assess a local optimisation method for estimating the soft tissue motion using intra-cortical pins screwed into the humerus in three subjects. The results show that local optimisation underestimates of 50% the marker displacements. Also it leads to a different marker ranking in terms of displacement. The limit of local optimisation comes from the fact that it does not consider all the components of the soft tissue motion, especially the in-unison component. The second aim of this thesis was to develop a numerical method that accounts for all the component of the soft tissue motion. More specifically, this method should provide similar kinematics and estimate large marker displacement and distinguish the two components to conventional approaches. The lower limb is modeled using a 10 degree of freedom chain model reconstructed using global optimisation and the markers placed only on the pelvis and the medial face of the shank. The original estimate of joint kinematics without considering the markers placed on the thigh and on the calf avoids the influences of these markers displacement on the kinematic model reconstruction. This method was tested on 13 subjects who performed hopping trials and obtained up to 2.1 times of marker displacement depending the method considered ensuring similar joint-kinematics. A vector approach shown that marker displacements is more induce by the in-unison component. A matrix approach combining the local optimisation and the kinematic model shown that the wobbling mass moves around the longitudinal axis and along the antero-posterior axis of the bone. The originality of this thesis is to numerically distinguish the bone kinematics from the wobbling mass kinematics and the two components of the soft tissue motion. The methods developed in this thesis increases the knowledge on soft tissue motion and allow future studies to consider their movement in joint kinetics calculation.

L’analyse biomécanique du mouvement humain en utilisant des systèmes optoélectroniques et des marqueurs cutanés considère les segments du corps comme des corps rigides. Cependant, le mouvement des tissus mous par rapport à l'os, c’est à dire les muscles et le tissu adipeux, provoque le déplacement des marqueurs. Ce déplacement est le fait de deux composantes, une composante propre correspondant au mouvement aléatoire de chaque marqueur et une composante à l’unisson provoquant le déplacement commun des marqueurs cutanés lié au mouvement des masses sous-jacentes. Si nombre d’études visent à minimiser ces déplacements, des simulations ont montré que le mouvement des masses molles réduit la dynamique articulaire. Cette observation est faite uniquement par la simulation, car il n'existe pas de méthodes capables de dissocier la cinématique des masses molles de celle de l’os. L’objectif principal de cette thèse consiste à développer une méthode numérique capable de distinguer ces deux cinématiques. Le premier objectif était d'évaluer une méthode d'optimisation locale pour estimer le mouvement des masses molles par rapport à l’humérus obtenu avec une tige intra-corticale vissée chez trois sujets. Les résultats montrent que l'optimisation locale sous-estime de 50% le déplacement des marqueurs et qu’elle conduit à un classement de marqueurs différents en fonction de leur déplacement. La limite de cette méthode vient du fait qu'elle ne tient pas compte de l’ensemble des composantes du mouvement des tissus mous, notamment la composante en unisson. Le second objectif était de développer une méthode numérique qui considère toutes les composantes du mouvement des tissus mous. Plus précisément, cette méthode devait fournir une cinématique similaire et une plus grande estimation du déplacement des marqueurs par rapport aux méthodes classiques et dissocier ces composantes. Le membre inférieur est modélisé avec une chaine cinématique de 10 degrés de liberté reconstruite par optimisation globale en utilisant seulement les marqueurs placés sur le pelvis et la face médiale du tibia. L’estimation de la cinématique sans considérer les marqueurs placés sur la cuisse et le mollet permet d'éviter l’influence de leur déplacement sur la reconstruction du modèle cinématique. Cette méthode testée sur 13 sujets lors de sauts a obtenu jusqu’à 2,1 fois plus de déplacement des marqueurs en fonction de la méthode considérée en assurant des cinématiques similaires. Une approche vectorielle a montré que le déplacement des marqueurs est surtout dû à la composante à l’unisson. Une approche matricielle associant l’optimisation locale à la chaine cinématique a montré que les masses molles se déplacent principalement autour de l'axe longitudinal et le long de l'axe antéro-postérieur de l'os. L'originalité de cette thèse est de dissocier numériquement la cinématique os de celle des masses molles et les composantes de ce mouvement. Les méthodes développées dans cette thèse augmentent les connaissances sur le mouvement des masses molles et permettent d’envisager l’étude de leur effet sur la dynamique articulaire. / Biomechanical analysis of human movement using optoelectronic system and skin markers considers body segments as rigid bodies. However the soft tissue motion relative to the bone, including muscles, fat mass, results in relative displacement of markers. This displacement is the results of two components, an own component which corresponds to a random motion of each marker and an in-unison component corresponding to the common movement of skin markers resulting from the movement of the underlying wobbling mass. While most studies aim to minimize these displacements, computer simulation models have shown that the movement of the soft tissue motion relative to the bones reduces the joint kinetics. This observation is only available using computer simulations because there are no methods able to distinguish the kinematics of wobbling mass of the bones kinematics. The main objective of this thesis is to develop a numerical method able to distinguish this different kinematics. The first aim of this thesis was to assess a local optimisation method for estimating the soft tissue motion using intra-cortical pins screwed into the humerus in three subjects. The results show that local optimisation underestimates of 50% the marker displacements. Also it leads to a different marker ranking in terms of displacement. The limit of local optimisation comes from the fact that it does not consider all the components of the soft tissue motion, especially the in-unison component. The second aim of this thesis was to develop a numerical method that accounts for all the component of the soft tissue motion. More specifically, this method should provide similar kinematics and estimate large marker displacement and distinguish the two components to conventional approaches. The lower limb is modeled using a 10 degree of freedom chain model reconstructed using global optimisation and the markers placed only on the pelvis and the medial face of the shank. The original estimate of joint kinematics without considering the markers placed on the thigh and on the calf avoids the influences of these markers displacement on the kinematic model reconstruction. This method was tested on 13 subjects who performed hopping trials and obtained up to 2.1 times of marker displacement depending the method considered ensuring similar joint-kinematics. A vector approach shown that marker displacements is more induce by the in-unison component. A matrix approach combining the local optimisation and the kinematic model shown that the wobbling mass moves around the longitudinal axis and along the antero-posterior axis of the bone. The originality of this thesis is to numerically distinguish the bone kinematics from the wobbling mass kinematics and the two components of the soft tissue motion. The methods developed in this thesis increases the knowledge on soft tissue motion and allow future studies to consider their movement in joint kinetics calculation.

With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is experiencing an unprecedented paradigm shift. These aerial platforms are specifically appealing for a variety of applications due to their rapid and flexible deployment, cost-effectiveness, and high chance of forming line-of-sight (LoS) links to the ground nodes. As with any new technology, the benefits of incorporating UAVs in existing cellular networks cannot be characterized without completely exploring the underlying trade space. This requires a detailed system-level analysis of drone cellular networks by taking the unique features of UAVs into account, which is the main objective of this dissertation. We first focus on a static setup and characterize the performance of a three-dimensional (3D) two-hop cellular network in which terrestrial base stations (BSs) coexist with UAVs to serve a set of ground user equipment (UE). In particular, a UE connects either directly to its serving terrestrial BS by an access link or connects first to its serving UAV which is then wirelessly backhauled to a terrestrial BS (joint access and backhaul). We consider realistic antenna radiation patterns for both BSs and UAVs using practical models developed by the third generation partnership project (3GPP). We assume a probabilistic channel model for the air-to-ground transmission, which incorporates both LoS and non-LoS links. Assuming the max-power association policy, we study the performance of the network in both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Using tools from stochastic geometry, we analyze the joint distribution of distance and zenith angle of the closest (and serving) UAV to the origin in a 3D setting. Further, we identify and extensively study key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution. Using these results, we obtain exact mathematical expressions for the coverage probability in both AF and DF relaying protocols. Furthermore, considering the fact that backhaul links could be quite weak because of the downtilted antennas at the BSs, we propose and analyze the addition of a directional uptilted antenna at the BS that is solely used for backhaul purposes. The superiority of having directional antennas with wirelessly backhauled UAVs is further demonstrated via extensive simulations. Second, we turn our attention to a mobile setup and characterize the performance of several canonical mobility models in a drone cellular network in which UAV base stations serve UEs on the ground. In particular, we consider the following four mobility models: (i) straight line (SL), (ii) random stop (RS), (iii) random walk (RW), and (iv) random waypoint (RWP), among which the SL mobility model is inspired by the simulation models used by the 3GPP for the placement and trajectory of UAVs, while the other three are well-known canonical models (or their variants) that offer a useful balance between realism and tractability. Assuming the nearest-neighbor association policy, we consider two service models for the UEs: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). While the serving UAV follows the same mobility model as the other UAVs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. We then present a unified approach to characterize the point process of UAVs for all the mobility and service models. Using this, we provide exact mathematical expressions for the average received rate and the session rate as seen by the typical UE. Further, using tools from the calculus of variations, we concretely demonstrate that the simple SL mobility model provides a lower bound on the performance of other general mobility models (including the ones in which UAVs follow curved trajectories) as long as the movement of each UAV in these models is independent and identically distributed (i.i.d.). Continuing our analysis on mobile setups, we analyze the handover probability in a drone cellular network, where the initial positions of the UAVs serving the ground UEs are modeled by a homogeneous Poisson point process (PPP). Inspired by the mobility model considered in the 3GPP studies, we assume that all the UAVs follow the SL mobility model, i.e., move along straight lines in random directions. We further consider two different scenarios for the UAV speeds: (i) same speed model (SSM), and (ii) different speed model (DSM). Assuming nearest-neighbor association policy, we characterize the handover probability of this network for both mobility scenarios. For the SSM, we compute the exact handover probability by establishing equivalence with a single-tier terrestrial cellular network, in which the BSs are static while the UEs are mobile. We then derive a lower bound for the handover probability in the DSM by characterizing the evolution of the spatial distribution of the UAVs over time. After performing these system-level analyses on UAV networks, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we first study the impact of UAV wobbling on the coherence time of the wireless channel between UAVs and a ground UE, using a Rician multi-path channel model. We consider two different scenarios for the number of UAVs: (i) single UAV scenario (SUS), and (ii) multiple UAV scenario (MUS). For each scenario, we model UAV wobbling by two random processes, i.e., the Wiener and sinusoidal processes, and characterize the channel autocorrelation function (ACF) which is then used to derive the coherence time of the channel. For the MUS, we further show that the UAV-UE channels for different UAVs are uncorrelated from each other. One key observation that is revealed from our analysis is that even for small UAV wobbling, the coherence time of the channel may degrade quickly, which may make it difficult to track the channel and establish a reliable communication link. Finally, we develop an impairments-aware air-to-ground unified channel model that incorporates the effect of both wobbling and hardware impairments, where the former is caused by random physical fluctuations of UAVs, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver, such as phase noise, in-phase/quadrature (I/Q) imbalance, and power amplifier (PA) nonlinearity. The impact of UAV wobbling is modeled by two stochastic processes, i.e., the canonical Wiener process and the more realistic sinusoidal process. On the other hand, the aggregate impact of all hardware impairments is modeled as two multiplicative and additive distortion noise processes, which is a well-accepted model. For the sake of generality, we consider both wide-sense stationary (WSS) and nonstationary processes for the distortion noises. We then rigorously characterize the ACF of the wireless channel, using which we provide a comprehensive analysis of four key channel-related metrics: (i) power delay profile (PDP), (ii) coherence time, (iii) coherence bandwidth, and (iv) power spectral density (PSD) of the distortion-plus-noise process. Furthermore, we evaluate these metrics with reasonable UAV wobbling and hardware impairment models to obtain useful insights. Similar to our observation above, this work again demonstrates that the coherence time severely degrades at high frequencies even for small UAV wobbling, which renders air-to-ground channel estimation very difficult at these frequencies. / Doctor of Philosophy / With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is changing dramatically. Owing to their ease of deployment and high chance of forming direct line-of-sight (LoS) links with the other UAVs and ground users, they are very appealing for numerous wireless applications. As with any new technology, exploring the full extent of the benefits of UAVs requires careful exploration of the underlying trade space. Therefore, in this dissertation, our main focus is on the analysis of such aerial networks, their interplay with the current terrestrial networks, and the unique features of UAVs that make them different from conventional ground nodes. One important aspect of aerial communication systems is their integration into our current cellular networks. Clearly, the addition of these new aerial components has the potential of benefiting both the ground users (such as mobile users watching a concert who need cellular connectivity to share the moments) and the cellular base station (BS). Therefore, careful analysis of these ``aerial-terrestrial" networks is of utmost importance. In the first phase of this dissertation, we perform this analysis by interpreting the network as a combination of one-hop (from the BS to the user) and two-hop (from the BS to the UAV and then from the UAV to the UE) links. Since the locations of BSs, UAVs, and users are irregular in general, we use tools from stochastic geometry to carry out our analysis, which is a field of mathematics that studies random shapes and patterns. Also, because existing terrestrial BSs are primarily designed to serve the ``ground", we propose the addition of a separate set of antennas at the BS site that is solely used to serve the ``air", i.e., to communicate with the UAVs, and demonstrate the benefits of this additional infrastructure in detail. One of our assumptions in the first phase of this dissertation was that the considered network was static, i.e., the UAVs were hovering in the air and the BSs/users were also not moving. In the second phase, on the other hand, we explore the benefits and challenges of a mobile network of UAVs and characterize the performance of several canonical mobility models in a drone cellular network. In particular, one of the models that we studied extensively is the so-called straight line (SL) mobility model, which was inspired by the simulation models used by the third generation partnership project (3GPP) for the placement and trajectory of UAVs. Since the locations of UAVs could be assumed random in general, we use tools from stochastic geometry and present a unified approach to characterize the point process of UAVs, using which we obtained exact mathematical expressions for the average received rate (i.e., throughput) as seen by the users. Continuing our analysis on mobile setups and using the SL mobility model, we also analyze the handover probability in a drone cellular network, which is defined as the event when the serving UAV of a user changes. By establishing equivalence between our aerial setup with a terrestrial cellular network, we compute the exact handover probability in drone cellular networks. In the final phase of this dissertation, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we propose an impairments-aware unified channel model for an air-to-ground wireless communication system and extensively analyze the link between a hovering UAV in the air and a static user on the ground. In particular, we consider two different types of impairments: (i) UAV wobbling, and (ii) hardware impairments, where the former is caused by random physical fluctuations, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver. Using appropriate models for each type of impairment, we rigorously characterize the autocorrelation function (ACF) of the wireless channel, using which we provide a comprehensive analysis of key channel-related metrics, such as coherence time and coherence bandwidth. One key observation that is revealed from our analysis is that even for small UAV wobbling and low hardware impairment levels, the coherence time of the channel may degrade quickly at high frequencies, which could make it difficult to track the channel and establish a reliable communication link at these frequencies.