In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases. / Negli ultimi decenni il lavoro di una parte sempre maggiore di ricercatori che si occupano di robotica si è concentrato su un particolare gruppo di robot appartenenti alla famiglia dei manipolatori paralleli: i robot a cavi. Nonostante i numerosi studi al riguardo, questi robot presentano ancora oggi numerose problematiche del tutto (o in parte) irrisolte. Lo studio della loro cinematica nello specifico, già complesso per i manipolatori paralleli tradizionali, è ulteriormente complicato dalla natura non lineare dei cavi, i quali possono esercitare sforzi di sola trazione. Il lavoro presentato in questa tesi si concentra dunque sullo studio della cinematica dei robot a cavi e sulla messa a punto di tecniche numeriche in grado di affrontare parte delle problematiche ad essa legate. La maggior parte del lavoro è incentrata sullo sviluppo di una procedura per la soluzione del problema geometrico diretto di un generico manipolatore a cavi basata sull'analisi per intervalli. Questa tecnica di analisi numeirica, oltre a consentire una rapida soluzione del problema, permette di garantire i risultati ottenuti in caso di errori di cancellazione e arrotondamento e consente di considerare eventuali incertezze presenti nel modello del problema. Il codice sviluppato è stato testato attraverso un piccolo prototipo di manipolatore a cavi la cui realizzazione, avvenuta durante il percorso di dottrato, è descritta all'interno dell'elaborato unitamente al lavoro collaterale svolto durante la fase di progettazione e simulazione. / Pendant les dernières décennies, le travail d'une partie toujours croissante de chercheurs qui s'occupent de robotique s'est focalisé sur un groupe spécifique de robots qui fait partie de la famille des manipulateurs parallèles: les robots à câbles. Malgré les nombreux études que l'on a consacré à ce sujet, ces robots présentent encore aujourd'hui plusieurs problématiques complètement ou partiellement irrésolues. En particulier l'étude de leur cinématique, qui se révèle déjà complexe pour les manipulateurs parallèles traditionnels, est rendu encore plus compliqué par la nature non linéaire des câbles qui peuvent seulement exercer des efforts de traction. Le travail présenté dans ma thèse concentre donc son attention sur l'étude de la cinématique des robots à câbles et sur la mise au point de techniques numériques capables d'aborder une partie des problématiques liées à cela. La plupart du travail se concentre sur l'élaboration d'un algorithme pour la résolution du problème géométrique direct d'un manipulateur à câbles général qui se fonde sur l'analyse par intervalles. Cette technique d'analyse permet non seulement de résoudre rapidement le problème mais également de garantir les résultats obtenus en cas d'erreur de cancellation et d'arrondi et de prendre en considération les incertitudes éventuellement presentes dans le modèle du problème. Le code développé a été testé grâce à un petit prototype de manipulateur à câbles dont la réalisation, qui a eu lieu pendant le parcours de doctorat, est décrite à l'intérieur du devoir en accord avec la phase de conception du projet et de simulation.

Recently, a prototype of a hand exoskeleton for post-stroke rehabilitation purpose was proposed by the Group of Robotics, Automation and Articular Biomechanics (GRAB) at the Department of Industrial Engineering, University of Bologna. The prototype comprises five planar mechanisms (one per finger) globally actuated by two DC motors. A total of fifteen human-machine connections are needed to fasten the device to the patient hand. The moving link of the thumb mechanism is actuated by a spatial RSSR mechanism whose frame link geometry must be ad hoc regulated every time the device is fitted on the patient hand. With the future goal to build a new version of the hand exoskeleton, in this dissertation three problems arising from this prototype were tackled. The first problem regards the need to lower the number of human-machine connections needed to fasten the exoskeleton to the patient hand. A new finger mechanism that permits to lower the total number of human-machine connections from fifteen to only six was proposed. The second problem regards the synthesis of the RSSR mechanism. A novel synthesis procedure was proposed in order to guarantee the optimal motion and force transmission to the thumb mechanism once the hand exoskeleton is fitted to a new patient, i.e. for different frame link geometries of the RSSR mechanism. The third problem regards the need to approximate the finger phalange motion as a rotation about a revolute axis. In this perspective, two different joint axes identification techniques were proposed. The techniques are based on the Burmester theory (a theory generally used for the synthesis of mechanisms), here used in an original way to identify an axis of rotation. A comparison of this two technique with a more standard technique based on the finite helical axis is reported.

The knee joint plays a central role in human motion for its dual function: providing a large range of motion in flexion/extension and stability in the other degrees of freedom. Computational modeling is a powerful tool to deepen our understanding of the joint mechanics, overcoming the main limitations of experimental investigations, i.e. time, cost and impracticability, and providing valuable insights for prosthetic design, rehabilitation and surgical planning. Within this background, the specific aim of this dissertation is threefold: to develop a sequentially-defined kinetostatic model of the knee, comparing the performance of spherical and anatomical surfaces; to develop a dynamic model of the knee to predict the quadriceps force during the squat activity; to estimate the compressive force that the implanted knee joint needs in order to reproduce natural stability. This dissertation presents novel and efficient procedures to model and evaluate the behavior of the natural and implanted knee under the effect of static and dynamic loading conditions, extending the current knowledge in the field of musculoskeletal computational modeling.

The knee is one of the most complex and studied joint of the musculoskeletal system provided its great importance in locomotion. Therefore, a deep understanding of its behaviour and of the role played by each of the structures composing it is fundamental. Knee joint models are an invaluable tool to understand the behaviour of the knee and their usefulness is proved in many fields such as surgical planning and prosthetic design. A huge amount of models has been proposed in the literature focusing on the kinematic, the kinetostatic and the dynamic behavior of the joint. Models can be based on in vivo or in vitro data. While the kinematic and the kinetostatic models are defined properly on in vitro data, the dynamic ones cannot. This discrepancy leads to a gap, a lack of coherence, between the usually in vitro defined kinematic and kinetostatic models and the study of the active structures of the joint. In order to achieve a comprehensive knee joint description in which the kinematic, kinetostatic and dynamic models coherently stem one from the other, the identification of a procedure that allows to obtaining reliable kinematic and kinetostatic models in vivo is needed. In the present dissertation a procedure is defined that allows for the identification of a subject specific knee joint model in vivo starting from standard clinical data obtained by the use of non invasive techniques such as computed tomography (CT), magnetic resonance imaging (MRI) and fluoroscopy. This procedure leads to an accurate identification of the parameters needed to personalize the 5-5 parallel mechanism and its patello-femoral extension on a single patient in order to accurately reply the knee joint original motion. Furthermore, following the sequential approach to the modelling of the joint, a stiffness model of the knee is specialized on the specific subject's anatomy.

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Machines with moving parts give rise to vibrations and consequently noise. The setting up and the status of each machine yield to a peculiar vibration signature. Therefore, a change in the vibration signature, due to a change in the machine state, can be used to detect incipient defects before they become critical. This is the goal of condition monitoring, in which the informations obtained from a machine signature are used in order to detect faults at an early stage. There are a large number of signal processing techniques that can be used in order to extract interesting information from a measured vibration signal. This study seeks to detect rotating machine defects using a range of techniques including synchronous time averaging, Hilbert transform-based demodulation, continuous wavelet transform, Wigner-Ville distribution and spectral correlation density function. The detection and the diagnostic capability of these techniques are discussed and compared on the basis of experimental results concerning gear tooth faults, i.e. fatigue crack at the tooth root and tooth spalls of different sizes, as well as assembly faults in diesel engine. Moreover, the sensitivity to fault severity is assessed by the application of these signal processing techniques to gear tooth faults of different sizes.

Mathematical models of the knee joint are important tools which have both theoretical and practical applications. They are used by researchers to fully understand the stabilizing role of the components of the joint, by engineers as an aid for prosthetic design, by surgeons during the planning of an operation or during the operation itself, and by orthopedists for diagnosis and rehabilitation purposes. The principal aims of knee models are to reproduce the restraining function of each structure of the joint and to replicate the relative motion of the bones which constitute the joint itself. It is clear that the first point is functional to the second one. However, the standard procedures for the dynamic modelling of the knee tend to be more focused on the second aspect: the motion of the joint is correctly replicated, but the stabilizing role of the articular components is somehow lost. A first contribution of this dissertation is the definition of a novel approach — called sequential approach — for the dynamic modelling of the knee. The procedure makes it possible to develop more and more sophisticated models of the joint by a succession of steps, starting from a first simple model of its passive motion. The fundamental characteristic of the proposed procedure is that the results obtained at each step do not worsen those already obtained at previous steps, thus preserving the restraining function of the knee structures. The models which stem from the first two steps of the sequential approach are then presented. The result of the first step is a model of the passive motion of the knee, comprehensive of the patello-femoral joint. Kinematical and anatomical considerations lead to define a one degree of freedom rigid link mechanism, whose members represent determinate components of the joint. The result of the second step is a stiffness model of the knee. This model is obtained from the first one, by following the rules of the proposed procedure. Both models have been identified from experimental data by means of an optimization procedure. The simulated motions of the models then have been compared to the experimental ones. Both models accurately reproduce the motion of the joint under the corresponding loading conditions. Moreover, the sequential approach makes sure the results obtained at the first step are not worsened at the second step: the stiffness model can also reproduce the passive motion of the knee with the same accuracy than the previous simpler model. The procedure proved to be successful and thus promising for the definition of more complex models which could also involve the effect of muscular forces.

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

This thesis deals with Visual Servoing and its strictly connected disciplines like projective geometry, image processing, robotics and non-linear control. More specifically the work addresses the problem to control a robotic manipulator through one of the largely used Visual Servoing techniques: the Image Based Visual Servoing (IBVS). In Image Based Visual Servoing the robot is driven by on-line performing a feedback control loop that is closed directly in the 2D space of the camera sensor. The work considers the case of a monocular system with the only camera mounted on the robot end effector (eye in hand configuration). Through IBVS the system can be positioned with respect to a 3D fixed target by minimizing the differences between its initial view and its goal view, corresponding respectively to the initial and the goal system configurations: the robot Cartesian Motion is thus generated only by means of visual informations. However, the execution of a positioning control task by IBVS is not straightforward because singularity problems may occur and local minima may be reached where the reached image is very close to the target one but the 3D positioning task is far from being fulfilled: this happens in particular for large camera displacements, when the the initial and the goal target views are noticeably different. To overcame singularity and local minima drawbacks, maintaining the good properties of IBVS robustness with respect to modeling and camera calibration errors, an opportune image path planning can be exploited. This work deals with the problem of generating opportune image plane trajectories for tracked points of the servoing control scheme (a trajectory is made of a path plus a time law). The generated image plane paths must be feasible i.e. they must be compliant with rigid body motion of the camera with respect to the object so as to avoid image jacobian singularities and local minima problems. In addition, the image planned trajectories must generate camera velocity screws which are smooth and within the allowed bounds of the robot. We will show that a scaled 3D motion planning algorithm can be devised in order to generate feasible image plane trajectories. Since the paths in the image are off-line generated it is also possible to tune the planning parameters so as to maintain the target inside the camera field of view even if, in some unfortunate cases, the feature target points would leave the camera images due to 3D robot motions. To test the validity of the proposed approach some both experiments and simulations results have been reported taking also into account the influence of noise in the path planning strategy. The experiments have been realized with a 6DOF anthropomorphic manipulator with a fire-wire camera installed on its end effector: the results demonstrate the good performances and the feasibility of the proposed approach.