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This diploma dissertation deals with straightness and flatness measurement and data evaluation. For all measurements laserinterferometer Renishaw has been used. The main purpose of this diploma work is to get values of straightness on the travel of microscope, decrypt computing methods leading to graphs of straightness, re-count it by ČSN standards and compare both sets of graphs. Flatness measurement is performed on a desk before and after lapping and these results are compared.

The effect of initial out-of-straightness of steel beams with wide flange cross-sections on their elastic lateral torsional buckling strength is investigated analytically and numerically. A variational principle is first developed and then used to obtain the governing equilibrium conditions and associated boundary conditions for a beam with general patterns of initial out-of-straightness and initial angles of twist. The principle is then used to develop a finite element formulation to characterize the lateral torsional response of beams with initial out-of-straightness under general transverse loading. The validity of the finite element formulation is verified through comparison against results from models based thin-walled beam finite element and shell element models available in ABAQUS. Since the load lateral displacement responses do not exhibit a distinct point of loss of stability, two design criteria are proposed for the characterization of the failure. The first criterion is based on a threshold value for additional lateral displacement and the second criterial is based on a threshold value for the normal stresses. Both criteria are applied in conjunction with the analytical solution and finite element formulation in order to determine a moment resistance based on lateral torsional buckling that incorporates the effect of initial out-of-straightness. The moment capacity based on the displacement-based criterion is shown to solely depend on the ratio between the initial out-of-straightness component associated with the first buckling mode and the additional displacement threshold value specified. To the contrary, moment capacity based on the stress criterion, was found to depend upon the initial out-of-straightness magnitude, the normal stress threshold value and the geometry of the cross-section. The effects of the above parameters on the predicted moment capacity were investigated for beams with common sections in a systematic parametric study. Possible means of modifying the present provisions of CAN-CSA S16 relating to elastic lateral torsional buckling to incorporate the effect of initial out-of-straightness effects are discussed and illustrated through examples. The load-deformation plots for beams with initial out-of-straightens as predicted by the formulations developed in the present study are then used to extend the Southwell plot technique, originally developed for buckling of column with initial out-of-straightness, to the lateral torsional buckling of beams with initial out-of-straightness. The study shows that the plot, either experimentally or analytically obtained, of the applied load versus lateral displacement, at any point or angle of twist at any section, for a beam with initial out-of-straightness case can predict (a) the elastic critical moment of an analogous initially straight beam, and (b) the first buckling mode contribution to the initial out-of-straightness.

Les produits longs se distinguent par une dimension, généralement la longueur plus importante que la hauteur et la largeur, à titre d'exemple les rails de chemin de fer. Ces produits sont obtenus par déformation plastique à chaud puis refroidissement. Au cours du processus de fabrication, l'hétérogénéité du refroidissement et de la déformation plastique induisent un défaut géométrique de rectitude. Pour parachever la rectitude du produit, un redressage à froid est alors nécessaire. Souvent des dresseuses à galets sont utilisées pour corriger la rectitude du centre de produit, cependant, il reste les abouts. Ces derniers sont redressés au moyen d'une presse à partir de l'image de leurs profils obtenus par mesurage optique. La procédure de mesure/redressage est répétée jusqu'à la conformité du produit. Le temps de réalisation est variable, il dépend de l'apprentissage des paramètres clés liés à la géométrie et au matériau du produit à redresser. Compte tenu des exigences de plus en plus sévères sur la rectitude des produits longs d'une part et une volonté d'augmenter la productivité d'autre part, l'objet de ce travail de recherche consiste à optimiser le procédé de redressage des abouts de produits longs. Dans un premier temps, les déformations élastiques générées au cours du mesurage d'un produit long ont été filtrées. Ensuite, les erreurs des moyens de mesure ont été séparées de la mesure du produit au moyen d'une analyse couplée ce qui a permis une meilleure évaluation de la rectitude du produit. Par ailleurs, en se basant sur l'image du profil du produit, une méthodologie de redressage semi-automatique a été mise en place. Cette dernière est essentiellement basée sur une interaction entre la métrologie et la mécanique et représente une contribution à l'automatisation du procédé de redressage des abouts des produits longs. / Long workpieces are characterized by one dimension, usually length is larger than the height and width, for example, railway rails. These products are obtained by hot rolling and then cooling. During manufacturing process, heterogeneity of cooling and plastic deformation induced straightness error. In order to correct this geometrical error, cold straightening process is necessary. Usually, straightening machines are used to correct the straightness of the workpiece center however; the ends' sides were still not straightened. Based on the optical measurement profile, these ends are straightened by mechanical press. The measuring/straightening closed loop is repeated until the straightness of the product is conformed. The process time depends on the knowledge of key parameters related to geometry and material of workpiece. The objective of this research work is to optimize straightening process of the ends of long workpieces. As a first step, the elastic deformation generated during the measurement of long workpiece has been filtered. Then, a coupled analysis of measurement was used to separate error of machine measurement from workpiece measurement, which allowed a better assessment of workpiece straightness profile. Furthermore, based on straightness profile, a semi-automatic straightening methodology has been developed. It is essentially based on an interaction between metrology and mechanics and it is a contribution to the automation of straightening process for ends parts of long workpieces.

For precise measurement of new TeV-scale physics and precision studies of the Higgs Boson, a new lepton collider is required. To enable meaningful analysis, a centre of mass energy of 500GeV and luminosity of 10³⁴cm^-2s^-1 is needed. The planned 31km long International Linear Collider is capable of meeting these targets, requiring a final emittance of 10 micro-radians horizontally and 35nmrad vertically. To achieve these demanding emittance values, the accelerator components in the main linacs must be aligned against an accurately mapped network of reference markers along the entire tunnel. An automated system could map this tunnel network quickly, accurately, safely and repeatedly; the Linear Collider Alignment and Survey (LiCAS) Rapid Tunnel Reference Surveyor (RTRS) is a working prototype of such a system. The LiCAS RTRS is a train of measurement units that accurately locate regularly spaced retro-reflector markers using Frequency Scanning Interferometry (FSI). The unit locations with respect to each other are precisely reconstructed using a Laser Straightness Monitor (LSM) and tilt sensor system, along with a system of internal FSI lines. The design, commissioning, practical usage, calibration, and reconstruction performance of the LSM is addressed in this work. The commissioned RTRS is described and the properties of the LSM components are investigated in detail. A method of finding the position of laser beam spots on the LSM cameras is developed, along with a process of combining individual spot positions into a more robust measurement compatible with the data from other sub-systems. Laser beam propagation along the LSM is modelled and a robust method of reconstructing CCD beam spot position measurements into positions and orientations of the LSM units is described. A method of calibrating LSM units using an external witness system is presented, along with a way of using the overdetermined nature of the LSM to improve calibration constant errors by including data taken from unwitnessed runs. The reconstruction uncertainty, inclusive of both statistical and systematic effects, of the LSM system is found to be of 5.8 microns × 5.3 microns in lateral translations and 27.6 microradians × 34.1 microradians in rotations perpendicular to the beam, with an uncertainty of 51.1 microradians in rotations around the beam coming from a tilt-sensor arrangement.

O desempenho metrológico de uma Máquina de Medir a Três Coordenadas (MM3C) está relacionado com a sua capacidade de medir peças com a precisão requerida ou desejada. No entanto, como todo instrumento de medição, essas máquinas possuem erros que afetam as medições gerando o que se convencionou chamar de erros volumétricos. Tais erros podem ser obtidos através de modelos matemáticos que descrevem como os erros individuais de todos os componentes da MM3C se combinam por todo o volume de trabalho. Atualmente, no modelamento dos erros, adota-se a independência entre os erros individuais, entretanto, se analisada a geometria estrutural da máquina, verifica-se que existe dependência entre os erros de retilineidade e os erros angulares. O objetivo deste trabalho é expressar o erro angular em função do erro de retilineidade, possibilitando assim minimizar o número de calibrações necessárias e, consequentemente, o tempo de máquina parada requerido para o levantamento do seu comportamento metrológico. Para que se pudesse atingir o objetivo proposto, foram levantados os erros de retilineidade e os angulares de uma Máquina de Medir a Três Coordenadas da marca Brown & Sharp do tipo Ponte Móvel. Com esses dados e o conhecimento da geometria da máquina, os erros angulares foram equacionados, calculados e comparados com os obtidos experimentalmente. / The metrological performance of a Three Coordinate Measuring Machines (CMM) is related to the capacity of measuring workpieces with a required precision. As every measurement instrument, these machines undergo the effects of internal and external factors that affect the measurement, generating what has been denominated as volumetric errors. Such errors can be obtained through a mathematical model that simulates how the individual errors of the CMM are combined and propagated to any point within the machine working volume. Usually, the independence among the individual errors is adopted when the machine error model is built. However, if the machine geometry is analyzed, the dependence between the straightness error and the angular error can be noted. The objective of this work is to express the angular error as a function of the straightness error. The formulation proposed in this work to express this correlation minimizes the number of calibrations necessary to evaluate the machine behavior. A Brown & Sharp Moving Bridge Coordinate Measuring Machine was used for the experimental evaluation. With this data set and knowing the machine geometry, a mathematical expression relating straightness and angular error was obtained. The calculated error values were then compared with the errors experimentally measured.

Cette thèse se situe à l'interface entre l'analyse d'images, dont l'objectif est la description automatique du contenu visuel, et la géométrie discrète, qui est l'un des domaines dédiés au traitement des images numériques. Pour être stocké et manipulé sur un ordinateur, un signal observé est régulièrement échantillonné. L'image numérique, qui est le résultat de ce processus d'acquisition, est donc constituée d'un ensemble fini d'éléments distincts. La géométrie discrète se propose d'étudier les propriétés géométriques d'un tel espace dépourvu de continuité. Dans ce cadre, nous avons considéré les régions homogènes et porteuses de sens d'une image, avec l'objectif de représenter leur contour au moyen de modèles géométriques ou de les décrire à l'aide de mesures. L'étendue des applications de ce travail en analyse d'images est vaste, que ce soit au cours du processus de segmentation, ou en vue de la reconnaissance d'un objet. Nous nous sommes concentrés sur trois modèles géométriques discrets définis par la discrétisation de Gauss : la partie convexe ou concave, l'arc de cercle discret et le segment de droite discrète. Nous avons élaboré des algorithmes dynamiques (mise à jour à la volée de la décision et du paramétrage), exacts (calculs en nombres entiers sans erreur d'approximation) et rapides (calculs simplifiés par l'exploitation de propriétés arithmétiques et complexité en temps linéaire) qui détectent ces modèles sur un contour. L'exécution de ces algorithmes le long d'un contour aboutit à des décompositions ou à des polygonalisations réversibles. De plus, nous avons défini des mesures de convexité, linéarité et circularité, qui vérifient un ensemble de propriétés fondamentales : elles sont robustes aux transformations rigides, elles s'appliquent à des parties de contour et leur valeur maximale est atteinte pour le modèle de forme qui sert de comparaison et uniquement sur celui-ci. Ces mesures servent à l'introduction de nouveaux modèles dotés d'un paramètre variant entre 0 et 1. Le paramètre est fixé à 1 quand on est sûr de la position du contour, mais fixé à une valeur inférieure quand le contour est susceptible d'avoir été déplacé par un bruit d'acquisition. Cette approche pragmatique permet de décomposer de manière robuste un contour en segments de droite ou en parties convexes et concaves. / The work presented in this thesis concerns the fields of image analysis and discrete geometry. Image analysis aims at automatically describing the visual content of a digital image and discrete geometry provides tools devoted to digital image processing. A two-dimensional analog signal is regularly sampled in order to be handled on computers. This acquisition process results in a digital image, which is made up of a finite set of discrete elements. The topic of discrete geometry is to study the geometric properties of such kind of discrete spaces. In this work, we consider homogeneous regions of an image having a meaning for a user. The objective is to represent their digital contour by means of geometric patterns and compute measures. The scope of applications is wide in image analysis. For instance, our results would be of great interest for segmentation or object recognition. We focus on three discrete geometric patterns defined by Gauss digitization: the convex or concave part, the digital straight segment and the digital circular arc. We present several algorithms that detect or recognize these patterns on a digital contour. These algorithms are on-line, exact (integer-only computations without any approximation error) and fast (simplified computations thanks to arithmetic properties and linear-time complexity). They provide a way for segmenting a digital contour or for representing a digital contour by a reversible polygon. Moreover, we define a measure of convexity, a measure of straightness and a measure of circularity. These measures fulfil the following important properties: they are robust to rigid transformations, they may be applied on any part of a digital contour, they reach their maximal value for the template with which the data are compared to. From these measures, we introduce new patterns having a parameter that ranges from 0 to 1. The parameter is set to 1 when the localisation of the digital contour is reliable, but is set to a lower value when the digital contour is expected to have been shifted because of some acquisition noise. This measure-based approach provides a way for robustly decomposing a digital contour into convex, concave or straight parts.

O desempenho metrológico de uma Máquina de Medir a Três Coordenadas (MM3C) está relacionado com a sua capacidade de medir peças com a precisão requerida ou desejada. No entanto, como todo instrumento de medição, essas máquinas possuem erros que afetam as medições gerando o que se convencionou chamar de erros volumétricos. Tais erros podem ser obtidos através de modelos matemáticos que descrevem como os erros individuais de todos os componentes da MM3C se combinam por todo o volume de trabalho. Atualmente, no modelamento dos erros, adota-se a independência entre os erros individuais, entretanto, se analisada a geometria estrutural da máquina, verifica-se que existe dependência entre os erros de retilineidade e os erros angulares. O objetivo deste trabalho é expressar o erro angular em função do erro de retilineidade, possibilitando assim minimizar o número de calibrações necessárias e, consequentemente, o tempo de máquina parada requerido para o levantamento do seu comportamento metrológico. Para que se pudesse atingir o objetivo proposto, foram levantados os erros de retilineidade e os angulares de uma Máquina de Medir a Três Coordenadas da marca Brown & Sharp do tipo Ponte Móvel. Com esses dados e o conhecimento da geometria da máquina, os erros angulares foram equacionados, calculados e comparados com os obtidos experimentalmente. / The metrological performance of a Three Coordinate Measuring Machines (CMM) is related to the capacity of measuring workpieces with a required precision. As every measurement instrument, these machines undergo the effects of internal and external factors that affect the measurement, generating what has been denominated as volumetric errors. Such errors can be obtained through a mathematical model that simulates how the individual errors of the CMM are combined and propagated to any point within the machine working volume. Usually, the independence among the individual errors is adopted when the machine error model is built. However, if the machine geometry is analyzed, the dependence between the straightness error and the angular error can be noted. The objective of this work is to express the angular error as a function of the straightness error. The formulation proposed in this work to express this correlation minimizes the number of calibrations necessary to evaluate the machine behavior. A Brown & Sharp Moving Bridge Coordinate Measuring Machine was used for the experimental evaluation. With this data set and knowing the machine geometry, a mathematical expression relating straightness and angular error was obtained. The calculated error values were then compared with the errors experimentally measured.

This diploma thesis deals with assessment of geometric accuracy of machining center MCV 754 QUICK. BlueSYSTEM digital inclinometers from WYLER AG, XL-80 laser interferometer from RENISHAW, Ballbar QC20-W from RENISHAW and LaserTRACER self-guiding laser interferometer from ETALON AG were used to measure accuracy. Error of the X straightness in the direction of the Z axis was assessed. The first part of the paper describes the geometric accuracy of the machine, currently available instruments for measuring geometric accuracy and an explanation of straightness. The second part consists of the design of measurements, experiment, evaluation and comparison of results and recommendations for teaching.

Em indivíduos saudáveis o desempenho motor e os parâmetros cinemáticos e espaçotemporais da tarefa de alcance já estão descritos na literatura. Até o momento nenhum estudo investigou a influência da dor crônica no ombro nessas variáveis durante a tarefa de apontamento com o corpo todo em diferentes demandas, e nem estabeleceram como é o comportamento motor. Por este motivo, o objetivo do presente estudo foi caracterizar o comportamento motor de uma tarefa de apontamento em indivíduos com dor no ombro e avaliar parâmetros de padrão de movimento, desempenho motor e equilíbrio. Trata-se de um estudo transversal realizado no Laboratório de Bioengenharia Elétrica da Escola Politécnica da USP. Participaram do estudo 20 sujeitos, sendo 11 no grupo controle (GC) e 9 no grupo com dor (GD). O experimento consistiu em realizar um alcance em três angulações distintas (menor, igual e maior que 90°) em duas velocidades (normal e rápida). Foram coletados dados de cinemática e plataforma de força. As principais medidas foram (1) índice de retidão (IR); (2) tempo de reação e movimento (3) deslocamentos angulares e lineares (4) COP e COM. Os resultados mostraram que o GD apresentou pior IR, maior tempo de reação e de movimento, os deslocamentos lineares e angulares foram mais estereotipados, os deslocamentos do COM e a velocidade de deslocamento do COP foram menores e as estratégias de equilíbrio foram menos utilizadas, gerando manutenção do controle em bloco. Desta forma, conclui-se que o comportamento motor é alterado no GD e as variáveis de padrão de movimento, desempenho motor e de equilíbrio foram piores na comparação com indivíduos saudáveis / In healthy subjects the motor performance and the kinematic parameters and spatiotemporal parameters of the task of reaching have already been described in the literature. Until now no study has investigated the influence of chronic shoulder pain on these variables during whole body pointing in different demands and did not establish how motor behavior works. For this reason, the aim of the present study was to characterize the motor behavior of a pointing task in individuals with shoulder pain and to evaluate patterns of movement pattern, motor performance and balance. This is a cross-sectional study conducted at the Bioengineering Laboratory of the Polytechnic School of USP. Twenty subjects participated in the study, being 11 in the control group (CG) and 9 in the pain group (PG). The experiment consisted in achieving a range in three distinct angles (smaller, equal and greater than 90 °) in two speeds (normal and fast). Kinematics and force platform data were collected. The main measures were (1) straightness index (RI); (2) reaction time and movement (3) angular and linear displacements (4) COP and COM. The results showed that the GD presented worse IR, longer reaction time and movement, linear and angular displacements were more stereotyped, the COM displacements and the COP displacement velocity were smaller and the equilibrium strategies were less used, generating maintenance of block control. However, we conclude that motor behavior is altered in GD and the variables of movement pattern, motor performance and balance were worse in comparison with healthy individuals