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O valor de uma grandeza é determinado por um conjunto de operações que caracterizam a medição. O resultado obtido por estas operações é o valor da grandeza, que nunca é o verdadeiro, porque toda medição possui erros de natureza sistemática ou aleatória, que acrescenta uma incerteza ao resultado. Assim, todo resultado de uma medição deve incluir informações sobre a sua incerteza, isto é, sobre o intervalo dentro do qual se estima que esteja o valor verdadeiro. Um consenso internacional sobre o assunto levou à elaboração da ISO-GUM (Guia para a Expressão da Incerteza de Medição), que fornece regras para a obtenção da expressão da incerteza da medição de grandezas físicas. No entanto, quando se trata da incerteza de medição por coordenadas, isto é, a incerteza na localização de um ponto no espaço, determinado através da indicação de uma máquina de medir a três coordenadas (MM3C), o problema é bem mais complexo. Assim, o objetivo deste trabalho é descrever uma metodologia para calcular a incerteza da medição por coordena das. Este cálculo envolve a calibração direta da máquina para a avaliação dos 21 possíveis erros geométricos, a análise destes erros para a determinação das equações que permitem calcular as incertezas de cada erro individualmente, e a análise geométrica da estrutura da máquina para determinar as equações de sintetização Ex, Ey e Ez, nas direções de seus eixos. Para definição da metodologia as equações que descrevem a variância combinada dos erros avaliados na calibração, foram substituídas nas equações que definem a variância do erro volumétrico das componentes Ex, Ey e Ez, dando origem às equações gerais que permitem determinar a incerteza do resultado da medição em uma MM3C. / The value of a magnitude is determined through a group of operations that characterize it. The result obtained by these operations is the value of the magnitude, and this value is never the true one because all measurements undergo errors of systematic or random nature, which increase an uncertainty to its result. Thus, all measurement result should include information about its uncertainty, that is, about the interval of values inside of which is considered that the true value is. An international accord, on that subject, allowed the elaboration of the ISO-GUM (Guide for the Expression of the Uncertainty of Measurement), that supplies rules for obtaining the expression of the measurement uncertainty for calibrations, linear dimensional measurements, among others. However, when the task is to estirnate the uncertainty of coordinate measurements, that is, the uncertainty of a point in the space, determined through the indication of a coordinate measuring machine (CMM), the problem is much more complex. Thus, the objective of this work is the description of a methodology to calculate the uncertainty measurements indication of a three coordinate measuring machine. This involves the direct calibration of the machine for the evaluation of the 21 possible geometric errors, the error analysis for defining the equations that allow to estimate the uncertainties of each error individually and the geometric analysis of the machine structure for determining the error synthetization equations Ex, Ey and Ez. The equations that describe the uncertainty of the geometric error measurements were substituted in the uncertainty equations of Ex, Ey and Ez, creating the general equations that allow to determine the uncertainty of the result of a measurement with a CMM.

Parallel manipulators have been the subject of study of much robotic research during the past three decades. A parallel manipulator typically consists of a moving platform that is connected to a fixed base by at least two kinematic chains in parallel. Parallel manipulators can provide several attractive advantages over their serial counterpart in terms of high stiffness, high accuracy, and low inertia, which enable them to become viable alternatives for wide applications. But parallel manipulators also have some disadvantages, such as complex forward kinematics, small workspace, complicated structures, and a high cost. To overcome the above shortcomings, progress on the development of parallel manipulators with less than 6-DOF has been accelerated. However, most of presented parallel manipulators have coupled motion between the position and orientation of the end-effector. Therefore, the kinematic model is complex and the manipulator is difficult to control. Only recently, research on parallel manipulators with less than six degrees of freedom has been leaning toward the decoupling of the position and orientation of the end-effector, and this has really interested scientists in the area of parallel robotics. Kinematic decoupling for a parallel manipulator is that one motion of the up-platform only corresponds to input of one leg or one group of legs. And the input cannot produce other motions. Nevertheless, to date, the number of real applications of decoupled motion actuated parallel manipulators is still quite limited. This is partially because effective development strategies of such types of closed-loop structures are not so obvious. In addition, it is very difficult to design mechanisms with complete decoupling, but it is possible for fewer DOF parallel manipulators. To realize kinematic decoupling, the parallel manipulators are needed to possess special structures; therefore, investigating a parallel manipulator with decoupling motion remains a challenging task. This thesis deals with lower mobility parallel manipulator with decoupled motions. A novel parallel manipulator is proposed in this thesis. The manipulator consists of a moving platform that is connecting to a fixed base by three legs. Each leg is made of one C (cylinder), one R (revolute) and one U (universal) joints. The mobility of the manipulator and structure of the inactive joint are analyzed. Kinematics of the manipulator including inverse and forward kinematics, velocity equation, kinematic singularities, and stiffness are studied. The workspace of the parallel manipulator is examined. A design optimization is conducted with the prescribed workspace. It has been found that due to the special arrangement of the legs and joints, this parallel manipulator performs three translational degrees of freedom with decoupled motions, and is fully isotropic. This advantage has great potential for machine tools and Coordinate Measuring Machine (CMM). / UOIT

This thesis consists of three chapters. The first chapter focuses on adaptive smoothing splines for fitting functions with varying roughness. In the first part of the first chapter, we study an asymptotically optimal procedure to choose the value of a discretized version of the variable smoothing parameter in adaptive smoothing splines. With the choice given by the multivariate version of the generalized cross validation, the resulting adaptive smoothing spline estimator is shown to be consistent and asymptotically optimal under some general conditions. In the second part, we derive the asymptotically optimal local penalty function, which is subsequently used for the derivation of the locally optimal smoothing spline estimator. In the second chapter, we propose a Lipschitz regularity based statistical model, and apply it to coordinate measuring machine (CMM) data to estimate the form error of a manufactured product and to determine the optimal sampling positions of CMM measurements. Our proposed wavelet-based model takes advantage of the fact that the Lipschitz regularity holds for the CMM data. The third chapter focuses on the classification of functional data which are known to be well separable within a particular interval. We propose an interval based classifier. We first estimate a baseline of each class via convex optimization, and then identify an optimal interval that maximizes the difference among the baselines. Our interval based classifier is constructed based on the identified optimal interval. The derived classifier can be implemented via a low-order-of-complexity algorithm.

O valor de uma grandeza é determinado por um conjunto de operações que caracterizam a medição. O resultado obtido por estas operações é o valor da grandeza, que nunca é o verdadeiro, porque toda medição possui erros de natureza sistemática ou aleatória, que acrescenta uma incerteza ao resultado. Assim, todo resultado de uma medição deve incluir informações sobre a sua incerteza, isto é, sobre o intervalo dentro do qual se estima que esteja o valor verdadeiro. Um consenso internacional sobre o assunto levou à elaboração da ISO-GUM (Guia para a Expressão da Incerteza de Medição), que fornece regras para a obtenção da expressão da incerteza da medição de grandezas físicas. No entanto, quando se trata da incerteza de medição por coordenadas, isto é, a incerteza na localização de um ponto no espaço, determinado através da indicação de uma máquina de medir a três coordenadas (MM3C), o problema é bem mais complexo. Assim, o objetivo deste trabalho é descrever uma metodologia para calcular a incerteza da medição por coordena das. Este cálculo envolve a calibração direta da máquina para a avaliação dos 21 possíveis erros geométricos, a análise destes erros para a determinação das equações que permitem calcular as incertezas de cada erro individualmente, e a análise geométrica da estrutura da máquina para determinar as equações de sintetização Ex, Ey e Ez, nas direções de seus eixos. Para definição da metodologia as equações que descrevem a variância combinada dos erros avaliados na calibração, foram substituídas nas equações que definem a variância do erro volumétrico das componentes Ex, Ey e Ez, dando origem às equações gerais que permitem determinar a incerteza do resultado da medição em uma MM3C. / The value of a magnitude is determined through a group of operations that characterize it. The result obtained by these operations is the value of the magnitude, and this value is never the true one because all measurements undergo errors of systematic or random nature, which increase an uncertainty to its result. Thus, all measurement result should include information about its uncertainty, that is, about the interval of values inside of which is considered that the true value is. An international accord, on that subject, allowed the elaboration of the ISO-GUM (Guide for the Expression of the Uncertainty of Measurement), that supplies rules for obtaining the expression of the measurement uncertainty for calibrations, linear dimensional measurements, among others. However, when the task is to estirnate the uncertainty of coordinate measurements, that is, the uncertainty of a point in the space, determined through the indication of a coordinate measuring machine (CMM), the problem is much more complex. Thus, the objective of this work is the description of a methodology to calculate the uncertainty measurements indication of a three coordinate measuring machine. This involves the direct calibration of the machine for the evaluation of the 21 possible geometric errors, the error analysis for defining the equations that allow to estimate the uncertainties of each error individually and the geometric analysis of the machine structure for determining the error synthetization equations Ex, Ey and Ez. The equations that describe the uncertainty of the geometric error measurements were substituted in the uncertainty equations of Ex, Ey and Ez, creating the general equations that allow to determine the uncertainty of the result of a measurement with a CMM.

Les travaux présentés dans cette thèse ont pour but la maîtrise des méthodes d'étalonnage par multilatération. Ils s'inscrivent dans une collaboration entre le Laboratoire national de métrologie et d'essais (LNE) et le Laboratoire Universitaire de Recherche en Production Automatisée (LURPA). Dans ces travaux, la multilatération est dite séquentielle car réalisée avec un unique Laser Tracer positionné successivement plusieurs points de l'espace. La détermination de ces positions ainsi que des bras-morts de l'interféromètre est le point clef de la méthode. Pour l'évaluation des incertitudes, le raccordement aux étalons est fait via les longueurs interférométriques délivrées par le Laser Tracer. Elles sont associées à des défauts caractéristiques d'une cinématique particulière ou aux coordonnées des points mesurés. Elles sont évaluées au travers de la stratégie de mesure et des performances de chaque composant intervenant lors de la procédure d'étalonnage. Mesurer les coordonnées d'un point cible de l'espace par multilatération implique de connaître les positions des points de vue depuis lesquels le point est visé, ainsi que les longueurs qui le séparent des points de vue qui en pratique sont les centres des Laser Tracer. La méthode que nous proposons permet d'identifier les positions et bras-morts des Laser Tracer qui constituent un repère de mesure qualifié de Système Mesurant de Référence (SMR), puis de réaliser la multilatération. Ensuite, l'extraction de défauts volumiques permet éventuellement d'identifier les défauts cinématiques d'une chaîne de solides particulière associée au volume de mesure. Dans cette optique, nous proposons une procédure type inspirée des travaux du LNE axés sur l'utilisation d'une barre à trous pour identifier les défauts cinématiques d'une MMT à trois axes cartésiens. Cette méthode se démarque des approches actuellement proposées car le SMR est construit indépendamment de l'identification des défauts de l'appareil de mesure. De plus, la procédure d'étalonnage que nous proposons repose sur une investigation axe par axe plutôt que par une optimisation globale du problème d'étalonnage. En nous focalisant sur les machines à mesurer tridimensionnelles (MMT), nous proposons un bilan d'incertitudes qui a inclus des facteurs dont le rôle n'était auparavant pas pris en compte dans la littérature. Ces facteurs sont liés au fait de n'utiliser qu'un seul Laser Tracer pour étalonner la MMT. Nous proposons un module d'évaluation des incertitudes qui permet, grâce à des simulations de Monte Carlo, d'identifier l'influence de chacun de facteurs d'incertitude. La pertinence d'une stratégie d'étalonnage peut donc être évaluée à priori de la mise en œuvre de la procédure. L'outil de simulation proposé s'appuie sur la simulation du comportement de la MMT et de celui du Laser Tracer lors de la mesure. Deux indicateurs d'incertitude sont proposés pour l'étude des incertitudes. L'un est lié à l'exactitude de calcul du SMR construit sur les positions successives du Laser Tracer, l'autre est une image de l'incertitude obtenu sur les profils des défauts cinématiques calculés. Cet outil de simulation a permis de valider l'importance des sources d'incertitudes établies initialement pour l'étalonnage d'une MMT à trois axes cartésiens. L’ensemble de la démarche a été appliqué et validé pour une MMT à 3 axes cartésiens en conditions de laboratoire chez un industriel. Cependant, l’approche proposée découple la construction du SMR de l’identification des défauts cinématiques. Elle peut donc être facilement étendue à des systèmes de mesure 3D variés. Nous montrons donc que la démarche globale peut s’appliquer à des espaces de mesure sans cinématique machine. Il s’agit alors d’identifier les défauts volumiques associés à l’espace de mesure, ainsi que les incertitudes associées à la méthode d’étalonnage mise en œuvre. Afin d’illustrer notre propos, nous traitons le cas d’espaces de travail associés à un système de mesure optique. / This thesis aims at developing calibration procedures and methods for measuring tools such as coordinate measuring machines (CMMs) and stereovision devices. This work is incorporated within the framework of a collaboration between the Laboratoire national de métrologie et d’essais (LNE) and the Automated Production Research Laboratory (LURPA). In the scope of this thesis, multilateration is qualified as sequential because it is carried out by a single tracking interferometer (Laser Tracer) that is placed in different positions during the calibration procedure. In order to assess the calibration uncertainties, the link to the length standards is obtained through the measured lengths provided by the interferometer. Each one of these measured lengths is linked to the kinematic chain parametric errors that cause the volumetric errors of the CMM or directly to the measured points coordinates. They are assessed thanks to the study of both the calibration procedure and the performance of each component that takes part in the calibration procedure.Performing multilateration to obtain the spatial coordinates of a point requires to know both the stand points from which the point is measured and the distances between the stand points and the measured point. Practically, the stand points are the Laser Tracer positions. The proposed method aims at identifying the Laser Tracer’s positions and dead-paths lengths first in order to build a reference measuring frame, then performing multilateration. Then, if the measuring device is a CMM, its kinematic chain parametric errors are identified. For this matter, we propose a specific procedure based on the LNE knowledge on CMM calibration carried out using hole-bars. The originality of the proposed method lies in the fact that the reference measuring frame and the measuring device errors are calculated independently from each other. Plus, when addressing the case of a CMM calibration, the kinematic chain parametric errors are extracted one by one when a global optimization algorithm is usually performed nowadays.We focus on the case of CMMs calibration and we propose a precise analysis of all the sources of errors. It includes factors which influence was not studied before. They appear to result from the fact that a single tracking interferometer is used to calibrate the CMM. A simulation module based on a Monte Carlo approach has been developed. It enables the study of the influence of each source of errors independently from the other ones. Hence, the relevance of a measuring strategy can be assessed beforehand. This module simulates the behaviour of both the CMM and the Laser Tracer to evaluate uncertainties. We propose two indicators to observe the relative influence of each uncertainty factor. The first one is linked to the reference frame that is built on the successive positions of the Laser Tracer. The second one represents the global uncertainty one the kinematic chain parametric errors. This uncertainty assessment module has been successfully used to highlight the importance of sources of errors which role used to not be studied.The calibration procedure and uncertainty assessment module we propose have been successfully applied to a 3-axis cartesian CMM in laboratory conditions. Plus, since the reference measuring frame and the kinematic chain parametric errors identification are performed separately, the method we propose can be applied to other measuring devices. We especially explain how to apply it in the case of a measuring device based on stereovision.

<p> Ink-jet printing onto flat paper is a widely established process. In this thesis, we make extensions to printing on target surfaces such as metals and glass, using a 5-axis orientable head. Original artwork is created using CAD, and is sampled to create the ink jet point cloud. The target surface location is registered using a standard Coordinate Measuring Machine (CMM) 5-axis touch trigger probe. The probe is then replaced with the ink jet head and the printing process is carried out. Demonstration of the system is illustrated using flat metal and glass samples, as well as rapid prototyped 3-D plastic shapes.</p> / Thesis / Master of Applied Science (MASc)

Com o crescimento industrial e tecnológico nas últimas décadas, as indústrias passaram a oferecer produtos customizados, ou seja, desenvolvidos com tolerâncias geométricas cada vez mais apertadas e geometrias cada vez mais complexas. Com isso, as máquinas de medir por coordenadas (MMC) vêm tornando-se instrumentos essenciais no ambiente industrial. A MMC é extremamente versátil o que possibilita a medição das mais diversas características geométricas e dimensionais. Padrões para calibração de MMC foram sugeridos e colocados em uso através dos anos, com a finalidade de utilizá-los em testes de aceitação e verificação periódica dos erros e da incerteza de medição de MMC. Novos artefatos para a calibração indireta de MMC visam melhorar os procedimentos de calibração para uso em sistemas de compensação de erros. Diante do exposto acima, este trabalho tem como objetivo desenvolver um procedimento de calibração indireta de MMC com o esquadro de esferas aliado a um modelo reduzido de sintetização de erros (MRSE) para uso em um Sistema de Compensação de Erros. O procedimento possibilita maior rapidez na obtenção dos valores e comportamentos dos erros quando comparado com outros procedimentos de calibração indireta. O procedimento proposto tem como vantagem o uso de um esquadro de esferas para medir todos os termos das equações das componentes do erro volumétrico, nas direções X, Y e Z de uma MMC. / With the technological and industrial growth in recent decades, the industries began to offer customized products, that is, products that fit individual specifications and often present increasingly tight tolerances and increasingly complex geometries. Therefore, the coordinate measuring machines (CMMs) have become an essential tool in the industrial environment. The CMM is very versatile since it allows the measurement of several geometric and dimensional features at once. Different standards for the calibration of CMMs were suggested and put into use through the years. This type of standard is traditionally used in acceptance tests and periodic verifications of the CMMs and in the evaluation of measurement uncertainties. New artifacts for indirect calibration of CMMs are proposed to allow the development of better procedures of error evaluation and compensation. Considering the above, this work aims to develop a procedure for indirect calibration of CMMs using a mechanical ball square combined with a reduced model of synthesis of Errors (MRSE). As a result, a compensation system for CMM errors is obtained. The procedure allows a faster evaluation of the values and behaviors of errors when compared with other indirect calibration procedures. Additionally, the proposed procedure has the advantage of using a single artifact to measure all the components of the volumetric error in the directions X, Y and Z of a CMM.

Com o crescimento industrial e tecnológico nas últimas décadas, as indústrias passaram a oferecer produtos customizados, ou seja, desenvolvidos com tolerâncias geométricas cada vez mais apertadas e geometrias cada vez mais complexas. Com isso, as máquinas de medir por coordenadas (MMC) vêm tornando-se instrumentos essenciais no ambiente industrial. A MMC é extremamente versátil o que possibilita a medição das mais diversas características geométricas e dimensionais. Padrões para calibração de MMC foram sugeridos e colocados em uso através dos anos, com a finalidade de utilizá-los em testes de aceitação e verificação periódica dos erros e da incerteza de medição de MMC. Novos artefatos para a calibração indireta de MMC visam melhorar os procedimentos de calibração para uso em sistemas de compensação de erros. Diante do exposto acima, este trabalho tem como objetivo desenvolver um procedimento de calibração indireta de MMC com o esquadro de esferas aliado a um modelo reduzido de sintetização de erros (MRSE) para uso em um Sistema de Compensação de Erros. O procedimento possibilita maior rapidez na obtenção dos valores e comportamentos dos erros quando comparado com outros procedimentos de calibração indireta. O procedimento proposto tem como vantagem o uso de um esquadro de esferas para medir todos os termos das equações das componentes do erro volumétrico, nas direções X, Y e Z de uma MMC. / With the technological and industrial growth in recent decades, the industries began to offer customized products, that is, products that fit individual specifications and often present increasingly tight tolerances and increasingly complex geometries. Therefore, the coordinate measuring machines (CMMs) have become an essential tool in the industrial environment. The CMM is very versatile since it allows the measurement of several geometric and dimensional features at once. Different standards for the calibration of CMMs were suggested and put into use through the years. This type of standard is traditionally used in acceptance tests and periodic verifications of the CMMs and in the evaluation of measurement uncertainties. New artifacts for indirect calibration of CMMs are proposed to allow the development of better procedures of error evaluation and compensation. Considering the above, this work aims to develop a procedure for indirect calibration of CMMs using a mechanical ball square combined with a reduced model of synthesis of Errors (MRSE). As a result, a compensation system for CMM errors is obtained. The procedure allows a faster evaluation of the values and behaviors of errors when compared with other indirect calibration procedures. Additionally, the proposed procedure has the advantage of using a single artifact to measure all the components of the volumetric error in the directions X, Y and Z of a CMM.