This thesis presents two unique micro-motion parallel kinematic manipulators (PKM): a three degrees of freedom (3-DOF) micro-motion manipulator and a 3-DOF micro-motion manipulator with actuation redundancy. The 3-DOF micro-motion manipulator has three linear-motion driving units, and the 3-DOF micro-motion manipulator with redundancy has four of these units. For both designs, the linear motion driving units are identical, and both machines have a passive link in the center of the structure. The purpose of this passive link is to restrain the movement of the manipulator and to improve the stiffness of the structure. As a result, both structures support 3-DOF, including one translation on the Z-axis and two rotations around the X and Y axes. The manipulator with redundancy is designed to prevent singularity and to improve stiffness. In this thesis, the inverse kinematic, Jacobian matrix and stiffness analyses have been conducted, followed by the design optimization for structures. Finally, the FEA (Finite Element Analysis) and dynamic analysis have also been performed. There are many practical applications for micro-motion parallel manipulators. The typical applications include micro-machine assembly, biological cell operation, and microsurgery . / UOIT

In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry. All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square case. Two applications are immediate: between-step updating of the approximate Jacobian of f(X,t) in a non-autonomous ODE system, and solving nonlinear systems of equations which depend on a parameter, such as occur in continuation methods. Both of these cases require extending the present updates to include the nx(n+l) Jacobian matrix, which is the issue we address here. Our approach is to stay with the least change secant formulation. Computational results for these new updates are also presented to illustrate their convergence behavior.

No description available.

In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

Voltage stability is a challenging problem in the design and operation of terrestrial and shipboard power systems. DC links can be integrated in the AC systems to increase the transmission capacity or to enhance the distribution performance. However, DC links introduce voltage stability issues related to the reactive power shortage due to power converters. Multi-infeed DC systems make this existing phenomenon more complicated. In addition, shipboard power systems have unique characteristics, and some concepts and methodologies developed for terrestrial power systems need to be investigated and modified before they are extended for shipboard power systems. One goal of this work was to develop a systematic method for voltage stability assessment of hybrid AC/DC systems, independent of system configuration. The static and dynamic approaches have been used as complementary methods to address different aspects in voltage stability. The other goal was to develop or to apply voltage stability indicators for voltage stability assessment. Two classical indicators (the minimum eigenvalue and loading margin) and an improvement (the 2nd order performance indicator) have been jointly used for the prediction of voltage stability, providing information on the system state and proximity to and mechanism of instability. The eliminated variable method has been introduced to calculate the partial derivatives of AC/DC systems for modal analysis. The previously mentioned methodologies and the associated indicators have been implemented for the application of integrated shipboard power system including DC zonal arrangement. The procedure of voltage stability assessment has been performed for three test systems, the WSCC 3-machine 9-bus system, the benchmark integrated shipboard power system, and the modified I RTS-96. The static simulation results illustrate the critical location and the contributing factors to the voltage instability, and screen the critical contingencies for dynamic simulation. The results obtained from various static methods have been compared. The dynamic simulation results demonstrate the response of dynamic characteristics of system components, and benchmark the static simulation results.

This work focuses on efficient modelling and adaptive control of friction damping in bladed disks. To efficiently simulate the friction contact, a full-3D time-discrete contact model is reformulated and an analytical expression for the Jacobian matrix is derived that reduces the computation time drastically with respect to the classical finite difference method. The developed numerical solver is applied on bladed disks with shroud contact and the advantage of full-3D contact model compared to a quasi-3D contact model is presented. The developed numerical solver is also applied on bladed disks with strip damper and multiple friction contacts and obtained results are discussed. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different nodal diameters of the bladed disk are systematically presented. The main parameters that influence the effectiveness of friction damping in bladed disks are engine excitation order,  contact stiffnesses,  friction coefficient, relative motion at the friction interface and the normal contact load. Due to variation in these parameters during operation, the obtained friction damping in practice may differ from the optimum value. Therefore, to control the normal load adaptively that will lead to an optimum damping in the system despite these variations, use of magnetostrictive actuator is proposed. The magnetostrictive material that develops an internal strain under the influence of an external magnetic field is employed to increase and decrease the normal contact load. A linearized model of the magnetostrictive actuator is used to characterize the magnetoelastic behavior of the actuator.  A nonlinear static contact analysis of the bladed disk reveals that a change of normal load more than 700 N can be achieved using a reasonable size of the actuator. This will give a very good control on friction damping once applied in practice. / <p>QC 20170310</p> / TurboPower

This study presents Computer-Aided Fixture Design Verification (CAFDV) - the methods and implementations to define, measure and optimize the quality of fixture designs. CAFDV verifies a fixture for its locating performance, machining surface accuracy, stability, and surface accessibility. CAFDV also optimizes a fixture for its locator layout design, initial clamping forces, and tolerance specification. The demand for CAFDV came from both fixture design engineers and today's supply chain managers. They need such a tool to inform them the quality of a fixture design, and to find potential problems before it is actually manufactured. For supply chain managers, they will also be able to quantitatively measure and control the product quality from vendors, with even little fixture design knowledge. CAFDV uses two models - one geometric and one kinetic - to represent, verify and optimize fixture designs. The geometric model uses the Jacobian Matrix to establish the relationship between workpiece-fixture displacements, and the kinetic model uses the Fixture Stiffness Matrix to link external forces with fixture deformation and workpiece displacement. Computer software for CAFDV has also been developed and integrated with CAD package I-DEAS TM. CAD integration and a friendly graphic user interface allows the user to have easy interactions with 3D models and visual feedback from analysis results.

This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the weighted minimum separator and natural order separator methods, to exploit the structure of the computational graph of the nonlinear system.This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments.

[pt] A identificação algorítmica de matrizes de Jacobi a partir de variáveis espectrais é um tema tradicional de análise numérica. Uma nova representação, as coordenadas bidiagonais, naturalmente exigiu que fosse considerado um novo algoritmo. O algoritmo é apresentado e confrontado com as técnicas habituais. / [en] Algorithms relating Jacobi matrices and spectral variables are standard objects in numerical analysis. The recent discovery of bidiagonal coordinates led to the search of an appropriate algorithm for these new variables. The new algorithm is presented and compared with previous techniques.

L’alignement d’images paramétrique a de nombreuses applications pour la réalité augmentée, la compression vidéo ou encore le suivi d’objets. Dans cette thèse, nous nous intéressons notamment aux techniques de recalage d’images (template matching) reposant sur l’optimisation locale d’une fonctionnelle d’erreur. Ces approches ont conduit ces dernières années à de nombreux algorithmes efficaces pour le suivi d’objets. Cependant, les performances de ces algorithmes ont été peu étudiées lorsque les images sont dégradées par un bruit important comme c’est le cas, par exemple, pour des captures réalisées dans des conditions de faible luminosité. Dans cette thèse, nous proposons un nouveau formalisme, appelé formalisme bidirectionnel, qui unifie plusieurs approches de l’état de l’art. Ce formalisme est utilisé dans un premier temps pour porter un éclairage nouveau sur un grand nombre d’approches de la littérature et en particulier sur l’algorithme ESM (Efficient Second-order Minimization). Nous proposons ensuite une étude théorique approfondie de l’influence du bruit sur le processus d’alignement. Cette étude conduit à la définition de deux nouvelles familles d’algorithmes, les approches ACL (Asymmetric Composition on Lie Groups) et BCL (Bidirectional Composition on Lie Groups) qui permettent d’améliorer les performances en présence de niveaux de bruit asymétriques (Rapport Signal sur Bruit différent dans les images). L’ensemble des approches introduites sont validées sur des données synthétiques et sur des données réelles capturées dans des conditions de faible luminosité. / Parametric image alignment is a fundamental task of many vision applications such as object tracking, image mosaicking, video compression and augmented reality. To recover the motion parameters, direct image alignment works by optimizing a pixel-based difference measure between a moving image and a fixed-image called template. In the last decade, many efficient algorithms have been proposed for parametric object tracking. However, those approaches have not been evaluated for aligning images of low SNR (Signal to Noise ratio) such as images captured in low-light conditions. In this thesis, we propose a new formulation of image alignment called Bidirectional Framework for unifying existing state of the art algorithms. First, this framework allows us to produce new insights on existing approaches and in particular on the ESM (Efficient Second-order Minimization) algorithm. Subsequently, we provide a theoretical analysis of image noise on the alignment process. This yields the definition of two new approaches : the ACL (Asymmetric Composition on Lie Groups) algorithm and the BCL (Bidirectional Composition on Lie Groups) algorithm, which outperform existing approaches in presence of images of different SNR. Finally, experiments on synthetic and real images captured under low-light conditions allow to evaluate the new and existing approaches under various noise conditions.