No description available.

The goal of this thesis is to design and fabricate a four degrees freedom underwater manipulator for small to midsize remotely operated vehicles. DC servo motors were used to actuate the manipulator joints such that the size and the necessary auxiliary components can be reduced. In terms of hardware design process, the selection of servo motors and their arrangement is the key to the overall performance of the manipulator. The design of any joint, including its location and fixture to the frame, is coupled with that of the neighboring joints such that the design itself is an iterative process. Proper choice of the torque and power of an actuator not only reduces its size but also ease the loading the joints proximal to the base. In this project, the water resistance between stationary and rotary interfaces are achieved by O-ring and mechanical seals respectively. A gripper, synthesized and analyzed with kinematic chain theory, was implemented with a single degree freedom six-bar linkage as the end-effector of the manipulator. Because the robot is designated to operate in underwater environment, the dynamics of the system is relative slow and insignificant. Therefore, the only the linearized kinematics of the manipulator is concerned, and the motion controller is implemented with Jacobian in Visual Basic. Under 50 Hz servo rate, gravity compensation is added for operation in the air, and in the water as well. For the operating speed limited to 20 mm/sec, the overall positioning error is confined to be less than 1 mm for all time.

For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method along a non-trivial reference trajectory does not directly apply in a geometric theory where the state space is a differentiable manifold. Indeed, the standard constructions involving the Jacobian are dependent on a choice of coordinates. The procedure of linearizing a control affine system along a non-trivial reference trajectory is studied from a differential geometric perspective. A coordinate-invariant setting for linearization is presented. With the linearization in hand, the controllability of the geometric linearization is characterized using an alternative version of the usual controllability test for time-varying linear systems. The various types of stability are defined using a metric on the fibers along the reference trajectory and Lyapunov's second method is recast for linear vector fields on tangent bundles. With the necessary background stated in a geometric framework, Kalman's theory of quadratic optimal control is understood from the perspective of the Maximum Principle. Finally, following Kalman, the resulting feedback from solving the infinite time optimal control problem is shown to uniformly asymptotically stabilize the linearization using Lyapunov's second method. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-12-19 16:59:47.76

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.

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For nearly three centuries mathematicians have been interested in polygons which simultaneously circumscribe and inscribe quadrics. They have shown in many contexts (real, complex, non-euclidean, higher dimensional, etc.) that such polygons may be ``rotated'' while maintaining their circum-inscribed quality. Of particular interest has been conditions on the quadrics which guarantee the existence of such polygons. In 1854 Arthur Cayley provided conditions for closure general to polygons of any size in the complex projective plane. We show that under suitable circumstances the curve, defined by Cayley's conditions, on a fibration of Jacobians over the space of families of quadrics is a reducible curve, particularly in genus two. We may infer additional information about points of finite order on the Jacobians based on the component of the reducible curve in which they lie. Using this information we are able to accomplish two tasks. First we provide sufficient closure conditions for Poncelet's Great Theorem in which each vertex of the polygon lies on a distinct quadric. Next, for a polygon circum-inscribed in quadrics in ℙ^3, we provide additional sufficient conditions for closure beyond what mathematicians had previously believed to be necessary and sufficient.

Underwater operation and sampling has been replaced by ROV (Remotely Operated Vehicle) and underwater manipulator gradually, which can avoid divers to face the dangers due to the environmental pressure and low temperature. When ROV to carry out the mission, the operator sees the undersea environment and the target with the information feedback from the sensors. Recently, we developed a general purpose controller for controlling underwater robotic systems. We plan to install the manipulator on the ROV with the same general purpose controller. One of the concerns in desgining is: the ROV generally mantains neutral buoyant in seawater. When adding or removing any components, the arrangement of balast weight needs to done again to keep the balance of the system. Moreover, the center of gravity will be changed such that dynamics of the ROV will be different when collaborating with the underwater manipulator. To resolve these problems, we review the design and hope to reduce the size and weight of each component.The new design also introduces the use of a junction box. The junction box keeps all the circuits, power converters and motor control card. It allows the reconfiguration of power and commands pathway much easier. To reduces of the size of the housings, the gear transmission set is moved out of the housing. According to the positioning accuray requirement of each axis, a DC servomotor or a DC motor is installed. Underwater manipulators do not require agile motion. Therefore we use a gear-worm set as the transmission between links to increase torque. The motion control is implemented with a Jacobian to calculate the increment joint angles for joint coordinate control. Human-interface was developed with Borland C++ Builder and OpenGL to let the operator to simulate and control of the manipulator with an input of a 3D joystick.

Supersymmetry is a theoretical model of particle physics that posits a symmetry between bosons and fermions. Supersymmetry proposes the existence of particles that we have not yet observed and through them, offers a more unified view of the universe. In the same way Feynman Diagrams represent Feynman Integrals describing subatomic particle behaviour, supersymmetry algebras can be represented by graphs called adinkras. In addition to being motivated by physics, these graphs are highly structured and mathematically interesting. No one has looked at the Jacobians of these graphs before, so we attempt to characterize them in this thesis. We compute Jacobians through the 11-cube, but do not discover any significant discernible patterns. We then dedicate the rest of our work to generalizing the notion of the Jacobian, specifically to be sensitive to edge directions. We conclude with a conjecture describing the form of the directed Jacobian of the directed $n$-topology. We hope for this work to be useful for theoretical particle physics and for graph theory in general.

Chronic Obstructive Pulmonary Disease (COPD), a growing health concern, is the fourth leading cause of death in the United States. While people habituated to smoking constitute the highest COPD susceptible population, people exposed to air pollution or other lung irritants also form a major group of potential COPD patients. COPD is a progressive disease that is characterized by the combination of chronic bronchitis, small airway obstruction, and emphysema that causes an overall decrease in the lung elasticity affecting the lung tissue. The current gold standard method to diagnose COPD is by pulmonary function tests (PFT) which measures the extent of COPD based on the lung volumes and is further classified into five severity stages. PFT measurements are insensitive to early stages of COPD and also its lack of reproducibility makes it hard to rely on, in assessing the disease progression. Alternatively, Pulmonary CT scans are considered as a major diagnostic tool in analyzing the COPD and CT measures are also closely related to the pathological extent of the disease. Quantification of COPD using features derived from CT images has been proven effective. The most common features are density based and texture based. We propose a new set of features called lung biomechanical features which capture the regional lung tissue deformation patterns during the respiratory cycle. We have tested these features on 75 COPD subjects and 15 normal subjects. We have done classification of COPD/Non COPD on the dataset using the three feature sets and also performed the classification all these subjects to their corresponding severity stage. It is shown that the lung biomechanical features were also able to classify COPD subjects with a good AUC. It is also shown that, by combining the best features from each feature set, there is an improvement in the classifier performance. Multiple regression analysis is performed to find the correlation between the CT derived features and PFT measurements.

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