At a platform singularity, a parallel manipulator loses constraint. Adding redundant actuation in an existing leg or new leg can eliminate these types of singularities. However, redundant manipulators have been designed with little attention to frame invariant techniques. In this dissertation, physically meaningful measures for closeness to singularities in non-redundant manipulators are developed. Two such frameworks are constructed. The first framework is a constrained optimization problem that unifies seemingly unrelated existing measures and facilitates development of new measures. The second is a clearance propagation technique based on workspace generation. These closeness measures are expanded to include redundancy and thus can be used as objective functions for designing redundant actuation. The constrained optimization framework is applied to a planar three degree of freedom redundant parallel manipulator to show feasibility of the technique.

I have structured my master's thesis in terms of an opposition between Kojeve's existentialist, Marxist philosophical formulation of Hegel's Phenomenology and Levinas's post-Heideggerian, anti-Hegelian phenomenology in Totality and Infinity. While Levinas's project is explicitly anti-totalitarian, Kojeve's reading of the Phenomenology emphasizes the End of History in Hegel's philosophy without shrinking from its totalizing aspects. While the philosophical project of each thinker is generally antithetical to the other, it is my contention that the universal and homogeneous state, conceived by Kojeve to be the rational realization of the end of history, is a legitimate moral project for Levinasian ethics. This thesis provides both an exegesis of Kojeve's reading of Hegel's master/slave dialectic in the Phenomenology and an interpretation of the tragedy of the slave understood in terms of Holderlin's theory of the tragic. It is through the master/slave dialectic that history consummates in the end of history. Later in the thesis, I outline Levinas's project as an ethics as first philosophy in opposition to the Eleatic traditions in Western philosophy. We can trace Levinas's project in his unconventional reading of the cogito and the idea of infinity. Whereas Descartes represents a philosophical return home for Hegel, Levinas's reading of Descartes represents a philosophical sojourn away from home in the second movement of the Meditations. With these notions, we have a formal basis in accounting for the conflict in Levinas's thought between the moral necessity of universal rights and the dangers of assimilation. Finally, I argue for why the universal and homogeneous state is an ethically worthy goal from a Levinasian perspective. On this question, I engage the thought of a number of thinkers of the left: Kojeve, Derrida, Horkheimer, Adorno and Zizek. I conclude that Levinas's thought on universalism and eschatology can serve as a moral basis for the left-Hegelian project of realizing a universal and homogeneous state. Because such a state is distinguishable from a totalizing End of History, the eschatological concern for one's singularity within history is compatible with the prophetic call to strive for political universality. Ultimately, it is the responsibility to this prophetic call that guarantees one's singularity.

The purpose of this thesis is to develop a position control method for parallel manipulators so that the end effector can follow a desired trajectory specified in the task space where joint flexibility that occurs at the actuated joints is also taken into consideration. At the beginning of the study, a flexible joint is modeled, and the equations of motion of the parallel manipulators are derived for both actuator variables and joint variables by using the Lagrange formulation under three assumptions regarding dynamic coupling between the links and the actuators. These equations of motion are transformed to an input/output relation between the actuator torques and the actuated joint variables to achieve the trajectory tracking control. Moreover, the singular configurations of the parallel manipulators are explained. As a case study, a three degree of freedom, two legged planar parallel manipulator is simulated considering joint flexibility. The structural damping of the active joints, viscous friction at the passive joints and the rotor damping are also considered throughout the study. Matlab&reg / and Simulink&reg / softwares are used for the simulations. The results of the simulations reveal that steady state errors are negligibly small and good tracking performances can be achieved.

In this thesis, a technique for the motion of parallel manipulators through drive singularities is investigated. To remedy the problem of unbounded inverse dynamics solution in the neighborhood of drive singularities, an inverse dynamics controller which uses a conventional inverse dynamics control law outside the neighborhood of singularities and switches to the mode based on the formerly derived modified equations inside the neighborhood of singularities is proposed. As a result, good tracking performance is obtained while the actuator forces remain within the saturation limits of the actuators around singular configurations.

The aim of this study is to question the relationality between conception of image, social condition of an era and architecture. With acceptance of a transition to a new kind of relationality in contemporary era, a trialectical analysis is carried on, in order to understand changes in this relationality and its effects on contemporary architecture. Image, mainly depicted as the tool for communication, loses its transcendental and ideal status and degrades to an artificial and tricky state under the contemporary social condition. Likewise, current state of both image and social condition manipulates architecture, architectural production and the position of architect. Therefore, in this study, for understanding the new social condition, it is referred to the world constituted as a system of sign in philosophy of French thinker, Jean Baudrillard which originates from new status of image. For comprehension of contemporary architecture, it is referred to the practice of French architect, Jean Nouvel who features special value to image in his architecture. Finally, for consequences of this collision and effects on architecture, it is referred to the analysis of the book of &ldquo / The Singular Objects of Architecture&rdquo / which is composed of dialogues between Jean Baudrillard and Jean Nouvel.

In the dissertation we discuss the rectangular elements, Adini's elements and $p-$order Lagrange elements, which were constructed in the rectangular finite spaces. The special rectangular partitions enable the finite element solutions $u_h$ more efficient in interpolation of the true solution for Elliptic equation $u_I$. The convergence rates of $|u_h-u_I|_1$ are one or two orders higher than the optimal convergence rates. For post-processings we construct higher order interpolation operation $Pi_p$ to reach superconvergence $|u-Pi_p u_h|_1$. To our best knowledge, we at the first time provided the a posteriori interpolant formulas of Adini's elements and biquadratic Lagrange elements to obtain the global superconvergence, and at the first time reported the numerical verification for supercloseness $O(h^4)-O(h^5) $, global superconvergence $O(h^5)$ in $H^1$-norm and the high rates $O(h^6|ln h|)$ in the infinity norm for Poisson's equation(i.e., $-Delta u = f$). Since the finite element methods is fail to deal with the singularity problems, in the dissertation, the combinations of the Ritz-Galerkin method and the finite element methods are used for the singularity problem, i.e., Motz's problem. To couple two methods along their common boundary, we adopt the simplified hybrid, penalty, and penalty plus hybrid techniques. The analysis are made in the dissertation to derive the almost best global superconvergence $O(h^{p+2-delta})$ in $H^1$-norm, $0<delta << 1$, for the combination using $p(geq 2)$-rectangles in the smooth subdomain, and the best global superconvergence $O(h^{3.5})$ in $H^1$-norm for combinations of Adini's elements in the smooth subdomain. The numerical experiments have been carried out for the combinations of the Ritz-Galerkin method and Adini's elements, to verify the theoretical superconvergence derived.

A survey of relevant literature on the topic of wave propagation and scattering in pipes is given first. This review is followed by a theoretical framework which is pertinent to wave propagation in homogeneous, isotropic, pipes. Emphasis is placed on approximate solutions stemming from a computer based, Semi-Analytical Finite Element (SAFE) formulation. A modal analysis of the dynamic response of homogeneous, isotropic pipes, when subjected to a transient ultrasonic excitation, demonstrates that dominant features, i.e., singularities in an unblemished pipe’s displacement Frequency Response Function (FRF) coincide with its cutoff frequencies. This behaviour is confirmed experimentally. A novel technique is developed to deduce such a pipe’s wall thickness and elastic properties from three cutoff frequencies. The resulting procedure is simulated numerically and verified experimentally. Agreement between the new ultrasonic procedure and traditional destructive tests is within experimental uncertainty. Then a hybrid-SAFE technique is used to simulate waves scattered by various open rectangular notches. The simulations show, for the first time, that singularities distinct from the unblemished pipe’s cutoff frequencies arise in a displacement FRF when an axisymmetric notch is introduced. They also suggest that the new singularities depend on the properties of the parent pipe and the finite element region but effects are local to a notch. It is demonstrated further that the difference between the frequency at which a singularity introduced by a notch occurs and the nearest corresponding unblemished pipe’s cutoff frequency is a function of the notch’s dimensions. By plotting contours of constant frequency differences, it is shown that it is usually possible to characterize the notch’s dimensions by using two modes. However, the frequency difference for a third mode may be also needed occasionally. The more general case of nonaxisymmetric notches is shown to be a straightforward extension of the axisymmetric case.

A survey of relevant literature on the topic of wave propagation and scattering in pipes is given first. This review is followed by a theoretical framework which is pertinent to wave propagation in homogeneous, isotropic, pipes. Emphasis is placed on approximate solutions stemming from a computer based, Semi-Analytical Finite Element (SAFE) formulation. A modal analysis of the dynamic response of homogeneous, isotropic pipes, when subjected to a transient ultrasonic excitation, demonstrates that dominant features, i.e., singularities in an unblemished pipe’s displacement Frequency Response Function (FRF) coincide with its cutoff frequencies. This behaviour is confirmed experimentally. A novel technique is developed to deduce such a pipe’s wall thickness and elastic properties from three cutoff frequencies. The resulting procedure is simulated numerically and verified experimentally. Agreement between the new ultrasonic procedure and traditional destructive tests is within experimental uncertainty. Then a hybrid-SAFE technique is used to simulate waves scattered by various open rectangular notches. The simulations show, for the first time, that singularities distinct from the unblemished pipe’s cutoff frequencies arise in a displacement FRF when an axisymmetric notch is introduced. They also suggest that the new singularities depend on the properties of the parent pipe and the finite element region but effects are local to a notch. It is demonstrated further that the difference between the frequency at which a singularity introduced by a notch occurs and the nearest corresponding unblemished pipe’s cutoff frequency is a function of the notch’s dimensions. By plotting contours of constant frequency differences, it is shown that it is usually possible to characterize the notch’s dimensions by using two modes. However, the frequency difference for a third mode may be also needed occasionally. The more general case of nonaxisymmetric notches is shown to be a straightforward extension of the axisymmetric case.

In this thesis, the kinematic properties of Single Gimballed Control Moment Gyroscopes (SGCMGs) are investigated. Singularity phenomenon inherent to them is explained. Furthermore, existing steering laws with their derivations are given. A novel steering law is developed that may provide singularity avoidance or may be used for quick transition through a singularity with small torque errors. To avoid singularity angular momentum trajectory of the maneuver is to be simulated in advance for the calculation of singularity free gimbal histories. The steering law, besides accurately generating required torques, also pushes the system to follow trajectories closely if there is a small difference between the planned and the realized momentum histories. Thus, it may be used in a feedback system. Also presented are number of approaches for singularity avoidance or quick transition through a singularity. The application of these ideas to the feedback controlled spacecraft is also presented. Existing steering laws and the proposed method are compared through computer simulations. It is shown that the proposed steering law is very effective in singularity avoidance and quick transition through singularities. Furthermore, the approach is demonstrated to be repeatable even singularity is encountered.

This thesis systematically derives an innovative approach, called FOMFE, for fingerprint ridge orientation modeling based on 2D Fourier expansions, and explores possible applications of FOMFE to various aspects of a fingerprint identification system. Compared with existing proposals, FOMFE does not require prior knowledge of the landmark singular points (SP) at any stage of the modeling process. This salient feature makes it immune from false SP detections and robust in terms of modeling ridge topology patterns from different typological classes. The thesis provides the motivation of this work, thoroughly reviews the relevant literature, and carefully lays out the theoretical basis of the proposed modeling approach. This is followed by a detailed exposition of how FOMFE can benefit fingerprint feature analysis including ridge orientation estimation, singularity analysis, global feature characterization for a wide variety of fingerprint categories, and partial fin gerprint identification. The proposed methods are based on the insightful use of theory from areas such as Fourier analysis of nonlinear dynamic systems, analytical operators from differential calculus in vector fields, and fluid dynamics. The thesis has conducted extensive experimental evaluation of the proposed methods on benchmark data sets, and drawn conclusions about strengths and limitations of these new techniques in comparison with state-of-the-art approaches. FOMFE and the resulting model-based methods can significantly improve the computational efficiency and reliability of fingerprint identification systems, which is important for indexing and matching fingerprints at a large scale.