Automotive and Tire companies spend extensive amounts of time and money to tune their products through prototype testing at dedicated test facilities. This is mainly due to the limitations in the simulation capabilities that exist today. With greater competence in simulation, comes more control over designs in the initial stages, which in turn lowers the demand on the expensive stage of tuning. The work presented, aims at taking today's simulation capabilities a step forward by integrating models that are best developed in different software interfaces. An in-plane rigid ring model is used to understand the transient response of tires to various high frequency events such as Anti-Lock Braking and short wavelength road disturbances. A rule based ABS model performs the high frequency braking operation. The tire and ABS models have been created in the Matlab-Simulink environment. The vehicle model has been developed in CarSim. The models developed in Simulink have been integrated with the vehicle model in CarSim, in the form of a design tool that can be used by tire as well as vehicle designers for further tuning of the vehicle functional performances as they relate to in-line braking scenarios. Outdoor validation tests were performed to obtain data from a vehicle that was measured on a suspension parameter measuring machine (SPMM) in order to complement this design tool. The results of the objective tests performed have been discussed and the correlations and variations with respect to the simulation results have been analyzed. / Master of Science

The main object of this thesis is to give a introductory study of the longitudinal motion of an aircraft, including some effects of nonuniform motion. Because this subject is connected with practical problems of importance in the domain of applied aerodynamics and control, a great effort has been given to setting up the physics of unsteady aerodynamics and its effects on the aircraft longitudinal modes. Numerical examples are given for both the two-dimensional and three-dimensional rigid wing, subsonic case. In this research, from the unsteady aerodynamic theory, through the frequency response calculation, system identification and the augmentation of the aircraft dynamic system, a carefully derived theory and a computer algorithm have been presented and used. It is our main purpose that a suitable unsteady aerodynamic transfer function be obtained and be coupled to the aircraft quasi-steady dynamic system. A new modified model which includes the unsteady aerodynamic effects has been constructed and been compared with the conventional model and the differences between them have been discussed. / Master of Science

Galois theory, the study of the structure and symmetry of a polynomial or associated field extension, is a standard tool for showing the insolvability of a quintic equation by radicals. On the other hand, the Inverse Galois Problem, given a finite group G, find a finite extension of the rational field Q whose Galois group is G, is still an open problem. We give an introduction to the Inverse Galois Problem and compare some radically different approaches to finding an extension of Q that gives a desired Galois group. In particular, a proof of the Kronecker-Weber theorem, that any finite extension of Q with an abelian Galois group is contained in a cyclotomic extension, will be discussed using an approach relying on the study of ramified prime ideals. In contrast, a different method will be explored that defines rigid groups to be groups where a selection of conjugacy classes satisfies a series of specific properties. Under the right conditions, such a group is also guaranteed to be the Galois group of an extension of Q. / Master of Science

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Optimal rigid-body angular maneuvers are investigated, using restricted control moments—a problem inspired in the context of rotational maneuvers for <i>super-maneuverable</i> aircraft. Most of the analysis is based on the formulation with no direct control over the roll component of angular velocity. The present research effort is conducted in two phases. In the first phase, optimal control of angular <i>rates</i> is closely examined. The second phase deals with the problem of optimal <i>attitude</i> control. Optimal rigid-body angular <i>rate</i> control is first examined via an <i>approximate</i> dynamic model. The proposed model admits analytical solutions of the optimality conditions. The analysis reveals that over a large range of boundary conditions, there are, in general, <i>several</i> distinct extremal solutions. Second-order necessary conditions are investigated to establish local optimality of candidate minimizers. Global optimality of the extremal solutions is discussed. Next, the optimal angular <i>rate</i> problem is studied using the <i>exact</i> dynamic model. Numerical solutions of optimality conditions are obtained which corroborate and extend the findings of the <i>approximate</i> problem. The qualitative feature of <i>multiple extremal solutions</i> is retained. Several of these extremal solutions did not satisfy the Jacobi necessary condition. The choice of <i>minimizing</i> solution could be narrowed down to two sub-families of extremal solutions. A locus of Darboux Points is obtained which demarcates the domain over which these two sub-families are globally minimal. The above studies look at <i>minimum control effort</i> families of extremal solutions. As a next step, we examine the <i>minimum time</i> control of angular rates, with prescribed hard bounds on available control. Existence of singular subarcs in time-optimal trajectories is explored. Qualitative features exhibited by the <i>exact</i> problem are preserved. In addition, the control space is deformed to allow roll control and its effect on extremal solutions is investigated. In the next phase, we introduce the <i>kinematics</i> into the optimal control problem. Minimum time <i>attitude</i> control of a rigid-body is investigated with prescribed hard bounds on available control. The attitude of the rigid-body is defined using Euler parameters. Existence of singular subarcs in time-optimal trajectories is explored. A numerical survey of first-order necessary conditions reveals that there are <i>several</i> distinct extremal solutions. The character of extremal solutions depend whether <i>pitch</i> or <i>yaw</i> motion assumes the dominating role in controlling <i>roll</i> motion. Moreover, certain <i>spatial symmetries</i> are identified. Maneuvers such as a <i>Roll Around the Velocity Vector</i> and <i>Fuselage Pointing</i> are analyzed. / Ph. D.

In this thesis a methodology for representing 3D subjects and their deformations in adverse situations is studied. The study is focused in providing methods based on registration techniques to improve the data in situations where the sensor is working in the limit of its sensitivity. In order to do this, it is proposed two methods to overcome the problems which can difficult the process in these conditions. First a rigid registration based on model registration is presented, where the model of 3D planar markers is used. This model is estimated using a proposed method which improves its quality by taking into account prior knowledge of the marker. To study the deformations, it is proposed a framework to combine multiple spaces in a non-rigid registration technique. This proposal improves the quality of the alignment with a more robust matching process that makes use of all available input data. Moreover, this framework allows the registration of multiple spaces simultaneously providing a more general technique. Concretely, it is instantiated using colour and location in the matching process for 3D location registration.

No description available.

Two types of connection are generally considered in the design of steel structures in practice. These are classified as completely rigid (moment) and simple (shear) connections. In theory, completely rigid connections can not undergo rotation and simple connections can not transfer moment. However, in reality rigid connections have a relative flexibility which makes them to rotate and simple connections have some reserve capacity to transfer moments. In many modern design specifications, this fact is realized and another type which is called partially restrained or semi-rigid connection is introduced. These types of connections have got the transfer of some beam moment to column together with shear. However, there is a lack of information on the amount of moment transferred and rotation of connection during the action of the moment transfer. The only way to quantify the moment and rotation of the partially restrained connections is to draw momentrotation curves. Nevertheless, drawing such curves requires great amount of expenses for experiments. Taking these into account, the use of finite elements with the help of increased computational power is one way to obtain moment-rotation curves of connections. Available test results guides the finite element analysis for justifications. So these analyses can be further implemented into design functions. This thesis is intended to conduct 3-D non-linear finite element analyses to compliment with tests results for different types of semi-rigid connections with angles and compare them with mathematical models developed by different researchers.

In flexible fitting, the high-resolution crystal structure of a molecule is deformed to optimize its position with respect to a low-resolution density map. Solving the flexible fitting problem entails answering the following questions: (A) How can the crystal structure be deformed? (B) How can the term "optimum" be defined? and (C) How can the optimization problem be solved? In this dissertation, we answer the above questions in reverse order. (C) We develop PFCorr, a non-uniform SO(3)-Fourier-based tool to efficiently conduct rigid-body correlations over arbitrary subsets of the space of rigid-body motions. (B) We develop PF2Fit, a rigid-body fitting tool that provides several useful definitions of the optimal fit between the crystal structure and the density map while using PFCorr to search over the space of rigid-body motions (A) We develop PF3Fit, a flexible fitting tool that deforms the crystal structure with a hierarchical domain-based flexibility model while using PF2Fit to optimize the fit with the density map. Our contributions help us solve the rigid-body and flexible fitting problems in unique and advantageous ways. They also allow us to develop a generalized framework that extends, breadth-wise, to other problems in computational structural biology, including rigid-body and flexible docking, and depth-wise, to the question of interpreting the motions inherent to the crystal structure. Publicly-available implementations of each of the above tools additionally provide a window into the technically diverse fields of applied mathematics, structural biology, and 3D image processing, fields that we attempt, in this dissertation, to span. / text

Static balance is the reduction or elimination of the actuating effort in quasi-static motion of a mechanical system by adding non-dissipative force interactions to the system. In recent years, there is increasing recognition that static balancing of elastic forces in compliant mechanisms leads to increased efficiency as well as good force feedback characteristics. The development of insightful and pragmatic design methods for statically balanced compliant mechanisms is the motivation for this work. In our approach, we focus on a class of compliant mechanisms that can be approximated as spring-loaded rigid-link mechanisms. Instead of developing static balancing techniques directly for the compliant mechanisms, we seek analytical balancing techniques for the simplified spring–loaded rigid–link approximations. Towards that, we first provide new static balancing techniques for a spring-loaded four-bar linkage. We also find relations between static balancing parameters of the cognates of a four-bar linkage. Later, we develop a new perfect static balancing method for a general n-degree-of-freedom revolute and spherical jointed rigid-body linkages. This general method distinguishes itself from the known techniques in the following respects: 1 It adds only springs and not any auxiliary bodies. 2 It is applicable to linkage shaving any number of links connected in any manner. 3 It is applicable to both constant(i.e., gravity type) and linear spring loads. 4 It works both in planar and spatial cases. This analytical method is applied on the approximated compliant mechanisms as well. Expectedly, the compliant mechanisms would only be approximately balanced. We study the effectiveness of this approximate balance through simulations and a prototype. The analytical static balancing technique for rigid-body linkages and the study of its application to approximated compliant mechanisms are among the main contributions of this thesis.