Neste trabalho estudaremos subconjuntos especiais da esfera unitária Sm-1 de Rm, m 2, comumente chamados na literatura de designs esféricos. Os objetivos principais são analisar várias equivalências para o conceito, suas conexões com ambos, rotações sobre Sm?1 e mergulhos em esferas de dimensão superior, e resultados sobre a cardinalidade dos designs esféricos / In this work we will study specials subsets of the unitary sphere Sm-1 of Rm, m 2, usually called in literature spherical designs. The main objectives are to analyze many equivalences for the concept, its connections with both, rotations on Sm?1 and embedded in spheres of higher dimension, and results on the cardinality of spherical designs

This thesis deals with the theoretical analysis of rays passing through lenses. Emphasis on optical defects, particularly focusing on spherical aberration lenses. It also includes the preparation of a workplace and the measurement of spherical aberration and evaluate the quality of different lenses. Furthermore, a program for simulation of spherical aberration lens.

The master’s thesis presents a design for the technology of manufacture of a chandelier hinge from the material ČSN 42 3005 (Cu99.5) with a sheet thickness of 0.5 mm. Due to the spherical shape of the part and the series 40 000 parts per year, the technology of deep drawing was chosen for two drawing operations, while the redrawing is performed by reverse deep drawing. Due to the nature of the component, the additional technology is shearing. The manufacturability of the part was verified using numerical simulation in the PAM-STAMP software. The forming process is performed using three forming tools on three different presses. For the first, combined tool, an LE 160C eccentric press is used. A hydraulic press ZHO100 is applied in the second tool for the reverse drawing, and finally, an eccentric press LEK160 is applied for the shearing in the third operation. With the selected profit value of 25 %, the final price for the component was set at CZK 104.17. The turning point occurs after reaching 16 248 parts.

The research results presented in this thesis provide tools and methods to aid in the design of developable mechanisms. This work will help engineers design compact mechanisms onto developable surfaces, making it possible for them to be used in future applications. The thesis introduces terminology and definitions to describe conical developable mechanisms. Models are developed to describe mechanism motion with respect to the apex of the conical surface, and connections are made to cylindrical developable mechanisms using projected angles. The Loop Sum Method is presented as an approach to determine the geometry of the cone to which a given spherical mechanism can be mapped. A method for position analysis is presented to determine the location of any point along the link of a mechanism with respect to the conical geometry. These methods are also applied to multiloop spherical mechanisms. This work created tools and methods to design cylindrical and conical developable mechanisms from flat, planar patterns. Equations are presented that relate the link lengths and link angles of planar and spherical mechanisms to the dimensions in a flat configuration. These flat patterns can then be formed into curved, developable mechanisms. Guidelines are established to determine if a mechanism described by a flat pattern can exhibit intramobile or extramobile behavior. A developable mechanism can only potentially exhibit intramobile or extramobile behavior if none of the links extend beyond half of the flat pattern. The behavior of a mechanism can change depending on the location of the cut of the flat pattern. Different joint designs are discussed including lamina emergent torsional (LET) joints. It is shown that developable mechanisms on regular cylindrical surfaces can be described using cyclic quadrilaterals. Mechanisms can exist in either an open or crossed configuration, and these configurations correspond to convex and crossed cyclic quadrilaterals. Using equations developed for both convex and crossed cyclic quadrilaterals, the geometry of the reference surface to which a four-bar mechanism can be mapped is found. Grashof mechanisms can be mapped to two surfaces in open or crossed configurations. The way to map a non-Grashof mechanism to a cylindrical surface is in its open configuration. Extramobile and intramobile behavior can be achieved depending on selected pairs within a cyclic quadrilateral and its position within the circumcircle. Selecting different sets of links as the ground link changes the potential behavior of the mechanism. Different cases are tabulated to represent all possibilities.

Spherical means are a widespread model in modern imaging modalities like photoacoustic tomography. We develop Fourier based algorithms for an efficient computation of mean values. Furthermore we consider iterative reconstruction schemes, where we employ different regularization techniques.

The thesis comprises effects of electric fields on a fundamental study of spheri­cal premixed flame propagation.Outwardly-propagating spherical laminar premixed flames have been investigated in a constant volume combustion vessel by applying au uni-directional electric potential.Direct photography and schlieren techniques have been adopted and captured images were analyzed through image processing. Unstretched laminar burning velocities under the influence of electric fields and their associated Markstein length scales have been determined from outwardly prop­agating spherical flame at a constant pressure. Methane and propane fuels have been tested to assess the effect of electric fields on the differential diffusion of the two fuels.The effects of varying equivalence ratios and applied voltages have been in­vestigated, while the frequency of AC was fixed at 1 KHz. Directional propagating characteristics were analyzed to identify the electric filed effect. The flame morphology varied appreciably under the influence of electric fields which in turn affected the burning rate of mixtures.The flame front was found to propagate much faster toward to the electrode at which the electric fields were supplied while the flame speeds in the other direction were minimally influenced. When the voltage was above 7 KV the combustion is markedly enhanced in the downward direction since intense turbulence is generated and as a result the mixing process or rather the heat and mass transfer within the flame front will be enhanced.The com­bustion pressure for the cases with electric fields increased rapidly during the initial stage of combustion and was relatively higher since the flame front was lengthened in the downward direction.

A new angles-only initial relative orbit determination (IROD) algorithm is derived using three line-of-sight observations. This algorithm accomplishes this by taking a Singular Value Decomposition of a 6x6 matrix to arrive at an approximate initial relative orbit determination solution. This involves the approximate solution of 6 polynomial equations in 6 unknowns. An iterative improvement algorithm is also derived that provides the exact solution, to numerical precision, of the 6 polynomial equations in 6 unknowns. The initial relative orbit algorithm is also expanded for more than three line-of-sight observations with an iterative improvement algorithm for more than three line-of-sight observations. The algorithm is tested for a range of relative motion cases in low earth orbit and geosynchronous orbit, with and without the inclusion of J2 perturbations and with camera measurement errors. The performance of the IROD algorithm is evaluated for these cases and show that the tool is most accurate at low inclinations and eccentricities. Results are also presented that show the importance of including J2 perturbations when modelling the relative orbital motion for accurate IROD estimates. This research was funded in part by the Air Force Research Lab, Albuquerque, NM.

Antennas are an important component of wireless ("without wires") communications, regardless of their use. As these systems have become increasingly complex, antenna design requirements have become more demanding. Conventional antenna design consists of selecting some canonical radiator structure described by a handful of key dimensions, and then adjusting these using an optimization algorithm that improves some performance-related objective function that is (during optimization) repeatedly evaluated via a full-wave computational electromagnetics model of the structure. This approach has been employed to great effect in the enormously successful development of wireless communications antenna technology thus far, but is limiting in the sense that the "design space" is restricted to a library of canonical (or regular near-canonical) shapes. As increased design constraints and more complicated placement requirements arise such an approach to antenna design could eventually become a bottleneck. The use of antenna shape synthesis, a process also referred to as inverse design, can widen the "design space", and include such aspects as occupancy and fabrication constraints, the presence of a platform, even weight constraints, and much more. Dielectric resonator antennas (DRAs) hold the promise of lower losses at higher frequencies. This thesis uses a three-dimensional shape optimization algorithm along with a characteristic mode analysis and a genetic algorithm to shape synthesize DRAs. Until now, a limited amount of work on such shape synthesis has been performed for single-feed fixed-beam DRAs. In this thesis we extend this approach by devising and implementing a new shaping methodology for significantly more complex problems, namely directivity-maximized multi-port fixed-beam DRAs, and multi-port DRAs capable of the beam-steering required to satisfy certain spherical coverage constraints, where the location, type and number of feed-ports need not be specified prior to shaping. The approach enables even low-profile enhanced-directivity DRAs to be shape synthesized.

10ABSTRACTEnergetic materials are widely used as rocket propellants and explosives in the field of aerospace and defense. Understanding the nature of impact in polymer-bonded explosives is crucial safety and transportation of energetic materials. The formation of hotpots in energetic materials leads to unexpected initiations, posing a safety hazard. An attempt was made to study the mechanical behavior of energetic materials under different shapes of impactors. In particular, the likelihood of hotspot formations was discussed in spherical and Spherical Impactors(SI). Spherical and planar-shaped impactors were modeled with a cohesive finite element frame work to simulate the behavior of granular energetic materials with cyclo-tetramethylene-tetranitramine(HMX) embedded in a hydroxyl-polybutadiene binder. Temperature distribution and stresses induced around crystals on expanding stress profile of SI and uniform pressure profile from a SI are compared to determine the possibility of detonation.<div><br></div><div>In this work, the dependence of sample morphology on induced stresses in the microstructure is highlighted by using three different microstructures. A digitized polymer-bonded-explosive microstructure was analyzed for possible initiations with different impact velocities. The effect of the shape of grains and volume fractions on the likeliness of hotspot formation were studied using rounded and sharp-edged idealized crystals. Impactor behavior on samples was compared based on force chains, temperature profiles, and stress distributions</div>

Lamina Emergent Mechanisms (LEMs) are a class of compliant mechanisms that can be manufactured from sheet goods and possess motion out of the plane of fabrication. LEMs can be designed to perform sophisticated motions. This thesis expands LEM understanding and increases the ability to utilize them in applications by introducing the fundamentals of spherical LEMs, creating joints suitable for LEMs, and providing an example of a LEM application. In this thesis, the fundamentals of spherical LEMs are developed. This includes classification of all possible spherical 4R LEMs and a discussion of the motion characteristics of the various mechanisms. The motion characteristics associated with spherical 4R LEMs are then used to predict the motion of spherical 6R LEMs and arrays of spherical LEMs. Multiple spherical LEM prototypes are shown and discussed. A common difficulty of working with compliant mechanisms, especially LEMs, is creating suitable joints. There is often a trade off between flexibility in the desired direction of deflection, and stiffness in directions of undesired deflection. For this thesis, LEM joints that possess higher off-axis stiffness, especially in tension and compression, than previous designs were developed: the I-LET, the T-LET, and the IT-LET. Joint geometries were optimized and then modeled in commercial finite element analysis (FEA) software capable of nonlinear analysis. These models were used to predict the bending of tensile/compressive stiffnesses of the joints. As a benchmark, lamina emergent torsional (LET) joints were modeled and optimized for maximum tension and compression loading while maintaining the same bending stiffness as the joint being compared. Mechanisms that utilized the new joints were created and are briefly discussed. The use of these joints allows for minimized parasitic motion under tension and compression loads and expands the capability of LEM joints. The Lens Lift™ was developed to demonstrate an application of LEMs. The Lens Lift™ is a LEM device that allows for easier and more sterile use of disposable contact lenses. It possesses a monolithic structure and can be fabricated using simple manufacturing processes. As the contact lens user opens the blister pack used to store the lens, the lens is lifted out of the pack and presented to the user. The user can then lift the lens with one touch and place it in the eye. A provisional patent has been filed for the device and the device currently being evaluated by a major contact lens manufacturer for further development.