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This research builds up on recent results in planar kinematic synthesis with contact direction and curvature constraints on the workpiece. The synthesis of spherical serial chains is considered to guide a rigid body, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. These constraints are transformed into conditions on the velocity and acceleration of points in the moving body to obtain synthesis equations which can be solved by algebraic elimination. Trajectory interpolation formulas yield the movement of the chain with the desired contact properties in each of the task positions. Example shows the application of the developed theory to the failure recovery of a robot manipulator.

No / This title provides detailed description of how Partial Differential Equations are used in the field of geometric design, and supplies clear and concise explanations of how to implement the techniques described. It also offers extensive discussions (with examples) or practical applications of Partial Differential Equations in geometric design.

The thesis focuses on the development of an experimental set up for a recently developed failure recovery technique of spatial robot manipulators. Assuming a general configuration of the spatial robot arm, a task is specified. This task contains constraints on position, velocity and acceleration to be satisfied. These constraints are derived from contact and curvature specifications. The technique synthesizes the serial chain and tests if the task can be satisfied in case of a joint failure. An experimental set up was developed in order to validate the failure recovery technique. It includes a robot arm mounted on a movable platform. The arm and platform are controlled by NI sbRIO board and are programmed in LabVIEW. The experimental results of the failure recovery technique were obtained for the case of Elbow failure in robot manipulators. The thesis considers two applications of the synthesis of spherical five –degree-of-freedom serial chains: Power assist for human therapeutic movement and Synthesis of Parallel Mechanical Linkages. A spherical TS chain has been synthesized for these two applications using the Mathematica software.

For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular. The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains? In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing <i>C</i>0 continuity between adjacent patches.

For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular. The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains? In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing <i>C</i>0 continuity between adjacent patches.

No one will question that computers are revolutionizing the design industry. It is pointed out in [Bezier84] that before CAD/CAM, a surface was defined by tracing cross sections on a drawing and then carving these sections in wood, plastic or metal. The final model was determined by someone interpolating between the sections. This labor intensive art is being replaced by techniques of computer aided geometric design.

Surface fitting methods play an important role in many scientific fields as well as in computer aided geometric design. The problem treated here is that of constructing a smooth surface that interpolates data values associated with scattered nodes in the plane. The data is said to be convex if there exists a convex interpolant. The problem of convexity-preserving interpolation is to determine if the data is convex, and construct a convex interpolant if it exists.

O número de acidentes de trânsito é crescente nas últimas décadas no Brasil. Uma das principais causas de acidentes em rodovias brasileiras é o excesso de velocidade, que contribui para a possibilidade de ocorrência de acidentes. As velocidades praticadas pelos motoristas são também função dos elementos geométricos que compõem a via (raio, rampa, largura da faixa, etc). A consistência de traçado não afeta a expectativa dos motoristas e garante uma operação segura. A maioria dos motoristas consegue perceber as falhas de coordenação, mas tecnicamente, por exemplo, desconhecem a origem das mesmas. Esta pesquisa apresenta como objetivo a análise de consistência de um trecho de uma determinada rodovia do país de múltiplas faixas, com elevado índice de acidentes e alto fluxo de veículos comerciais. Os pontos com maior ocorrência de acidentes foram identificados e realizaram-se medições de velocidade para elaboração de um modelo de previsão de velocidade operacional (V85) do trecho de estudo. De posse deste modelo, procedeu-se à análise de consistência através do método dos critérios de segurança, que identificou 2 seções com problemas de consistência. Por fim, verificou-se se estas seções correspondiam aos locais de maior número de acidentes: a tangente T5 precede uma curva com alto índice de acidentes (km 511+000); o local com maior concentração de acidentes (km 514) foi classificado como RAZOÁVEL. / In Brazil, the number of traffic accidents is increasing in recent decades, and speeding is one of the major causes of accidents on highways, which contributes to the possibility of accidents. The speed used by the driver is determined by the geometric elements of the road (radius, slope, lane width, etc). Geometric design consistency does not affect the expectation of drivers and ensures a safe operation. Most drivers can perceive coordination failures, but, technically, they are unaware of their source. This research aims to perform a consistency analysis of a stretch of a Brazilian multiple lane highway with a high rate of accidents and large number of commercial vehicles. Thus, the sections with a higher accident occurrence were identified, and speeds were measured to determine the operating speed (V85) and, subsequently, to develop a model to predict operating speeds. With this model, the design consistency was analyzed using the method of the safety criteria. This analysis identified two sections with consistency problems. Finally, it was verified if these sections correspond to the sites with higher accident occurrence: tangent T5 precedes a curve with a high number of accidents (km 511+000); the site with higher accident occurrence (km 514) was classified as FAIR.

O setor rodoviário no Brasil é o maior responsável pelo transporte de passageiros e de cargas. A indústria de veículos de carga tem realizado modificações nas características dos veículos e a tendência neste mercado é o aumento na capacidade de transporte, obtida com a fabricação de veículos com maiores dimensões, com um maior número de eixos, bem como a utilização de combinações de veículos de carga (CVCs). Estas alterações atendem uma exigência do mercado, que é o aumento da produtividade nos serviços de transporte. Para uma operação segura, entretanto, se faz necessário garantir a compatibilidade entre os veículos e a malha rodoviária ofertada para absorver este tráfego. O objetivo principal deste trabalho é investigar as características e padrões dos veículos que trafegam nas rodovias brasileiras, visando à proposição de parâmetros de projeto geométrico compatíveis, contemplando os aspectos da interação dos veículos e da via, com ênfase para os veículos de grande porte, e em particular os veículos do tipo CVC. São propostos ajustes nos padrões técnicos estabelecidos pelo DNER, atual DNIT, de forma a adequar a geometria das rodovias às características e restrições dos veículos em operação. Foi realizado ainda um estudo de caso para um conjunto de trechos de rodovias no Estado de São Paulo e no Estado do Ceará, com características técnicas diferentes, onde trafegam CVCs de diversas configurações com restrições, permitindo que sejam identificados os ajustes necessários na geometria para adequação ao tráfego, bem como orientar a concepção de outros projetos. / In Brazil the majority of passenger and goods transportation is carried out by the highway transportation system. Vehicle industry does a continuous job of designing new models in order to increase capacities, producing bigger vehicles, with more axles, as well as long combination vehicles (LCVs). These modifications aim to attend a market demand that is looking for better productivity figures for transportations services. However, to assure a good level of safety in the operation of these vehicles, it is necessary a guarantee of compatibility of them with the roads where they will circulate. The main objective of this thesis is the research of the characteristics and standards of vehicles traveling on brazilian roads, in order to analyze design parameters, considering the interaction between vehicles and roads. The problem of the flow of large vehicles, in particular LCVs, is emphasized. Adjustments on the design standards, established by the DNER (presently named DNIT), are proposed with the intention of adequate the road geometry to the vehicles characteristics and restrictions. A case study was carried out for a set of highway segments of the states of São Paulo and Ceará. These segments present different technical characteristics and are traversed, with some restrictions, by different types of LCVs. This study allows not only the identification of necessary adjustment on the road geometry to hold up the existing traffic flow, but also the design of new projects standards.