Freeform curve design has existed in various forms for at least two millennia, and is important throughout computer-aided design and manufacture. With the increasing importance of animation and robotics, coupled with the increasing power of computers, there is now interest in freeform motion design, which, in part, extends techniques from curve design, as well as introducing some entirely distinct challenges. There are several approaches to freeform motion construction, and the first step in designing freeform motions is to choose a representation. Unlike for curves, there is no "standard" way of representing freeform motions, and the different tools available each have different properties. A motion can be viewed as a continuously-varying pose, where a pose is a position and an orientation. This immediately presents a problem; the dimensions of rotations and translations are different, and it is not clear how the two can be compared, such as to define distance along a motion. One solution is to treat the rotational and translational components of a motion separately, but this is inelegant and clumsy. The philosophy of this thesis is that a motion is not defined purely by rotations and translations, but that the body following a motion is a part of that motion. Specifically, the part of the body that is accounted for is its inertia tensor. The significance of the inertia tensor is that it allows the rotational and translational parts of a motion to be, in some sense, compared in a dimensionally- consistent way. Using the inertia tensor, this thesis finds the form of kinetic energy in <;1'4, and also discusses extensions of the concepts of arc length and curvature to the space of motions, allowing techniques from curve fairing to be applied to motion fairing. Two measures of motion fairness are constructed, and motion fairing is the process of minimizing the measure of a motion by adjusting degrees of freedom present in the motion's construction. This thesis uses the geometric algebra <;1'4 in the generation offreeform motions, and the fairing of such motions. <;1'4 is chosen for its particular elegance in representing rigid-body transforms, coupled with an equivalence relation between elements representing transforms more general than for ordinary homogeneous coordinates. The properties of the algebra germane to freeform motion design and improvement are given, and two distinct frameworks for freeform motion construction and modification are studied in detail.

Electron beam freeform fabrication (EBF3) is a rapid metal deposition process that works efficiently with the wieldable alloy Inconel 718 (IN 718). EBF3 is a developing additive manufacturing (AM) process that can manufacture IN 718 parts directly from computer aided design (CAD) data. EBF3 can produce parts significantly faster and more energy efficient than competing IN 718 AM technologies. The EBF3 process utilizes metal wire feedstock which is induced into a molten pool using a focused electron beam in a vacuum environment. This allows parts to be built layer by layer, creating intricate shapes that can be produced cheaper and faster than traditionally manufactured IN 718 parts. Furthermore, it allows traditionally manufactured parts to be modified as additional form is added to them using EBF3. Multiple industries rely on IN 718 parts and can utilize this technology including aerospace engineering, oil refinery, nuclear power generation, and food processing.A main drawback of EBF3 is the lack of knowledge of the effect different EBF3 build techniques will have on the properties of the deposited materials. Most of the reliable data on the mechanical properties relate to a linear build-up strategy and focus on the mechanical properties in the deposition direction (DD). There is no data related to other build-up techniques such as rotation build-up or transitional builds from forged material to EBF3 material. Reliable data on the behavior and microstructure of EBF3 material in a direction other than the DD is also difficult to find. Previous studies showed build-up height influenced mechanical properties but its role is not fully understood yet. This paper presents the mechanical properties and microstructure of an IN 718 plate built using a EBF3 rotational build-up strategy through utilizing a forged plug in the center. The tensile properties of samples at the transition from forged to EBF3 material showed higher ductility and reduced strength than pure EBF3 material. This is likely due the influence of the forge material in one half of the specimen. Samples taken at approximately 15 degree increments from 0 to 90 degrees rotation to the DD in the additive portion of the plate were subjected to tensile testing. Along the build height, or the transverse direction (TD), the lowest strength was demonstrated and the TD aligned strongly to a <001> texture. Samples 45 degrees to the DD showed the greatest strength due to their preference for aligning to a <111> texture. Samples low on the build height demonstrated a higher strength than those on the top and displayed grain structures along the TD which were long, linear, and narrow across multiple deposition layers.

The quality of parts fabricated using Laser Solid Freeform Fabrication (LSFF) is highly dependent on the physical phenomena and operating parameters which govern the process. For instance, the thermal stress patterns and intensity, induced throughout the process domain due to the layer-by-layer material deposition and the temperature distribution characteristics, contribute significantly to potential delamination and crack formation across the fabricated part. In this research, some of the main features as well as drawbacks of this technique are studied through a multi-physics analysis of the process. For this purpose, a coupled time-dependent 3D model is developed with which the geometry of the deposited material as well as temperature and thermal stress fields across the process domain can be predicted. In the proposed approach, coupled thermal and stress domains are numerically obtained assuming a decoupled interaction between the laser beam and powder stream. To predict the geometry of the deposited material, once the melt pool boundary is obtained, the process domain is discretized in a cross-sectional fashion based on the powder feed rate, elapsed time, and intersection of the melt pool and powder stream projected on the substrate. Layers of additive material are then added onto the non-planar domain. The main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces, such as powder catchment, are incorporated into the modelling approach to enhance the accuracy of the results. To demonstrate the proposed algorithm and to study the main features of the process, a four-layer thin wall of AISI 304L steel on a substrate of the same material is numerically and experimentally fabricated. The numerical analyses along with the experimental results are then used to investigate the correlation between the temperature-thermal stress fields and crack formation across the fabricated parts. The trend of the results reveals that by preheating the substrate prior to the fabrication process, it is possible to substantially reduce the formed micro-cracks. To demonstrate the feasibility of preheating on the reduction of micro-cracks, several simulations and experiments are performed in which a crack-free result is obtained, with a 22 per cent reduction in thermal stresses when the substrate is preheated to 800 K. The numerical and experimental results are also used to study the circumstances of the microstructural formation during the fabrication process. To conclude this research, the developed modelling approach is further extended to briefly discuss the effects of the path patterns and the main operating parameters on the outcomes of the process. The effects of the material properties and their variations on the temperature distributions and thermal stress fields are studied by fabrication of a thin wall of two Stellite 6 layers and two Ti layers on a stainless steel substrate.

The quality of parts fabricated using Laser Solid Freeform Fabrication (LSFF) is highly dependent on the physical phenomena and operating parameters which govern the process. For instance, the thermal stress patterns and intensity, induced throughout the process domain due to the layer-by-layer material deposition and the temperature distribution characteristics, contribute significantly to potential delamination and crack formation across the fabricated part. In this research, some of the main features as well as drawbacks of this technique are studied through a multi-physics analysis of the process. For this purpose, a coupled time-dependent 3D model is developed with which the geometry of the deposited material as well as temperature and thermal stress fields across the process domain can be predicted. In the proposed approach, coupled thermal and stress domains are numerically obtained assuming a decoupled interaction between the laser beam and powder stream. To predict the geometry of the deposited material, once the melt pool boundary is obtained, the process domain is discretized in a cross-sectional fashion based on the powder feed rate, elapsed time, and intersection of the melt pool and powder stream projected on the substrate. Layers of additive material are then added onto the non-planar domain. The main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces, such as powder catchment, are incorporated into the modelling approach to enhance the accuracy of the results. To demonstrate the proposed algorithm and to study the main features of the process, a four-layer thin wall of AISI 304L steel on a substrate of the same material is numerically and experimentally fabricated. The numerical analyses along with the experimental results are then used to investigate the correlation between the temperature-thermal stress fields and crack formation across the fabricated parts. The trend of the results reveals that by preheating the substrate prior to the fabrication process, it is possible to substantially reduce the formed micro-cracks. To demonstrate the feasibility of preheating on the reduction of micro-cracks, several simulations and experiments are performed in which a crack-free result is obtained, with a 22 per cent reduction in thermal stresses when the substrate is preheated to 800 K. The numerical and experimental results are also used to study the circumstances of the microstructural formation during the fabrication process. To conclude this research, the developed modelling approach is further extended to briefly discuss the effects of the path patterns and the main operating parameters on the outcomes of the process. The effects of the material properties and their variations on the temperature distributions and thermal stress fields are studied by fabrication of a thin wall of two Stellite 6 layers and two Ti layers on a stainless steel substrate.

Applications involving high electrical conduction require complex components that are difficult to be manufactured by conventional processes. Laser sintering (LS) is an additive manufacturing technique that overcomes these drawbacks by offering design flexibility. This study focuses upon optimizing the process of laser sintering to manufacture functional prototypes of components used in high electrical conduction applications. Specifically, components for two systems – high current sliding electrical contacts and fuel cells – were designed, manufactured and tested. C-asperity rails were made by LS and tested in a high current sliding electrical setup. Corrugated flow field plates were created by LS and their performance in a direct methanol fuel cell (DMFC) was tested. This is the first experimental attempt at using laser sintering for manufacturing such complex components for use in high electrical conduction applications. The second part of this study involves optimization the laser sintering process. Towards this, efforts were made to improve the green strength of parts made by LS. Particle size of graphite/ phenolic resin and addition of nylon/11 and wax were tested for their effect upon green strength. Of these, significant improvement of green strength was observed by altering the particle size of the graphite/ phenolic resin system. New methods of improving green strength by employing fast cure phenolic resins with carbon fiber additions were successfully demonstrated. This study also identified a binder system and process parameters for indirect LS of stainless steel –for bipolar plate compression/ injection mold tooling. All the experimental results of this study lead us to believe that laser sintering can be developed as a robust and efficient process for the manufacture of specialized components used in advanced electrical conduction systems. / text

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Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

This dissertation investigates various design metrologies on designing freeform surfaces for LED illumination applications. The major goal of this dissertation is to study designing freeform optical surfaces to redistribute the radiance (which can be simplified as intensity distribution for point source) of LED sources for various applications. Nowadays many applications, such as road lighting systems, automotive headlights, projection displays and medical illuminators, require an accurate control of the intensity distribution. Freeform optical lens is commonly used in illumination system because there are more freedoms in controlling the ray direction. Design methods for systems with rotational and translational symmetry were well discussed in the 1930's. However, designing freeform optical lenses or reflectors required to illuminate targets without such symmetries have been proved to be much more challenging. For the simplest case when the source is an ideal point source, the determination of the freeform surface in a rigorous manner usually leads to the tedious Monge-Ampère second order nonlinear partial different equation, which cannot be solved with standard numerical integration techniques. Instead of solving the differential equation, ray mapping is an easier and more efficient method in controlling one or more freeform surfaces for prescribed irradiance patterns. In this dissertation, we investigate the ray mapping metrologies in different coordinate systems to meet the integrability condition for generating smooth and continuous freeform surfaces. To improve the illumination efficiency and uniformity, we propose a composite ray mapping method for designing the total internal reflective (TIR) freeform lens for non-rotational illumination. Another method called "double pole" ray mapping method is also proposed to improve system performance. The ray mapping designs developed for the point source do not work well for extended sources, we have investigated different design methodologies including optimization method, deconvolution method and feedback modification method to design freeform optical surfaces for extended sources.

The subject of this bachelor thesis is the design of the spatially adaptable 3D printer for Contour Crafting. Aiming to apply megascale aditive technology in a field of construction industry.

No / In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.