Morphological Considerations in Lingual Appliance Design: A Descriptive Study

Submitted in partial fulfillment of the requirements for a Certificate in Orthodontics, Dept. of Orthodontics, University of Connecticut Health Center, 1986

Radiolarian biostratigraphy in the central Indian Ocean

Identifiable radiolarians of stratigraphic importance were recovered at eight of the sites drilled on Leg 115. The assemblages range in age from Holocene to middle Eocene (Dictyoprora mongolfieri Zone, about 48 Ma). Faunal preservation is particularly good in two stratigraphic intervals: the Holocene through upper Miocene (0-9 Ma), and the lowermost Oligocene to middle Eocene (35-48 Ma). Fluctuating rates of silica accumulation at these drill sites during the Cenozoic reflect changing tectonic and paleoceanographic conditions. In particular, the gradual closure of the Indonesian and Tethyan seaways and the northward migration of the Indian subcontinent severely restricted zonal circulation and silica accumulation in tropical latitudes during the late Oligocene through middle Miocene. By the late Miocene the Indian subcontinent had moved sufficiently north of the equator to allow trans-Indian zonal circulation patterns to become reestablished, and biosiliceous sedimentation resumed. The composition of the radiolarian assemblages in the tropical Indian Ocean is closely comparable with that of the 'stratotype' sequences in the equatorial Pacific. However, there are some notable exceptions in Indian Ocean assemblages: (1) the scarcity of the genera Pterocanium and Spongaster in the Neogene; (2) the absence of the stratigraphically important Podocyrtis lineage, P. diamesa -> P. phyxis -> P. ampla, in the middle Eocene; and (3) the scarcity of taxa of the genus Dorcadospyris, with the exception of D. ateuchus. The succession of radiolarian events was tabulated for those stratigraphic intervals where the assemblages were well preserved. We identified 55 events in the middle Eocene to earliest Oligocene, and 31 events in the late Miocene to Holocene. The succession of events is closely comparable with that of the tropical Pacific. However, there are exceptions that appear to be real, rather than artifacts of sample preservation, mixing, and core disturbance.

Adhesión de ionómeros vítreos convencionales a dentina tratada con distintas sustancias

El objetivo de este trabajo fue evaluar la fuerza adhesiva de los ionómeros vítreos convencionales a la dentina tratada con ácido fosfórico, con ácido poliacrílico y con solución de hipoclorito de sodio. Los ensayos se realizaron sobre dentina de premolares extraídos por razones ortodóncicas o periodontales, los cuales se asignaron al azar en tres grupos de 10 elementos cada uno. A cada grupo se le practicó un tratamiento distinto (descalcificación, desproteinización o eliminación del barro dentinario). Sobre cada espécimen se le adhirió un cilindro de ionómero vítreo convencional preparado según las especificaciones de su fabricante. Posteriormente las muestras fueron sometidas a fuerzas de cargas de corte utilizando una máquina de ensayos universal (Instron). Los resultados obtenidos fueron sometidos a análisis de ANOVA de una entrada y a post test de comparación múltiple de Tukey. Por lo que puede expresarse que no hubo diferencia estadísticamente significativa (p>0,05) en la fuerza adhesiva de los ionómeros vítreos que fueron adheridos a dentina con tratamiento de ácido poliacrílico, y los que fueron adheridos a dentina con tratamiento de descalcificación (acción del ácido fosfórico). Se encontró diferencia estadísticamente significativa en las muestras adheridas a dentina tratadas con poliacrílico y ácido fosfórico (p<0.01 y p<0.05 respectivamente), con respecto a las que fueron tratadas con hipoclorito.

Transposición dentaria canino-premolar : caso clínico

En este artículo se describe la resolución por medios ortodóncicos de una transposición dentaria completa unilateral superior canino-primer premolar, en dentición permanente, con persistencia de los caninos temporarios

Isotopic and chemical compositions of rocks and minerals from the TAG hydrothermal mound, ODP Site 957

Strontium- and oxygen-isotopic measurements of samples recovered from the Trans-Atlantic Geotraverse (TAG) hydrothermal mound during Leg 158 of the Ocean Drilling Program provide important constraints on the nature of fluid-rock interactions during basalt alteration and mineralization within an active hydrothermal deposit. Fresh Mid-Ocean Ridge Basalt (MORB), with a 87Sr/86Sr of 0.7026, from the basement beneath the TAG mound was altered at both low and high temperatures by seawater and altered at high temperature by near end-member black smoker fluids. Pillow breccias occurring beneath the margins of the mound are locally recrystallized to chlorite by interaction with large volumes of conductively heated seawater (>200°C). The development of a silicified, sulfide-mineralized stockwork within the basaltic basement follows a simple paragenetic sequence of chloritization followed by mineralization and the development of a quartz+pyrite+paragonite stockwork cut by quartz-pyrite veins. Initial alteration involved the development of chloritic alteration halos around basalt clasts by reaction with a Mg-bearing mixture of upwelling, high-temperature (>300°C), black smoker-type fluid with a minor (<10%) proportion of seawater. Continued high-temperature (>300°C) interaction between the wallrock and these Mg-bearing fluids results in the complete recrystallization of the wallrock to chlorite+quartz+pyrite. The quartz+pyrite+paragonite assemblage replaces the chloritized basalts, and developed by reaction at 250-360°C with end-member hydrothermal fluids having 87Sr/86Sr ~0.7038, similar to present-day vent fluids. The uniformity of the 87Sr/86Sr ratios of hydrothermal assemblages throughout the mound and stockwork requires that the 87Sr/86Sr ratio of end-member hydrothermal fluids has remained relatively constant for a time period longer than that required to change the interior thermal structure and plumbing network of the mound and underlying stockwork. Precipitation of anhydrite in breccias and as late-stage veins throughout most of the mound and stockwork, down to at least 125 mbsf, records extensive entrainment of seawater into the hydrothermal deposit. 87Sr/86Sr ratios indicate that most of the anhydrite formed from ~2:1 mixture of seawater and black smoker fluids (65%±15% seawater). Oxygen-isotopic compositions imply that anhydrite precipitated at temperatures between 147°C and 270°C and require that seawater was conductively heated to between 100°C and 180°C before mixing and precipitation occurred. Anhydrite from the TAG mound has a Sr-Ca partition coefficient Kd ~0.60±0.28 (2 sigma). This value is in agreement with the range of experimentally determined partition coefficients (Kd ~0.27-0.73) and is similar to those calculated for anhydrite from active black smoker chimneys from 21°N on the East Pacific Rise. The d18O (for SO4) of TAG anhydrite brackets the value of seawater sulfate oxygen (~9.5?). Dissolution of anhydrite back into the oceans during episodes of hydrothermal quiescence provides a mechanism of buffering seawater sulfate oxygen to an isotopically light composition, in addition to the precipitation and dissolution of anhydrite within the oceanic basement during hydrothermal recharge at the mid-ocean ridges.

Middle Miocene to Quaternary diatom biostratigraphy of DSDP Site 90-594

A diatom biostratigraphy is presented for middle Miocene through Quaternary sediments recovered from the Chatham Rise east of New Zealand's South Island. The upper 590 m of the 639.5-m composite-section Site 594 represents approximately 16 m.y. and is characterized by moderately to very poorly preserved diatoms of antarctic to temperate affinity. Pliocene through Quaternary assemblages are poorly preserved and dominated by antarctic-subantarctic species which provide detailed biostratigraphic control. Recognized are 11 of 14 zones of the middle upper Miocene to Quaternary Neogene Southern Ocean diatom zonation (NSD 7-NSD 20) of Ciesielski (1983; this chapter). Four Neogene Southern Ocean diatom zones (NSD 3-NSD 6) are recognized in the lower middle Miocene to middle upper Miocene of Site 594. Assemblages of this interval have a mixed high-latitude and temperate affinity; however, poor preservation limits correlation to high- and temperate-latitude zonal schemes. Neogene North Pacific diatom zones and subzones of NNPD 3 through NNPD 5 (Barron, in press, b) are correlated to Neogene Southern Ocean diatom zones NSD 3 through NSD 7: the upper portions of the Actinocyclus ingens Zone (NNPD 3) is correlative to the upper Nitzschia maleinterpretaria Zone (NSD 3); the Denticulopsis lauta Zone (NNPD 4) and Subzones a and b are correlative to the lower Coscinodiscus lewisianus Zone (NSD 4); and the D. hustedtü-D. lauta Zone (NNPD 5) and its Subzones a through d encompass the upper C. lewisianus Zone (NSD 4), N. grossepunctata Zone (NSD 5), N. denticuloides Zone (NSD 6), and the lower D. hustedtii-D. lauta Zone (NSD 7). A major disconformity spans the late Gilbert to early Gauss Chron (3.9-2.8 Ma). A second disconformity brackets the Miocene/Pliocene boundary; the section missing covers late Chron 5 and the early Gilbert chron (5.5-4.6 Ma). The remainder of the siliceous-fossil-bearing Miocene sediments at Site 594 appear to be correlative to lower paleomagnetic Chronozone 5 through upper Chronozone 16. Uppermost lower Miocene or lowermost middle Miocene sediments in the basal 50 m of Hole 594A are barren of diatoms.

Core alignment and composite depth scale of DSDP Site 86-577

Deep Sea Drilling Project Site 577 on Shatsky Rise (North Pacific Ocean) recovered a series of cores at three holes that contain calcareous nannofossil ooze of latest Cretaceous (late Maastrichtian) through early Eocene age. Several important records have been generated using samples from these cores, but the stratigraphy has remained outdated and confusing. Here we revise the stratigraphy at Site 577. This includes refining several age datums, realigning cores in the depth domain, and placing all stratigraphic markers on a current time scale. The work provides a template for appropriately bringing latest Cretaceous and Paleogene data sets at old drill sites into current paleoceanographic literature for this time interval. While the Paleocene Eocene Thermal Maximum (PETM) lies within core gaps at Holes 577* and 577A, the sedimentary record at the site holds other important events and remains crucially relevant to understanding changes in oceanographic conditions from the latest Cretaceous through early Paleogene.

Geochemistry of ocean floor and forearc serpentinites

We provide new insights into the geochemistry of serpentinites from mid-ocean ridges (Mid-Atlantic Ridge and Hess Deep), passive margins (Iberia Abyssal Plain and Newfoundland) and fore-arcs (Mariana and Guatemala) based on bulk-rock and in situ mineral major and trace element compositional data collected on drill cores from the Deep Sea Drilling Project and Ocean Drilling Program. These data are important for constraining the serpentinite-hosted trace element inventory of subduction zones. Bulk serpentinites show up to several orders of magnitude enrichments in Cl, B, Sr, U, Sb, Pb, Rb, Cs and Li relative to elements of similar compatibility during mantle melting, which correspond to the highest primitive mantle-normalized B/Nb, B/Th, U/Th, Sb/Ce, Sr/Nd and Li/Y among subducted lithologies of the oceanic lithosphere (serpentinites, sediments and altered igneous oceanic crust). Among the elements showing relative enrichment, Cl and B are by far the most abundant with bulk concentrations mostly above 1000 µg/g and 30 µg/g, respectively. All other trace elements showing relative enrichments are generally present in low concentrations (µg/g level), except Sr in carbonate-bearing serpentinites (thousands of µg/g). In situ data indicate that concentrations of Cl, B, Sr, U, Sb, Rb and Cs are, and that of Li can be, increased by serpentinization. These elements are largely hosted in serpentine (lizardite and chrysotile, but not antigorite). Aragonite precipitation leads to significant enrichments in Sr, U and B, whereas calcite is important only as an Sr host. Commonly observed brucite is trace element-poor. The overall enrichment patterns are comparable among serpentinites from mid-ocean ridges, passive margins and fore-arcs, whereas the extents of enrichments are often specific to the geodynamic setting. Variability in relative trace element enrichments within a specific setting (and locality) can be several orders of magnitude. Mid-ocean ridge serpentinites often show pronounced bulk-rock U enrichment in addition to ubiquitous Cl, B and Sr enrichment. They also exhibit positive Eu anomalies on chondrite-normalized rare earth element plots. Passive margin serpentinites tend to have higher overall incompatible trace element contents than mid-ocean ridge and fore-arc serpentinites and show the highest B enrichment among all the studied serpentinites. Fore-arc serpentinites are characterized by low overall trace element contents and show the lowest Cl, but the highest Rb, Cs and Sr enrichments. Based on our data, subducted dehydrating serpentinites are likely to release fluids with high B/Nb, B/Th, U/Th, Sb/Ce and Sr/Nd, rendering them one of the potential sources of some of the characteristic trace element fingerprints of arc magmas (e.g. high B/Nb, high Sr/Nd, high Sb/Ce). However, although serpentinites are a substantial part of global subduction zone chemical cycling, owing to their low overall trace element contents (except for B and Cl) their geochemical imprint on arc magma sources (apart from addition of H2O, B and Cl) can be masked considerably by the trace element signal from subducted crustal components.

C and H geochemistry of altered oceanic crus of ODP/IODP Hole 1256D

Carbon and hydrogen concentrations and isotopic compositions were measured in 19 samples from altered oceanic crust cored in ODP/IODP Hole 1256D through lavas, dikes down to the gabbroic rocks. Bulk water content varies from 0.32 to 2.14 wt% with dD values from -64per mil to -25per mil. All samples are enriched in water relative to fresh basalts. The dD values are interpreted in terms of mixing between magmatic water and another source that can be either secondary hydrous minerals and/or H contained in organic compounds such as hydrocarbons. Total CO2, extracted by step-heating technique, ranges between 564 and 2823 ppm with d13C values from -14.9per mil to -26.6per mil. As for water, these altered samples are enriched in carbon relative to fresh basalts. The carbon isotope compositions are interpreted in terms of a mixing between two components: (1) a carbonate with d13C = -4.5per mil and (2) an organic compound with d13C = -26.6per mil. A mixing model calculation indicates that, for most samples (17 of 19), more than 75% of the total C occurs as organic compounds while carbonates represent less than 25%. This result is also supported by independent estimates of carbonate content from CO2 yield after H3PO4 attack. A comparison between the carbon concentration in our samples, seawater DIC (Dissolved Inorganic Carbon) and DOC (Dissolved Organic Carbon), and hydrothermal fluids suggests that CO2 degassed from magmatic reservoirs is the main source of organic C addition to the crust during the alteration process. A reduction step of dissolved CO2 is thus required, and can be either biologically mediated or not. Abiotic processes are necessary for the deeper part of the crust (>1000 mbsf) because alteration temperatures are greater than any hyperthermophilic living organism (i.e. T > 110 °C). Even if not required, we cannot rule out the contribution of microbial activity in the low-temperature alteration zones. We propose a two-step model for carbon cycling during crustal alteration: (1) when "fresh" oceanic crust forms at or close to ridge axis, alteration starts with hot hydrothermal fluids enriched in magmatic CO2, leading to the formation of organic compounds during Fischer-Tropsch-type reactions; (2) when the crust moves away from the ridge axis, these interactions with hot hydrothermal fluids decrease and are replaced by seawater interactions with carbonate precipitation in fractures. Taking into account this organic carbon, we estimate C isotope composition of mean altered oceanic crust at ? -4.7per mil, similar to the d13C of the C degassed from the mantle at ridge axis, and discuss the global carbon budget. The total flux of C stored in the altered oceanic crust, as carbonate and organic compound, is 2.9 ± 0.4 * 10**12 molC/yr.

Chemistry of fluid inclusions in rock samples from Dronning Maud Land

Dense, CO2-rich fluid inclusions hosted by plagioclases, An45 to An54, of the O.-v.-Gruber- Anorthosite body, central Dronning Maud Land, East Antarctica, contain varying amounts of small calcite, paragonite and pyrophyllite crystals detected by Raman microspectroscopy. These crystals are reaction products that have formed during cooling of the host and the original CO2-rich H2O-bearing enclosed fluid. Variable amounts of these reaction products illustrates that the reaction did not take place uniformly in all fluid inclusions, possibly due to differences in kinetics as caused by differences in shape and size, or due to compositional variation in the originally trapped fluid. The reaction albite + 2anorthite + 2H2O + 2CO2 = pyrophyllite + paragonite + 2calcite was thermodynamically modelled with consideration of different original fluid compositions. Although free H2O is not detectable in most fluid inclusions, the occurrence of OH-bearing sheet silicates indicates that the original fluid was not pure CO2, but contained significant amounts of H2O. Compared to an actual fluid inclusion it is obvious, that volume estimations of solid phases can be used as a starting point to reverse the retrograde reaction and recalculate the compositional and volumetrical properties of the original fluid. Isochores for an unmodified inclusion can thus be reconstructed, leading to a more realistic estimation of P-T conditions during earlier metamorphic stages or fluid capturing.

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Caracterización de un robot para aplicaciones de mecanizado con requerimientos de tolerancias

El presente Trabajo fin Fin de Máster, versa sobre una caracterización preliminar del comportamiento de un robot de tipo industrial, configurado por 4 eslabones y 4 grados de libertad, y sometido a fuerzas de mecanizado en su extremo. El entorno de trabajo planteado es el de plantas de fabricación de piezas de aleaciones de aluminio para automoción. Este tipo de componentes parte de un primer proceso de fundición que saca la pieza en bruto. Para series medias y altas, en función de las propiedades mecánicas y plásticas requeridas y los costes de producción, la inyección a alta presión (HPDC) y la fundición a baja presión (LPC) son las dos tecnologías más usadas en esta primera fase. Para inyección a alta presión, las aleaciones de aluminio más empleadas son, en designación simbólica según norma EN 1706 (entre paréntesis su designación numérica); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). Para baja presión, EN AC AlSi7Mg0,3 (EN AC 42100). En los 3 primeros casos, los límites de Silicio permitidos pueden superan el 10%. En el cuarto caso, es inferior al 10% por lo que, a los efectos de ser sometidas a mecanizados, las piezas fabricadas en aleaciones con Si superior al 10%, se puede considerar que son equivalentes, diferenciándolas de la cuarta. Las tolerancias geométricas y dimensionales conseguibles directamente de fundición, recogidas en normas como ISO 8062 o DIN 1688-1, establecen límites para este proceso. Fuera de esos límites, las garantías en conseguir producciones con los objetivos de ppms aceptados en la actualidad por el mercado, obligan a ir a fases posteriores de mecanizado. Aquellas geometrías que, funcionalmente, necesitan disponer de unas tolerancias geométricas y/o dimensionales definidas acorde a ISO 1101, y no capaces por este proceso inicial de moldeado a presión, deben ser procesadas en una fase posterior en células de mecanizado. En este caso, las tolerancias alcanzables para procesos de arranque de viruta se recogen en normas como ISO 2768. Las células de mecanizado se componen, por lo general, de varios centros de control numérico interrelacionados y comunicados entre sí por robots que manipulan las piezas en proceso de uno a otro. Dichos robots, disponen en su extremo de una pinza utillada para poder coger y soltar las piezas en los útiles de mecanizado, las mesas de intercambio para cambiar la pieza de posición o en utillajes de equipos de medición y prueba, o en cintas de entrada o salida. La repetibilidad es alta, de centésimas incluso, definida según norma ISO 9283. El problema es que, estos rangos de repetibilidad sólo se garantizan si no se hacen esfuerzos o éstos son despreciables (caso de mover piezas). Aunque las inercias de mover piezas a altas velocidades hacen que la trayectoria intermedia tenga poca precisión, al inicio y al final (al coger y dejar pieza, p.e.) se hacen a velocidades relativamente bajas que hacen que el efecto de las fuerzas de inercia sean menores y que permiten garantizar la repetibilidad anteriormente indicada. No ocurre así si se quitara la garra y se intercambia con un cabezal motorizado con una herramienta como broca, mandrino, plato de cuchillas, fresas frontales o tangenciales… Las fuerzas ejercidas de mecanizado generarían unos pares en las uniones tan grandes y tan variables que el control del robot no sería capaz de responder (o no está preparado, en un principio) y generaría una desviación en la trayectoria, realizada a baja velocidad, que desencadenaría en un error de posición (ver norma ISO 5458) no asumible para la funcionalidad deseada. Se podría llegar al caso de que la tolerancia alcanzada por un pretendido proceso más exacto diera una dimensión peor que la que daría el proceso de fundición, en principio con mayor variabilidad dimensional en proceso (y por ende con mayor intervalo de tolerancia garantizable). De hecho, en los CNCs, la precisión es muy elevada, (pudiéndose despreciar en la mayoría de los casos) y no es la responsable de, por ejemplo la tolerancia de posición al taladrar un agujero. Factores como, temperatura de la sala y de la pieza, calidad constructiva de los utillajes y rigidez en el amarre, error en el giro de mesas y de colocación de pieza, si lleva agujeros previos o no, si la herramienta está bien equilibrada y el cono es el adecuado para el tipo de mecanizado… influyen más. Es interesante que, un elemento no específico tan común en una planta industrial, en el entorno anteriormente descrito, como es un robot, el cual no sería necesario añadir por disponer de él ya (y por lo tanto la inversión sería muy pequeña), puede mejorar la cadena de valor disminuyendo el costo de fabricación. Y si se pudiera conjugar que ese robot destinado a tareas de manipulación, en los muchos tiempos de espera que va a disfrutar mientras el CNC arranca viruta, pudiese coger un cabezal y apoyar ese mecanizado; sería doblemente interesante. Por lo tanto, se antoja sugestivo poder conocer su comportamiento e intentar explicar qué sería necesario para llevar esto a cabo, motivo de este trabajo. La arquitectura de robot seleccionada es de tipo SCARA. La búsqueda de un robot cómodo de modelar y de analizar cinemática y dinámicamente, sin limitaciones relevantes en la multifuncionalidad de trabajos solicitados, ha llevado a esta elección, frente a otras arquitecturas como por ejemplo los robots antropomórficos de 6 grados de libertad, muy populares a nivel industrial. Este robot dispone de 3 uniones, de las cuales 2 son de tipo par de revolución (1 grado de libertad cada una) y la tercera es de tipo corredera o par cilíndrico (2 grados de libertad). La primera unión, de tipo par de revolución, sirve para unir el suelo (considerado como eslabón número 1) con el eslabón número 2. La segunda unión, también de ese tipo, une el eslabón número 2 con el eslabón número 3. Estos 2 brazos, pueden describir un movimiento horizontal, en el plano X-Y. El tercer eslabón, está unido al eslabón número 4 por la unión de tipo corredera. El movimiento que puede describir es paralelo al eje Z. El robot es de 4 grados de libertad (4 motores). En relación a los posibles trabajos que puede realizar este tipo de robot, su versatilidad abarca tanto operaciones típicas de manipulación como operaciones de arranque de viruta. Uno de los mecanizados más usuales es el taladrado, por lo cual se elige éste para su modelización y análisis. Dentro del taladrado se elegirá para acotar las fuerzas, taladrado en macizo con broca de diámetro 9 mm. El robot se ha considerado por el momento que tenga comportamiento de sólido rígido, por ser el mayor efecto esperado el de los pares en las uniones. Para modelar el robot se utiliza el método de los sistemas multicuerpos. Dentro de este método existen diversos tipos de formulaciones (p.e. Denavit-Hartenberg). D-H genera una cantidad muy grande de ecuaciones e incógnitas. Esas incógnitas son de difícil comprensión y, para cada posición, hay que detenerse a pensar qué significado tienen. Se ha optado por la formulación de coordenadas naturales. Este sistema utiliza puntos y vectores unitarios para definir la posición de los distintos cuerpos, y permite compartir, cuando es posible y se quiere, para definir los pares cinemáticos y reducir al mismo tiempo el número de variables. Las incógnitas son intuitivas, las ecuaciones de restricción muy sencillas y se reduce considerablemente el número de ecuaciones e incógnitas. Sin embargo, las coordenadas naturales “puras” tienen 2 problemas. El primero, que 2 elementos con un ángulo de 0 o 180 grados, dan lugar a puntos singulares que pueden crear problemas en las ecuaciones de restricción y por lo tanto han de evitarse. El segundo, que tampoco inciden directamente sobre la definición o el origen de los movimientos. Por lo tanto, es muy conveniente complementar esta formulación con ángulos y distancias (coordenadas relativas). Esto da lugar a las coordenadas naturales mixtas, que es la formulación final elegida para este TFM. Las coordenadas naturales mixtas no tienen el problema de los puntos singulares. Y la ventaja más importante reside en su utilidad a la hora de aplicar fuerzas motrices, momentos o evaluar errores. Al incidir sobre la incógnita origen (ángulos o distancias) controla los motores de manera directa. El algoritmo, la simulación y la obtención de resultados se ha programado mediante Matlab. Para realizar el modelo en coordenadas naturales mixtas, es preciso modelar en 2 pasos el robot a estudio. El primer modelo se basa en coordenadas naturales. Para su validación, se plantea una trayectoria definida y se analiza cinemáticamente si el robot satisface el movimiento solicitado, manteniendo su integridad como sistema multicuerpo. Se cuantifican los puntos (en este caso inicial y final) que configuran el robot. Al tratarse de sólidos rígidos, cada eslabón queda definido por sus respectivos puntos inicial y final (que son los más interesantes para la cinemática y la dinámica) y por un vector unitario no colineal a esos 2 puntos. Los vectores unitarios se colocan en los lugares en los que se tenga un eje de rotación o cuando se desee obtener información de un ángulo. No son necesarios vectores unitarios para medir distancias. Tampoco tienen por qué coincidir los grados de libertad con el número de vectores unitarios. Las longitudes de cada eslabón quedan definidas como constantes geométricas. Se establecen las restricciones que definen la naturaleza del robot y las relaciones entre los diferentes elementos y su entorno. La trayectoria se genera por una nube de puntos continua, definidos en coordenadas independientes. Cada conjunto de coordenadas independientes define, en un instante concreto, una posición y postura de robot determinada. Para conocerla, es necesario saber qué coordenadas dependientes hay en ese instante, y se obtienen resolviendo por el método de Newton-Rhapson las ecuaciones de restricción en función de las coordenadas independientes. El motivo de hacerlo así es porque las coordenadas dependientes deben satisfacer las restricciones, cosa que no ocurre con las coordenadas independientes. Cuando la validez del modelo se ha probado (primera validación), se pasa al modelo 2. El modelo número 2, incorpora a las coordenadas naturales del modelo número 1, las coordenadas relativas en forma de ángulos en los pares de revolución (3 ángulos; ϕ1, ϕ 2 y ϕ3) y distancias en los pares prismáticos (1 distancia; s). Estas coordenadas relativas pasan a ser las nuevas coordenadas independientes (sustituyendo a las coordenadas independientes cartesianas del modelo primero, que eran coordenadas naturales). Es necesario revisar si el sistema de vectores unitarios del modelo 1 es suficiente o no. Para este caso concreto, se han necesitado añadir 1 vector unitario adicional con objeto de que los ángulos queden perfectamente determinados con las correspondientes ecuaciones de producto escalar y/o vectorial. Las restricciones habrán de ser incrementadas en, al menos, 4 ecuaciones; una por cada nueva incógnita. La validación del modelo número 2, tiene 2 fases. La primera, al igual que se hizo en el modelo número 1, a través del análisis cinemático del comportamiento con una trayectoria definida. Podrían obtenerse del modelo 2 en este análisis, velocidades y aceleraciones, pero no son necesarios. Tan sólo interesan los movimientos o desplazamientos finitos. Comprobada la coherencia de movimientos (segunda validación), se pasa a analizar cinemáticamente el comportamiento con trayectorias interpoladas. El análisis cinemático con trayectorias interpoladas, trabaja con un número mínimo de 3 puntos máster. En este caso se han elegido 3; punto inicial, punto intermedio y punto final. El número de interpolaciones con el que se actúa es de 50 interpolaciones en cada tramo (cada 2 puntos máster hay un tramo), resultando un total de 100 interpolaciones. El método de interpolación utilizado es el de splines cúbicas con condición de aceleración inicial y final constantes, que genera las coordenadas independientes de los puntos interpolados de cada tramo. Las coordenadas dependientes se obtienen resolviendo las ecuaciones de restricción no lineales con el método de Newton-Rhapson. El método de las splines cúbicas es muy continuo, por lo que si se desea modelar una trayectoria en el que haya al menos 2 movimientos claramente diferenciados, es preciso hacerlo en 2 tramos y unirlos posteriormente. Sería el caso en el que alguno de los motores se desee expresamente que esté parado durante el primer movimiento y otro distinto lo esté durante el segundo movimiento (y así sucesivamente). Obtenido el movimiento, se calculan, también mediante fórmulas de diferenciación numérica, las velocidades y aceleraciones independientes. El proceso es análogo al anteriormente explicado, recordando la condición impuesta de que la aceleración en el instante t= 0 y en instante t= final, se ha tomado como 0. Las velocidades y aceleraciones dependientes se calculan resolviendo las correspondientes derivadas de las ecuaciones de restricción. Se comprueba, de nuevo, en una tercera validación del modelo, la coherencia del movimiento interpolado. La dinámica inversa calcula, para un movimiento definido -conocidas la posición, velocidad y la aceleración en cada instante de tiempo-, y conocidas las fuerzas externas que actúan (por ejemplo el peso); qué fuerzas hay que aplicar en los motores (donde hay control) para que se obtenga el citado movimiento. En la dinámica inversa, cada instante del tiempo es independiente de los demás y tiene una posición, una velocidad y una aceleración y unas fuerzas conocidas. En este caso concreto, se desean aplicar, de momento, sólo las fuerzas debidas al peso, aunque se podrían haber incorporado fuerzas de otra naturaleza si se hubiese deseado. Las posiciones, velocidades y aceleraciones, proceden del cálculo cinemático. El efecto inercial de las fuerzas tenidas en cuenta (el peso) es calculado. Como resultado final del análisis dinámico inverso, se obtienen los pares que han de ejercer los cuatro motores para replicar el movimiento prescrito con las fuerzas que estaban actuando. La cuarta validación del modelo consiste en confirmar que el movimiento obtenido por aplicar los pares obtenidos en la dinámica inversa, coinciden con el obtenido en el análisis cinemático (movimiento teórico). Para ello, es necesario acudir a la dinámica directa. La dinámica directa se encarga de calcular el movimiento del robot, resultante de aplicar unos pares en motores y unas fuerzas en el robot. Por lo tanto, el movimiento real resultante, al no haber cambiado ninguna condición de las obtenidas en la dinámica inversa (pares de motor y fuerzas inerciales debidas al peso de los eslabones) ha de ser el mismo al movimiento teórico. Siendo así, se considera que el robot está listo para trabajar. Si se introduce una fuerza exterior de mecanizado no contemplada en la dinámica inversa y se asigna en los motores los mismos pares resultantes de la resolución del problema dinámico inverso, el movimiento real obtenido no es igual al movimiento teórico. El control de lazo cerrado se basa en ir comparando el movimiento real con el deseado e introducir las correcciones necesarias para minimizar o anular las diferencias. Se aplican ganancias en forma de correcciones en posición y/o velocidad para eliminar esas diferencias. Se evalúa el error de posición como la diferencia, en cada punto, entre el movimiento teórico deseado en el análisis cinemático y el movimiento real obtenido para cada fuerza de mecanizado y una ganancia concreta. Finalmente, se mapea el error de posición obtenido para cada fuerza de mecanizado y las diferentes ganancias previstas, graficando la mejor precisión que puede dar el robot para cada operación que se le requiere, y en qué condiciones. -------------- This Master´s Thesis deals with a preliminary characterization of the behaviour for an industrial robot, configured with 4 elements and 4 degrees of freedoms, and subjected to machining forces at its end. Proposed working conditions are those typical from manufacturing plants with aluminium alloys for automotive industry. This type of components comes from a first casting process that produces rough parts. For medium and high volumes, high pressure die casting (HPDC) and low pressure die casting (LPC) are the most used technologies in this first phase. For high pressure die casting processes, most used aluminium alloys are, in simbolic designation according EN 1706 standard (between brackets, its numerical designation); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). For low pressure, EN AC AlSi7Mg0,3 (EN AC 42100). For the 3 first alloys, Si allowed limits can exceed 10% content. Fourth alloy has admisible limits under 10% Si. That means, from the point of view of machining, that components made of alloys with Si content above 10% can be considered as equivalent, and the fourth one must be studied separately. Geometrical and dimensional tolerances directly achievables from casting, gathered in standards such as ISO 8062 or DIN 1688-1, establish a limit for this process. Out from those limits, guarantees to achieve batches with objetive ppms currently accepted by market, force to go to subsequent machining process. Those geometries that functionally require a geometrical and/or dimensional tolerance defined according ISO 1101, not capable with initial moulding process, must be obtained afterwards in a machining phase with machining cells. In this case, tolerances achievables with cutting processes are gathered in standards such as ISO 2768. In general terms, machining cells contain several CNCs that they are interrelated and connected by robots that handle parts in process among them. Those robots have at their end a gripper in order to take/remove parts in machining fixtures, in interchange tables to modify position of part, in measurement and control tooling devices, or in entrance/exit conveyors. Repeatibility for robot is tight, even few hundredths of mm, defined according ISO 9283. Problem is like this; those repeatibilty ranks are only guaranteed when there are no stresses or they are not significant (f.e. due to only movement of parts). Although inertias due to moving parts at a high speed make that intermediate paths have little accuracy, at the beginning and at the end of trajectories (f.e, when picking part or leaving it) movement is made with very slow speeds that make lower the effect of inertias forces and allow to achieve repeatibility before mentioned. It does not happens the same if gripper is removed and it is exchanged by an spindle with a machining tool such as a drilling tool, a pcd boring tool, a face or a tangential milling cutter… Forces due to machining would create such big and variable torques in joints that control from the robot would not be able to react (or it is not prepared in principle) and would produce a deviation in working trajectory, made at a low speed, that would trigger a position error (see ISO 5458 standard) not assumable for requested function. Then it could be possible that tolerance achieved by a more exact expected process would turn out into a worst dimension than the one that could be achieved with casting process, in principle with a larger dimensional variability in process (and hence with a larger tolerance range reachable). As a matter of fact, accuracy is very tight in CNC, (its influence can be ignored in most cases) and it is not the responsible of, for example position tolerance when drilling a hole. Factors as, room and part temperature, manufacturing quality of machining fixtures, stiffness at clamping system, rotating error in 4th axis and part positioning error, if there are previous holes, if machining tool is properly balanced, if shank is suitable for that machining type… have more influence. It is interesting to know that, a non specific element as common, at a manufacturing plant in the enviroment above described, as a robot (not needed to be added, therefore with an additional minimum investment), can improve value chain decreasing manufacturing costs. And when it would be possible to combine that the robot dedicated to handling works could support CNCs´ works in its many waiting time while CNCs cut, and could take an spindle and help to cut; it would be double interesting. So according to all this, it would be interesting to be able to know its behaviour and try to explain what would be necessary to make this possible, reason of this work. Selected robot architecture is SCARA type. The search for a robot easy to be modeled and kinematically and dinamically analyzed, without significant limits in the multifunctionality of requested operations, has lead to this choice. Due to that, other very popular architectures in the industry, f.e. 6 DOFs anthropomorphic robots, have been discarded. This robot has 3 joints, 2 of them are revolute joints (1 DOF each one) and the third one is a cylindrical joint (2 DOFs). The first joint, a revolute one, is used to join floor (body 1) with body 2. The second one, a revolute joint too, joins body 2 with body 3. These 2 bodies can move horizontally in X-Y plane. Body 3 is linked to body 4 with a cylindrical joint. Movement that can be made is paralell to Z axis. The robt has 4 degrees of freedom (4 motors). Regarding potential works that this type of robot can make, its versatility covers either typical handling operations or cutting operations. One of the most common machinings is to drill. That is the reason why it has been chosen for the model and analysis. Within drilling, in order to enclose spectrum force, a typical solid drilling with 9 mm diameter. The robot is considered, at the moment, to have a behaviour as rigid body, as biggest expected influence is the one due to torques at joints. In order to modelize robot, it is used multibodies system method. There are under this heading different sorts of formulations (f.e. Denavit-Hartenberg). D-H creates a great amount of equations and unknown quantities. Those unknown quatities are of a difficult understanding and, for each position, one must stop to think about which meaning they have. The choice made is therefore one of formulation in natural coordinates. This system uses points and unit vectors to define position of each different elements, and allow to share, when it is possible and wished, to define kinematic torques and reduce number of variables at the same time. Unknown quantities are intuitive, constrain equations are easy and number of equations and variables are strongly reduced. However, “pure” natural coordinates suffer 2 problems. The first one is that 2 elements with an angle of 0° or 180°, give rise to singular positions that can create problems in constrain equations and therefore they must be avoided. The second problem is that they do not work directly over the definition or the origin of movements. Given that, it is highly recommended to complement this formulation with angles and distances (relative coordinates). This leads to mixed natural coordinates, and they are the final formulation chosen for this MTh. Mixed natural coordinates have not the problem of singular positions. And the most important advantage lies in their usefulness when applying driving forces, torques or evaluating errors. As they influence directly over origin variable (angles or distances), they control motors directly. The algorithm, simulation and obtaining of results has been programmed with Matlab. To design the model in mixed natural coordinates, it is necessary to model the robot to be studied in 2 steps. The first model is based in natural coordinates. To validate it, it is raised a defined trajectory and it is kinematically analyzed if robot fulfils requested movement, keeping its integrity as multibody system. The points (in this case starting and ending points) that configure the robot are quantified. As the elements are considered as rigid bodies, each of them is defined by its respectively starting and ending point (those points are the most interesting ones from the point of view of kinematics and dynamics) and by a non-colinear unit vector to those points. Unit vectors are placed where there is a rotating axis or when it is needed information of an angle. Unit vectors are not needed to measure distances. Neither DOFs must coincide with the number of unit vectors. Lengths of each arm are defined as geometrical constants. The constrains that define the nature of the robot and relationships among different elements and its enviroment are set. Path is generated by a cloud of continuous points, defined in independent coordinates. Each group of independent coordinates define, in an specific instant, a defined position and posture for the robot. In order to know it, it is needed to know which dependent coordinates there are in that instant, and they are obtained solving the constraint equations with Newton-Rhapson method according to independent coordinates. The reason to make it like this is because dependent coordinates must meet constraints, and this is not the case with independent coordinates. When suitability of model is checked (first approval), it is given next step to model 2. Model 2 adds to natural coordinates from model 1, the relative coordinates in the shape of angles in revoluting torques (3 angles; ϕ1, ϕ 2 and ϕ3) and distances in prismatic torques (1 distance; s). These relative coordinates become the new independent coordinates (replacing to cartesian independent coordinates from model 1, that they were natural coordinates). It is needed to review if unit vector system from model 1 is enough or not . For this specific case, it was necessary to add 1 additional unit vector to define perfectly angles with their related equations of dot and/or cross product. Constrains must be increased in, at least, 4 equations; one per each new variable. The approval of model 2 has two phases. The first one, same as made with model 1, through kinematic analysis of behaviour with a defined path. During this analysis, it could be obtained from model 2, velocities and accelerations, but they are not needed. They are only interesting movements and finite displacements. Once that the consistence of movements has been checked (second approval), it comes when the behaviour with interpolated trajectories must be kinematically analyzed. Kinematic analysis with interpolated trajectories work with a minimum number of 3 master points. In this case, 3 points have been chosen; starting point, middle point and ending point. The number of interpolations has been of 50 ones in each strecht (each 2 master points there is an strecht), turning into a total of 100 interpolations. The interpolation method used is the cubic splines one with condition of constant acceleration both at the starting and at the ending point. This method creates the independent coordinates of interpolated points of each strecht. The dependent coordinates are achieved solving the non-linear constrain equations with Newton-Rhapson method. The method of cubic splines is very continuous, therefore when it is needed to design a trajectory in which there are at least 2 movements clearly differents, it is required to make it in 2 steps and join them later. That would be the case when any of the motors would keep stopped during the first movement, and another different motor would remain stopped during the second movement (and so on). Once that movement is obtained, they are calculated, also with numerical differenciation formulas, the independent velocities and accelerations. This process is analogous to the one before explained, reminding condition that acceleration when t=0 and t=end are 0. Dependent velocities and accelerations are calculated solving related derivatives of constrain equations. In a third approval of the model it is checked, again, consistence of interpolated movement. Inverse dynamics calculates, for a defined movement –knowing position, velocity and acceleration in each instant of time-, and knowing external forces that act (f.e. weights); which forces must be applied in motors (where there is control) in order to obtain requested movement. In inverse dynamics, each instant of time is independent of the others and it has a position, a velocity, an acceleration and known forces. In this specific case, it is intended to apply, at the moment, only forces due to the weight, though forces of another nature could have been added if it would have been preferred. The positions, velocities and accelerations, come from kinematic calculation. The inertial effect of forces taken into account (weight) is calculated. As final result of the inverse dynamic analysis, the are obtained torques that the 4 motors must apply to repeat requested movement with the forces that were acting. The fourth approval of the model consists on confirming that the achieved movement due to the use of the torques obtained in the inverse dynamics, are in accordance with movements from kinematic analysis (theoretical movement). For this, it is necessary to work with direct dynamics. Direct dynamic is in charge of calculating the movements of robot that results from applying torques at motors and forces at the robot. Therefore, the resultant real movement, as there was no change in any condition of the ones obtained at the inverse dynamics (motor torques and inertial forces due to weight of elements) must be the same than theoretical movement. When these results are achieved, it is considered that robot is ready to work. When a machining external force is introduced and it was not taken into account before during the inverse dynamics, and torques at motors considered are the ones of the inverse dynamics, the real movement obtained is not the same than the theoretical movement. Closed loop control is based on comparing real movement with expected movement and introducing required corrrections to minimize or cancel differences. They are applied gains in the way of corrections for position and/or tolerance to remove those differences. Position error is evaluated as the difference, in each point, between theoretical movemment (calculated in the kinematic analysis) and the real movement achieved for each machining force and for an specific gain. Finally, the position error obtained for each machining force and gains are mapped, giving a chart with the best accuracy that the robot can give for each operation that has been requested and which conditions must be provided.