Design and kinematic analysis of 3PSS-1S wrist for needle insertion guidance

In this work it is presented a complete kinematic analysis of the 3PSS-1S parallel mechanism for its implementation as a spherical wrist for a needle insertion guidance robot. The spherical 3PSS-1S mechanism is a low weight and reduced dimension parallel mechanism that allows spherical movements providing the requirements needed for the serial–parallel robotic arm for needle insertion guidance. The solution of its direct kinematic is computed with a numerical method based on the Newton–Raphson formulation and a constraint function of the mechanism. The input–output velocity equation is obtained with the use of screw theory. Three types of singular postures are identified during simulations and verified in the real prototype. The 3PSS-1S can perform pure rotations of ±45°±45°, ±40°±40°, ±60°±60° along the View the MathML sourcex, View the MathML sourcey, View the MathML sourcez axes respectively.

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.

Human-robot interaction for telemanipulation in large workspaces

Independientemente de la existencia de técnicas altamente sofisticadas y capacidades de cómputo cada vez más elevadas, los problemas asociados a los robots que interactúan con entornos no estructurados siguen siendo un desafío abierto en robótica. A pesar de los grandes avances de los sistemas robóticos autónomos, hay algunas situaciones en las que una persona en el bucle sigue siendo necesaria. Ejemplos de esto son, tareas en entornos de fusión nuclear, misiones espaciales, operaciones submarinas y cirugía robótica. Esta necesidad se debe a que las tecnologías actuales no pueden realizar de forma fiable y autónoma cualquier tipo de tarea. Esta tesis presenta métodos para la teleoperación de robots abarcando distintos niveles de abstracción que van desde el control supervisado, en el que un operador da instrucciones de alto nivel en la forma de acciones, hasta el control bilateral, donde los comandos toman la forma de señales de control de bajo nivel. En primer lugar, se presenta un enfoque para llevar a cabo la teleoperación supervisada de robots humanoides. El objetivo es controlar robots terrestres capaces de ejecutar tareas complejas en entornos de búsqueda y rescate utilizando enlaces de comunicación limitados. Esta propuesta incorpora comportamientos autónomos que el operador puede utilizar para realizar tareas de navegación y manipulación mientras se permite cubrir grandes áreas de entornos remotos diseñados para el acceso de personas. Los resultados experimentales demuestran la eficacia de los métodos propuestos. En segundo lugar, se investiga el uso de dispositivos rentables para telemanipulación guiada. Se presenta una aplicación que involucra un robot humanoide bimanual y un traje de captura de movimiento basado en sensores inerciales. En esta aplicación, se estudian las capacidades de adaptación introducidas por el factor humano y cómo estas pueden compensar la falta de sistemas robóticos de alta precisión. Este trabajo es el resultado de una colaboración entre investigadores del Biorobotics Laboratory de la Universidad de Harvard y el Centro de Automática y Robótica UPM-CSIC. En tercer lugar, se presenta un nuevo controlador háptico que combina velocidad y posición. Este controlador bilateral híbrido hace frente a los problemas relacionados con la teleoperación de un robot esclavo con un gran espacio de trabajo usando un dispositivo háptico pequeño como maestro. Se pueden cubrir amplias áreas de trabajo al cambiar automáticamente entre los modos de control de velocidad y posición. Este controlador háptico es ideal para sistemas maestro-esclavo con cinemáticas diferentes, donde los comandos se transmiten en el espacio de la tarea del entorno remoto. El método es validado para realizar telemanipulación hábil de objetos con un robot industrial. Por último, se introducen dos contribuciones en el campo de la manipulación robótica. Por un lado, se presenta un nuevo algoritmo de cinemática inversa, llamado método iterativo de desacoplamiento cinemático. Este método se ha desarrollado para resolver el problema cinemático inverso de un tipo de robot de seis grados de libertad donde una solución cerrada no está disponible. La eficacia del método se compara con métodos numéricos convencionales. Además, se ha diseñado una taxonomía robusta de agarres que permite controlar diferentes manos robóticas utilizando una correspondencia, basada en gestos, entre los espacios de trabajo de la mano humana y de la mano robótica. El gesto de la mano humana se identifica mediante la lectura de los movimientos relativos del índice, el pulgar y el dedo medio del usuario durante las primeras etapas del agarre. ABSTRACT Regardless of the availability of highly sophisticated techniques and ever increasing computing capabilities, the problems associated with robots interacting with unstructured environments remains an open challenge. Despite great advances in autonomous robotics, there are some situations where a humanin- the-loop is still required, such as, nuclear, space, subsea and robotic surgery operations. This is because the current technologies cannot reliably perform all kinds of task autonomously. This thesis presents methods for robot teleoperation strategies at different levels of abstraction ranging from supervisory control, where the operator gives high-level task actions, to bilateral teleoperation, where the commands take the form of low-level control inputs. These strategies contribute to improve the current human-robot interfaces specially in the case of slave robots deployed at large workspaces. First, an approach to perform supervisory teleoperation of humanoid robots is presented. The goal is to control ground robots capable of executing complex tasks in disaster relief environments under constrained communication links. This proposal incorporates autonomous behaviors that the operator can use to perform navigation and manipulation tasks which allow covering large human engineered areas of the remote environment. The experimental results demonstrate the efficiency of the proposed methods. Second, the use of cost-effective devices for guided telemanipulation is investigated. A case study involving a bimanual humanoid robot and an Inertial Measurement Unit (IMU) Motion Capture (MoCap) suit is introduced. Herein, it is corroborated how the adaptation capabilities offered by the human-in-the-loop factor can compensate for the lack of high-precision robotic systems. This work is the result of collaboration between researchers from the Harvard Biorobotics Laboratory and the Centre for Automation and Robotics UPM-CSIC. Thirdly, a new haptic rate-position controller is presented. This hybrid bilateral controller copes with the problems related to the teleoperation of a slave robot with large workspace using a small haptic device as master. Large workspaces can be covered by automatically switching between rate and position control modes. This haptic controller is ideal to couple kinematic dissimilar master-slave systems where the commands are transmitted in the task space of the remote environment. The method is validated to perform dexterous telemanipulation of objects with a robotic manipulator. Finally, two contributions for robotic manipulation are introduced. First, a new algorithm, the Iterative Kinematic Decoupling method, is presented. It is a numeric method developed to solve the Inverse Kinematics (IK) problem of a type of six-DoF robotic arms where a close-form solution is not available. The effectiveness of this IK method is compared against conventional numerical methods. Second, a robust grasp mapping has been conceived. It allows to control a wide range of different robotic hands using a gesture based correspondence between the human hand space and the robotic hand space. The human hand gesture is identified by reading the relative movements of the index, thumb and middle fingers of the user during the early stages of grasping.

Quantitative assessment based on kinematic measures of functional impairments during upper extremity movements: a review

Quantitative measures of human movement quality are important for discriminating healthy and pathological conditions and for expressing the outcomes and clinically important changes in subjects' functional state. However the most frequently used instruments for the upper extremity functional assessment are clinical scales, that previously have been standardized and validated, but have a high subjective component depending on the observer who scores the test. But they are not enough to assess motor strategies used during movements, and their use in combination with other more objective measures is necessary. The objective of the present review is to provide an overview on objective metrics found in literature with the aim of quantifying the upper extremity performance during functional tasks, regardless of the equipment or system used for registering kinematic data.

Effects of different swimming race constraints on turning movements

The aim of this study was to investigate the effects of different swimming race constraints on the evolution of turn parameters. One hundred and fifty-eight national and regional level 200-m (meters) male swimming performances were video-analyzed using the individualized-distance model in the Open Comunidad de Madrid tournament. Turn (p < .001, ES = 0.36) and underwater distances (p < .001, ES = 0.38) as well as turn velocity (p < .001, ES = 0.69) significantly dropped throughout the race, although stroke velocity and underwater velocity were maintained in the last lap of the race (p > .05). Higher expertise swimmers obtained faster average velocities and longer distances in all the turn phases (p < .001, ES = 0.59), except the approach distance. In addition, national level swimmers showed the ability to maintain most of the turn parameters throughout the race, which assisted them in improving average velocity at the end of races. Therefore, the variations in the turning movements of a swimming race were expertise-related and focused on optimizing average velocity. Turning skills should be included in the swimming race action plan.

Modeling and Simulation of Upper Brachial Plexus Injury

This article presents the first musculoskeletal model and simulation of upper plexus brachial injury. From this model is possible to analyse forces and movement ranges in order to develop a robotic exoskeleton to improve rehabilitation. The software that currently exists for musculoskeletal modeling is varied and most have advanced features for proper analysis and study of motion simulations. Whilst more powerful computer packages are usually expensive, there are other free and open source packages available which offer different tools to perform animations and simulations and which obtain forces and moments of inertia. Among them, Musculoskeletal Modeling Software was selected to construct a model of the upper limb, which has 7 degrees of freedom and 10 muscles. These muscles are important for two of the movements simulated in this article that are part of the post-surgery rehabilitation protocol. We performed different movement animations which are made using the inertial measurement unit to capture real data from movements made by a human being. We also performed the simulation of forces produced in elbow flexion-extension and arm abduction-adduction of a healthy subject and one with upper brachial plexus injury in a postoperative state to compare the force that is capable of being produced in both cases.

Morphogenetic movements at gastrulation require the SH2 tyrosine phosphatase Shp2

The SH2 domain-containing tyrosine phosphatase Shp2 plays a pivotal role during the gastrulation of vertebrate embryos. However, because of the complex phenotype observed in mouse mutant embryos, the precise role of Shp2 during development is unclear. To define the specific functions of this phosphatase, Shp2 homozygous mutant embryonic stem cells bearing the Rosa-26 LacZ transgene were isolated and used to perform a chimeric analysis. Here, we show that Shp2 mutant cells amass in the tail bud of embryonic day 10.5 chimeric mouse embryos and that this accumulation begins at the onset of gastrulation. At this early stage, Shp2 mutant cells collect in the primitive streak of the epiblast and thus show deficiencies in their contribution to the mesoderm lineage. In high-contribution chimeras, we show that overaccumulation of Shp2 mutant cells at the posterior end of the embryo results in two abnormal phenotypes: spina bifida and secondary neural tubes. Consistent with a failure to undergo morphogenic movements at gastrulation, Shp2 is required for embryo fibroblast cells to mount a positive chemotactic response to acidic fibroblast growth factor in vitro. Our results demonstrate that Shp2 is required at the initial steps of gastrulation, as nascent mesodermal cells form and migrate away from the primitive streak. The aberrant behavior of Shp2 mutant cells at gastrulation may result from their inability to properly respond to signals initiated by fibroblast growth factors.

Dynamic characteristics and adaptability of mouse vestibulo-ocular and optokinetic response eye movements and the role of the flocculo-olivary system revealed by chemical lesions

The dynamic characteristics of reflex eye movements were measured in two strains of chronically prepared mice by using an infrared television camera system. The horizontal vestibulo-ocular reflex (HVOR) and horizontal optokinetic response (HOKR) were induced by sinusoidal oscillations of a turntable, in darkness, by 10° (peak to peak) at 0.11–0.50 Hz and of a checked-pattern screen, in light, by 5–20°at 0.11–0.17 Hz, respectively. The gains and phases of the HVOR and HOKR of the C57BL/6 mice were nearly equivalent to those of rabbits and rats, whereas the 129/Sv mice exhibited very low gains in the HVOR and moderate phase lags in the HOKR, suggesting an inherent sensory-motor anomaly. Adaptability of the HOKR was examined in C57BL/6 mice by sustained screen oscillation. When the screen was oscillated by 10° at 0.17 Hz, which induced sufficient retinal slips, the gain of the HOKR increased by 0.08 in 1 h on average, whereas the stimuli that induced relatively small or no retinal slips affected the gain very little. Lesions of the flocculi induced by local applications of 0.1% ibotenic acid and lesions of the inferior olivary nuclei induced by i.p. injection of 3-acetylpyridine in C57BL/6 mice little affected the dynamic characteristics of the HVOR and HOKR, but abolished the adaptation of the HOKR. These results indicate that the olivo-floccular system plays an essential role in the adaptive control of the ocular reflex in mice, as suggested in other animal species. The data presented provide the basis for analyzing the reflex eye movements of genetically engineered mice.

Centrosome positioning and directionality of cell movements

In several cell types, an intriguing correlation exists between the position of the centrosome and the direction of cell movement: the centrosome is located behind the leading edge, suggesting that it serves as a steering device for directional movement. A logical extension of this suggestion is that a change in the direction of cell movement is preceded by a reorientation, or shift, of the centrosome in the intended direction of movement. We have used a fusion protein of green fluorescent protein (GFP) and γ-tubulin to label the centrosome in migrating amoebae of Dictyostelium discoideum, allowing us to determine the relationship of centrosome positioning and the direction of cell movement with high spatial and temporal resolution in living cells. We find that the extension of a new pseudopod in a migrating cell precedes centrosome repositioning. An average of 12 sec elapses between the initiation of pseudopod extension and reorientation of the centrosome. If no reorientation occurs within approximately 30 sec, the pseudopod is retracted. Thus the centrosome does not direct a cell’s migration. However, its repositioning stabilizes a chosen direction of movement, most probably by means of the microtubule system.

Chromosomal arm replacement generates a high level of intraspecific polymorphism in the terminal inverted repeats of the linear chromosomal DNA of Streptomyces ambofaciens

The chromosomal DNA of the bacteria Streptomyces ambofaciens DSM40697 is an 8-Mb linear molecule that ends in terminal inverted repeats (TIRs) of 210 kb. The sequences of the TIRs are highly variable between the different linear replicons of Streptomyces (plasmids or chromosomes). Two spontaneous mutant strains harboring TIRs of 480 and 850 kb were isolated. The TIR polymorphism seen is a result of the deletion of one chromosomal end and its replacement by 480 or 850 kb of sequence identical to the end of the undeleted chromosomal arm. Analysis of the wild-type sequences involved in these rearrangements revealed that a recombination event took place between the two copies of a duplicated DNA sequence. Each copy was mapped to one chromosomal arm, outside of the TIR, and encoded a putative alternative sigma factor. The two ORFs, designated hasR and hasL, were found to be 99% similar at the nucleotide level. The sequence of the chimeric regions generated by the recombination showed that the chromosomal structure of the mutant strains resulted from homologous recombination events between the two copies. We suggest that this mechanism of chromosomal arm replacement contributes to the rapid evolutionary diversification of the sequences of the TIR in Streptomyces.

Active hair-bundle movements can amplify a hair cell’s response to oscillatory mechanical stimuli

To enhance their mechanical sensitivity and frequency selectivity, hair cells amplify the mechanical stimuli to which they respond. Although cell-body contractions of outer hair cells are thought to mediate the active process in the mammalian cochlea, vertebrates without outer hair cells display highly sensitive, sharply tuned hearing and spontaneous otoacoustic emissions. In these animals the amplifier must reside elsewhere. We report physiological evidence that amplification can stem from active movement of the hair bundle, the hair cell’s mechanosensitive organelle. We performed experiments on hair cells from the sacculus of the bullfrog. Using a two-compartment recording chamber that permits exposure of the hair cell’s apical and basolateral surfaces to different solutions, we examined active hair-bundle motion in circumstances similar to those in vivo. When the apical surface was bathed in artificial endolymph, many hair bundles exhibited spontaneous oscillations of amplitudes as great as 50 nm and frequencies in the range 5 to 40 Hz. We stimulated hair bundles with a flexible glass probe and recorded their mechanical responses with a photometric system. When the stimulus frequency lay within a band enclosing a hair cell’s frequency of spontaneous oscillation, mechanical stimuli as small as ±5 nm entrained the hair-bundle oscillations. For small stimuli, the bundle movement was larger than the stimulus. Because the energy dissipated by viscous drag exceeded the work provided by the stimulus probe, the hair bundles powered their motion and therefore amplified it.

LC2, the Chlamydomonas Homologue of the t Complex-encoded Protein Tctex2, Is Essential for Outer Dynein Arm Assembly

Tctex2 is thought to be one of the distorter genes of the mouse t haplotype. This complex greatly biases the segregation of the chromosome that carries it such that in heterozygous +/t males, the t haplotype is transmitted to >95% of the offspring, a phenomenon known as transmission ratio distortion. The LC2 outer dynein arm light chain of Chlamydomonas reinhardtii is a homologue of the mouse protein Tctex2. We have identified Chlamydomonas insertional mutants with deletions in the gene encoding LC2 and demonstrate that the LC2 gene is the same as the ODA12 gene, the product of which had not been identified previously. Complete deletion of the LC2/ODA12 gene causes loss of all outer arms and a slow jerky swimming phenotype. Transformation of the deletion mutant with the cloned LC2/ODA12 gene restores the outer arms and rescues the motility phenotype. Therefore, LC2 is required for outer arm assembly. The fact that LC2 is an essential subunit of flagellar outer dynein arms allows us to propose a detailed mechanism whereby transmission ratio distortion is explained by the differential binding of mutant (t haplotype encoded) and wild-type dyneins to the axonemal microtubules of t-bearing or wild-type sperm, with resulting differences in their motility.

The Mr 140,000 Intermediate Chain of Chlamydomonas Flagellar Inner Arm Dynein Is a WD-Repeat Protein Implicated in Dynein Arm Anchoring

Previous structural and biochemical studies have revealed that the inner arm dynein I1 is targeted and anchored to a unique site located proximal to the first radial spoke in each 96-nm axoneme repeat on flagellar doublet microtubules. To determine whether intermediate chains mediate the positioning and docking of dynein complexes, we cloned and characterized the 140-kDa intermediate chain (IC140) of the I1 complex. Sequence and secondary structural analysis, with particular emphasis on β-sheet organization, predicted that IC140 contains seven WD repeats. Reexamination of other members of the dynein intermediate chain family of WD proteins indicated that these polypeptides also bear seven WD/β-sheet repeats arranged in the same pattern along each intermediate chain protein. A polyclonal antibody was raised against a 53-kDa fusion protein derived from the C-terminal third of IC140. The antibody is highly specific for IC140 and does not bind to other dynein intermediate chains or proteins in Chlamydomonas flagella. Immunofluorescent microscopy of Chlamydomonas cells confirmed that IC140 is distributed along the length of both flagellar axonemes. In vitro reconstitution experiments demonstrated that the 53-kDa C-terminal fusion protein binds specifically to axonemes lacking the I1 complex. Chemical cross-linking indicated that IC140 is closely associated with a second intermediate chain in the I1 complex. These data suggest that IC140 contains domains responsible for the assembly and docking of the I1 complex to the doublet microtubule cargo.

The Chlamydomonas IDA7 Locus Encodes a 140-kDa Dynein Intermediate Chain Required to Assemble the I1 Inner Arm Complex

To identify new loci that are involved in the assembly and targeting of dynein complexes, we have screened a collection of motility mutants that were generated by insertional mutagenesis. One such mutant, 5B10, lacks the inner arm isoform known as the I1 complex. This isoform is located proximal to the first radial spoke in each 96-nm axoneme repeat and is an important target for the regulation of flagellar motility. Complementation tests reveal that 5B10 represents a new I1 locus, IDA7. Biochemical analyses confirm that ida7 axonemes lack at least five I1 complex subunits. Southern blots probed with a clone containing the gene encoding the 140-kDa intermediate chain (IC) indicate that the ida7 mutation is the result of plasmid insertion into the IC140 gene. Transformation with a wild-type copy of the IC140 gene completely rescues the mutant defects. Surprisingly, transformation with a construct of the IC140 gene lacking the first four exons of the coding sequence also rescues the mutant phenotype. These studies indicate that IC140 is essential for assembly of the I1 complex, but unlike other dynein ICs, the N-terminal region is not critical for its activity.