Kinematic of a configurable manipulator using screw theory

[EN] This paper addresses the kinematic analysis of a redundant parallel manipulator with a configurable platform equipped with two end-effectors. The closure equations of the position analysis generate a system of quadratic equations which is solved by applying the Newton-homotopy method. Subsequently, the instantaneous kinematics of the robot is solved by resorting to the theory of screws. The efficiency of the method is such that the calculation of passive joint rates of the robot is not required form the determination of the input-outputn equation of velocity of the parallel manipulator. Numerical examples are compared with the outcome of a commercial software demonstrating the approach correctness.[ES] En este trabajo se aborda el análisis cinemático de un m manipulador redundante con una plataforma configurable equipada con dos efectores finales. Las ecuaciones de clausura del análisis de posición generan un sistema de ecuaciones cuadráticas el cual se resuelve aplicando Newton-homotopía. Posteriormente, la cinemática instantánea del robot se resuelve recurriendo a la teoría de tornillos. La eficiencia del método es tal que no se requiere del cálculo de las velocidades articulares pasivas del robot para la determinación de la ecuación entrada-salida de velocidad del manipulador paralelo. Ejemplos numéricos se comparan con los resultados de un software comercial lo cual demuestra veracidad del método.Este trabajo ha sido realizado gracias al apoyo del Consejo Nacional de Ciencia y Tecnología de México, Conacyt, a través de la membresía del Dr. Jaime Gallardo–Alvarado al Sistema Nacional de Investigadores.Gallardo-Alvarado, J.; Tinajero-Campo, JH.; Sánchez-Rodríguez, Á. (2020). Cinemática de un manipulador configurable por medio de la teoría de tornillos. 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Novel Design and Analysis of Parallel Robotic Mechanisms

A parallel manipulator has several limbs that connect and actuate an end effector from the base. The design of parallel manipulators usually follows the process of prescribed task, design evaluation, and optimization. This dissertation focuses on interference-free designs of dynamically balanced manipulators and deployable manipulators of various degrees of freedom (DOFs). 1) Dynamic balancing is an approach to reduce shaking loads in motion by including balancing components. The shaking loads could cause noise and vibration. The balancing components may cause link interference and take more actuation energy. The 2-DOF (2-RR)R or 3-DOF (2-RR)R planar manipulator, and 3-DOF 3-RRS spatial manipulator are designed interference-free and with structural adaptive features. The structural adaptions and motion planning are discussed for energy minimization. A balanced 3-DOF (2-RR)R and a balanced 3-DOF 3-RRS could be combined for balanced 6-DOF motion. 2) Deployable feature in design allows a structure to be folded. The research in deployable parallel structures of non-configurable platform is rare. This feature is demanded, for example the outdoor solar tracking stand has non-configurable platform and may need to lie-flat on floor at stormy weathers to protect the structure. The 3-DOF 3-PRS and 3-DOF 3-RPS are re-designed to have deployable feature. The 6-DOF 3-[(2-RR)UU] and 5-DOF PRPU/2-[(2-RR)UU] are designed for deployable feature in higher DOFs. Several novel methods are developed for rapid workspace evaluation, link interference detection and stiffness evaluation. The above robotic manipulators could be grouped as a robotic system that operates in a green way and works harmoniously with nature

Modelagem e otimização de forças e torques aplicados por robôs com redundância cinemática e de atuação em contato com o meio

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2011O aumento da complexidade das tarefas de robôs industriais e a expansão da utilização de robôs de serviço requerem o aprofundamento de estudos sobre a interação de robôs com o meio. Esta interação pode ser estática, quando não existe movimento relativo do robô com o meio, ou dinâmica, quando existe movimento relativo do robô em relação ao meio, mas o contato é mantido durante esta movimentação. Quando a movimentação é lenta, é possível considerar a interação como quase-estática, pois os efeitos dinâmicos podem ser desprezados. Na execução de determinadas tarefas, os robôs industriais e os robôs de serviço podem ser levados ao limite de sua capacidade de força-momento. Se a capacidade de força-momento do robô é excedida, danos materiais e ferimentos em pessoas podem ocorrer durante a execução de uma tarefa. A capacidade de força-momento de um robô depende dos torques em seus atuadores, de sua configuração, da posição e orientação de seu efetuador e das ações presentes no contato com o meio. O objetivo principal deste trabalho é o desenvolvimento de uma metodologia para determinação da capacidade de forçamomento de robôs em condições estáticas ou quase-estáticas. Esta metodologia é estendida para a otimização da capacidade de força-momento ao longo de uma trajetória. Em comparação com as abordagens existentes na literatura, a metodologia proposta diferencia-se por abranger robôs com redundância cinemática e de atuação. Além disso, o ponto de contato com o meio, a orientação do efetuador e o modo de trabalho (working mode) do robô não necessitam ser constantes ao longo do processo de otimização. Devido à redundância cinemática e às variáveis geométricas presentes, a função objetivo do problema de timização de capacidade de força-momento é descrita por equações não-lineares e não-convexas, apresentando mínimos locais. Para resolver este problema de otimização global, é utilizado um algoritmo evolutivo chamado Evolução Diferencial. A modelagem das equações estáticas é realizada através da utilização da teoria dos helicoides e do método de Davies. A metodologia proposta é validada na determinação da capacidade de força-momento de um robô paralelo e de um robô serial de sete graus de liberdade chamado Roboturb. A otimização da força ao longo de uma trajetória é realizada para um manipulador serial planar. Os principais fatores que influenciam a capacidade de força-momento dos robôs manipuladores são discutidos.The increasing complexity of task performed by industrial robots and the widespread use of service robots demands deeper knowledge of robot interaction with the environment. This interaction can be static, when there is no relative movement between robot and environment or dynamic when exist relative movement but the contact is maintained during this movement. When this relative movement is performed in slow velocity, the interaction is considered quasi-static and the dynamics effects can be neglected. In certain tasks, industrial and service robots can be demanded to their wrench capabilities limits. If robots wrench capabilities are exceeded when executing a task, material damages and personal injuries can occur. Wrench capabilities depends on robot configuration, position, orientation, actuators limits and on wrenches at interaction. The development of new methodology to evaluate the wrench capabilities of robots in static or quasi-statics conditions is the main purpose of this thesis. This methodology is also extended to the optimization of wrench capability along a path. Different from previous approach, the proposed methodology deals with kinematic and actuation redundant robots. Add to that, the contact point with the environment, the robots working mode and orientation must not remain constant during optimization process. Due to kinematic redundancy and geometric variable parameters, the wrench capability optimization objective function is described by non-linear and non-convex equations with local minima. To solve this global optimization problem, an evolutionary algorithm called Differential Evolution is used. Static modeling uses as background Screw Theory and Kirchhoff- Davies cutset method. The efficiency and feasibility of the proposed methodology is demonstrated on an optimization problem, where the wrench capabilities of a planar parallel manipulator and a seven degree of freedom serial robot called Roboturb are evaluated. Wrench capabilities along a path for a planar serial manipulator are also evaluated. The main factors that affect wrench capabilities are discussed