(1993) The Stewart platform of general geometry has 40 configurations. Proceedings Institution of Mechanical Engineers. (1962) Proceedings of the FISITA Ninth International Technical Congress. International Symposium on Robotics Research, MIT Press. (1989) Kinematic analysis of the 6R manipulator of general geometry. (1988) Displacement analysis of the general spatial 7-link 7R mechanism. ASME Journal of Mechanisms, Transmissions and Automations in Design. (1985) Solving the kinematics of the most general six- and five-degree of freedom manipulators by continuation methods. ASME Journal of Engineering for Industry. (1963) Synthesis of path-generating mechanisms by numerical methods. Keywords : Dyalitic elimination, Homotopy, Kinematics, Newton-Raphson, Polynomial equation. The mathematical methods here treated are applied in a case study. For this motivation, the presented work is dedicated to those people who are initiated in the subject. However, undergraduate students undergo certain difficulties in their application in fundamental courses as mechanisms given the structure of the mathematics courses. Both methods have been applied successfully in diverse problems in the area of robotics, especially in the direct kinematics of spatial manipulators. In this paper we describe in a simple and detailed way two methods of solution of equations composed by polynomials that usually arise in the analysis and synthesis of mechanisms: i) the dialytic Sylvester method of elimination, ii) the Newton-homotopy method. Palabras Clave: Cinemática, Eliminación dialítica, Newton-Raphson, Homotopía, Polinomio. Los métodos matemáticos aquí expuestos se aplican en un caso de estudio. Por tal motivo, el presenta trabajo está dedicado a aquellas personas que se inician en el tema. Sin embargo, estudiantes de ingeniería experimentan ciertas dificultades en su aplicación en materias fundamentales como mecanismos dada la estructura de las materias de matemáticas correspondientes. Ambos métodos han sido aplicados de manera exitosa en diversos problemas en el área de robótica, especialmente en el análisis cinemático directo de manipuladores espaciales. En este trabajo se describen de manera simple y detallada dos métodos de solución de ecuaciones compuestas por polinomios que usualmente surgen en el análisis y síntesis de mecanismos: i) la eliminación dialítica de Sylvester, ii) el método de Newton-homotopía.
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