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Inicio Revista Iberoamericana de Automática e Informática Industrial RIAI Análisis Cinemático del Manipulador Paralelo 4-PRUR Mediante la Teoría de Tor...
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Vol. 14. Núm. 3.
Páginas 299-306 (Julio - Septiembre 2017)
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Vol. 14. Núm. 3.
Páginas 299-306 (Julio - Septiembre 2017)
DOI: 10.1016/j.riai.2017.03.001
Open Access
Análisis Cinemático del Manipulador Paralelo 4-PRUR Mediante la Teoría de Tornillos
Kinematics by Means of Screw Theory of The 4-PRUR Parallel Manipulator
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Jaime Gallardo-Alvaradoa, Mario A. Garcia-Murillob,
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garcia.mario@ugto.mx

Autor para correspondencia.
a Departamento de Ingeniería Mecánica, Instituto Tecnológico de Celaya, 38010 Celaya, Gto., México
b Departamento de Ingeniería Mecánica, División de Ingenierías, Campus Irapuato-Salamanca, Universidad de Guanajuato, 36885 Salamanca, Gto., México
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En este trabajo se presenta el análisis cinemático de un robot paralelo generador del movimiento de Schönflies por medio de la teoría de tornillos. Como un paso intermedio, el análisis de posición se obtiene en forma semi-cerrada con base en las coordenadas de dos puntos de la plataforma móvil. Esta estrategia requiere de sólo un marco de referencia, evitando así el cálculo de la matriz de rotación. Las ecuaciones entrada-salida de velocidad y de aceleración se obtienen sistemáticamente recurriendo a la teoría de tornillos recíprocos. Para ello, el robot se modela como si fuese un manipulador paralelo de seis grados de libertad gracias a la incorporación de pares cinemáticos ficticios que conectan las extremidades con la plataforma fija y una cadena cinemática virtual con la finalidad de aplicar sin restricciones el álgebra de Lie se(3) del grupo Euclideo SE(3). El análisis de singularidades se aborda con base en la ecuación entrada-salida de velocidad. Se incluyen ejemplos numéricos que muestran la aplicación del método.

Palabras clave:
Robot paralelo
movimientos de Schönflies
Teoría de tornillos
Cinemática
Abstract

In this work the kinematics of a parallel manipulator performing Schönflies motion is investigated by means of the theory of screws. As an intermediate step, the displacement analysis is reported in semi-closed form solution based on the coordinates of two points embedded in the moving platform. This strategy allows to employ only one reference frame avoiding the computation of the rotation matrix. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. To this aim, the robot is treated as a six-degrees-of-freedom parallel manipulator incorporating pseudo kinematic pairs connecting the limbs to the fixed platform and one virtual kinematic chain in order to apply without restrictions the Lie algebra se(3) of the Euclidean group SE(3). The singularity analysis is investigated based on the input-output equation of velocity. Numerical examples are included in order to show the application of the method.

Keywords:
Parallel robot
Schönflies motion
Screw theory
Kinematics
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