ISSN 0718-3291 Versión Impresa

ISSN 0718-3305 Versión en línea

Volumen 15 N° 2, Mayo - Agosto 2007

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Análisis de la cinemática de un robot paralelo con un segmento pasivo

Abdelhakim Cherfia1   Abdelouahab Zaatri1   Max Giordano2

1 Mechanical Engineering Department. Mentouri University . Road Ain El Bey 25000. Constantine, Algeria. E-mail: cherfia_abdelhakim@yahoo.fr

2 LMECA, ESIA - Savoie University BP 806, 74016. Annecy Cedex France . E-mail: max.giordano@esia.univ-savoie.fr


RESUMEN

Este trabajo presenta el modelo geométrico de un robot paralelo con tres grados de libertad (d.o.f) agregados a un segmento central pasivo del PPP. Esta estructura proporciona un movimiento de translación pura. También determinaremos las relaciones entre las velocidades generalizadas y articulares usando la matriz Jacobiana inversa. Además, determinamos las relaciones recíprocas entre las velocidades cartesianas y angulares del end-effector vía velocidades articulares por la derivación simple de las expresiones del modelo geométrico directo. Una determinación del espacio de trabajo basado en el análisis del modelo geométrico es derivado seguido por un cálculo numérico de todos los puntos que deben alcanzarse permitiendo una visualización gráfica de tal espacio de trabajo. Por otra parte, el análisis de los coeficientes de la matriz Jacobiana permite asegurar que no haya singularidades del tipo 1 y 2 en tal estructura. Se ha realizado un prototipo de robot paralelo en nuestro laboratorio para validar los modelos propuestos.
Palabras clave: Modelo geométrico, manipulador paralelo, segmento pasivo, matriz Jacobiana, espacio de trabajo, singularidad.



ABSTRACT

This paper presents a geometrical model of a constrained robot of three degrees of freedom (d.o.f) added to a PPP passive central segment. This structure provides a pure translation motion. We will also determine the relations between generalized and articular velocities by using the inverse Jacobian matrix. Further, we determine the reciprocal relations between cartesian and angular velocities of the end-effector via articular velocities by simple derivation of the direct geometrical model expressions. A determination of the workspace based on the geometrical model analysis is derived followed by a numerical calculation of all the atteignables points enabling a graphical visualisation of such a workspace. Moreover, the analysis of the Jacobian matrix has permitted to ensure that there are no singularities of type 1 and 2 in such a structure. A prototype of a parallel robot has been built up in our laboratory in order to validate the proposed models.
Keywords: Geometrical model, parallel manipulator, passive segment, Jacobian matrix, workspace, singularity.


 

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