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Ingeniare. Revista chilena de ingeniería, vol. 15 Nº 2,Cherfia, Zaatri and Giordano: Kinematics analysis of a parallel robot with a passive segment 2007, pp. 141-148

KINEMATICS ANALYSIS OF A PARALLEL ROBOT WITH A PASSIVE SEGMENT ANÁLISIS DE LA CINEMÁTICA DE UN ROBOT PARALELO CON UN SEGMENTO PASIVO
Abdelhakim Cherfia1 Abdelouahab Zaatri1 Max Giordano2

Recibido 12 de diciembre de 2005,aceptado 13 de abril de 2007 Received: December 12, 2005 Accepted: April 13, 2007

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 traslación pura. También determinaremos las relaciones entre las velocidades generalizadas y articulares usando la matrizJacobiana 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 debenalcanzarse 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 thereciprocal 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 ofthe 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.

INTRODUCTION These last years, the manipulators with a parallelstructure have constituted a pole of interest for many researchers and industrialists because of their interesting performances: high load capacity, movements at high rate, high mechanical rigidity, low mobile mass, simplicity of mechanical

engineering and possibility of locating the actuators and the sensors on the base, or close to the base. Historically, these mechanical systems were initiallydeveloped for applications other than the pure robotics field. The first mechanical system of this type was the machine built by Gough [1] in 1949 to test the tires of

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Mechanical Engineering Department. Mentouri University. Road Ain El Bey 25000. Constantine, Algeria. E-mail: cherfia_abdelhakim@yahoo.fr LMECA, ESIA - Savoie University BP 806, 74016. Annecy Cedex France. E-mail:max.giordano@esia.univ-savoie.fr Ingeniare. Revista chilena de ingeniería, vol. 15 Nº 2, 2007 141

Ingeniare. Revista chilena de ingeniería, vol. 15 Nº 2, 2007

the planes. Thereafter, Stewart [2] used this structure as a flight simulator. However, the idea to use parallel structures in robotics is in fact more recent. Indeed, Hunt [3] has identified certain parallel architectures that offer more...