ICIC Express Letters Part B: Applications ICIC International c ⃝2011 ISSN 2185-2766 Volume 2, Number 2, April 2011 pp. 421–425 KINEMATICS FOR THE SCARA AND THE CYLINDRICAL MANIPULATORS Victor Hernadez, Gustavo Bravo, Jose de Jesus Rubio and Jaime Pacheco Seccion de Estudios de Posgrado e Investigacion ESIME Azcapotzalco – Instituto Politecnico Nacional Av. de las Granjas no. 682, Col. Santa Catarina, CP 02250, Mexico D.F., Mexico jrubioa@ipn.mx Received July 2010; accepted October 2010 Abstract. Kinematics analysis is divided into: forward and inverse kinematics. For- ward kinematics showed how to determine the end-effector position and orientation in terms of the joint variables. The problem of inverse kinematics is to find the joint vari- ables in terms of the end-effector position and orientation. The Jacobian presents the relation between the joint and the end effector position velocities. The paper shows the kinematics of the SCARA robot with four degrees of freedom, the four degrees are dif- ferent from others. The paper shows the kinematics of the cylindrical robot with three degrees of freedom. Keywords: Kinematics, SCARA manipulator, Cylindrical manipulator 1. Introduction. Now, the presition in the homeworks is required in robotics [2] which is applied in the manufacture and the education [12] and in other repetitive homeworks made by humans in the past [2]. These homeworks are frequently with a defined trajectory [5], that is way it is an open research in robotics [4, 5, 10, 13] which present interesting results. The homeworks in the education [12] and in the medicine [2] are improved using a kinematic model [4, 5, 10, 13]. There are some books that consider the kinematics as are [3, 9, 11, 14], however, it is strange that in one book are considered the forward and the inverse kinematics of the SCARA or the Cylindrical arms. Kinematics analysis is divided into: forward and inverse kinematics. Forward kine- matics showed how to determine the end-effector position and orientation in terms of the joint variables. The problem of inverse kinematics is to find the joint variables in terms of the end-effector position and orientation. The Jacobian presents the relation between the joint and the end effector position velocities. The paper shows the kinematics of the SCARA robot with four degrees of freedom, the four degrees manipulator is different from others. The paper shows the kinematics of the cylindrical robot with three degrees of freedom. 2. SCARA Robot. The SCARA arm (for Selective Compliant Articulated Robot for Assembly) is a popular manipulator, which, as its name suggests, is tailored for assembly operations. Although the SCARA has an RRP structure, it is quite different from the spherical manipulator in both appearance and in its range of applications. Unlike the spherical design, which has z 0 perpendicular to z 1 , and z 1 perpendicular to z 2 , the SCARA has z 0 , z 1 and z 2 mutually parallel. 421