In this article , the equation of motion of an industrial robot is formulated by kinematics. The main problem of kinematics is to determine the state function. The vector and coordinate transfer methods for the spatial movement of the industrial robot are effective for solving this problem. In order to solve the correct problem of kinematics about the position of the industrial robot gripper, the coordinate exchange method is usually used [1 ] . In forming the kinematic equation of an industrial robot , it is important to specify the technological application of the robot and the coordinate system in which its movement is presented [2].

position function, exact problem of kinematics, cylindrical coordinate system, spherical and polar coordinate system