Kinematics of a Robotic Manipulator

Abstract

Robotic manipulators are widely used in industry. They are simpler than mobile robots in that they perform tasks in a fixed and known environment. They are more complex than mobile robots because they move in the three spatial dimensions and in the three dimensions of rotation. Using a simplified planar model of a robotic arm, the two central problems of manipulators are presented. Forward kinematics asks where the end effector of the arm will be following a sequence of rotations of the joints of the arm. Inverse kinematics asks what rotations of the joints will bring the end effector to a specified position. A rotation of a robotic manipulator is described by a rotation matrix whose elements are trigonometric functions of the angle of rotation. The rotation matrix for a planar rotation is derived followed by an overview of three-dimensional rotations.