Mathematical Modelling of a Two – Link Planar Manipulator Arm Using The Denavit – Hartenberg Matrices

Abstract

The Remote Manipulator System (R.M.S) is a typical example of a robotic manipulator. It is a two – link planar system which is made up of the base link (link 0), the upper arm link (link 1) and the end – effector or forearm link (link 2). The two joints are revolute and are respectively located at the shoulder and the elbow. In this work, frames are assigned to all the links; the direct and inverse kinematics modelling of the manipulator arm is also being discussed. The complete homogeneous transformation matrices relating gripper’s (generally known as the end – effector) frame with the base / reference frame have being derived using Denavit – Hartenberg matrix.

Keywords: Manipulator Arm, Frame, Link, Joint, End – Effector, Mapping, Kinematics.

Journal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 139 – 150