This short series of tutorials focuses on the kinematics of robotic manipulators, specifically the widely used type known as a *six axis robot*, often called a *general industrial robot*. This topic can be considered a specialist subject within mechanics of machines.

I consider these "tutorials" more as study notes broadly at the level of the early stages of an undergraduate level course in robotics. My sources are primarily video lectures and other material online. Acknowledgements are stated in the introductory tutorial.

Tutorials in the **Robotics** series are as follows.

Kinematics of robotic manipulators - Introduction

Terminology for robot manipulators; illustration of revolute and prismatic joints; illustration of six axis robot with six revolute joints as the model for subsequent tutorials; definitions of forward and inverse kinematics.

Kinematics of robotic manipulators - forward kinematics 1 (by homogeneous transformation matrices)

Setting up co-ordinate frames for each joint of a six axis robot with known joint angles for forward kinematic analysis; constructing a kinematic diagram incorporating co-ordinate frames, link lengths and offsets; derivation of homogeneous transformation matrices for combined rotation and translation of co-ordinate frames; worked example of forward homogeneous transformations for the adopted robot model.

Kinematics of robot manipulators - forward kinematics 2 (by the Denavit Hartenberg method)

Setting up co-ordinate frames for each joint of a six axis robot with known joint angles for forward kinematic analysis using Denavit Hartenberg rules; defining the four Denavit Hartenberg parameters for rotation and displacement of co-ordinate frames; derivation of the transformation matrix incorporating Denavit Hartenberg parameters for combined rotation and translation of co-ordinate frames; worked example of forward Denavit Hartenberg transformations for the adopted robot model.

Kinematics of robot manipulators - inverse kinematics

Overview of inverse kinematic methods for resolving joint angles of a six axis robot for given tool tip co-ordinates; worked example of a geometric solution to resolve 4 unknown joint angles; illustration of second solution arising from a different orientation of joint elbow angle; illustration of the effect of link offsets on rotation angle depending on the direction of rotation; derivation of an analytic method of resolving rotation angles for a spherical wrist configuration of joints using rotation matrices; worked example of complete inverse kinematic analysis for a six axis robot with spherical wrist using combined geometric and rotational matrix methods.

I welcome feedback at: