# 1. Introduction

This article is meant as a brief introduction to the mathematics required for Legged Robotic Motion. In this article, I will discuss the three topics needed to understand how you can make a robotic limb track a certain trajectory. The three topics that will be discussed are:

- Forward Kinematics,
- Inverse Kinematics, and finally
- Trajectory Planning.

In this article, I will use a 2-joint leg from a Robot Dog as the basis for my discussions. I have chosen this as an example as the 2-joint leg can only move in two dimensions, this means the 2-joint leg can be defined by an *xy* Cartesian coordinate system, and as such the mathematics is relatively simple.

If you were to go beyond a 2-joint robotic limb the mathematics becomes significantly harder (involving matrix algebra) and possibly a three dimensional *xyz* Cartesian coordinate system.

I have decided to keep this article as simple and practical as possible, with detailed graphs and complete mathematical solutions where applicable. I hope you find the contents of this article interesting and informative.