# Spatial Vectors and Rigid-Body Dynamics

## Materials for the Spatial Vectors Courses at IIT, March 2019

Introduction to Spatial (6D) Vectors
Computational Robot Dynamics
In both courses, you will be expected to take notes and solve problems during the classes, so remember to bring pen/pencil and paper with you; and you should also bring either a printed copy of the course notes or a laptop/tablet/etc. for reading the notes in electronic form.  For Computational Robot Dynamics only, you will be asked to write and execute some small Matlab (or Octave) functions during class; so you should try very hard to bring a laptop with you.

## A Short Course on Spatial Vector Algebra

This is an introductory course (written in 2008) that takes approximately one or two days.  The materials below are (believed to be) suitable for self study.

## Some Books and Papers

• Robot Dynamics Algorithms (1987).  [link to Amazon].  This is the original book on dynamics algorithms and spatial vectors.  Although it is still worth reading, it has been superceded by the book below.  The treatment of spatial vectors in this book is a little different from the modern treatment.
• Rigid Body Dynamics Algorithms (2008).  [publisher's web page].  This is the new book on dynamics algorithms and spatial vectors.  The software listed below is based on this book.
• Springer Handbook of Robotics (2008).  [publisher's web page].  Chapter 2 in this handbook (co-authored by myself and Prof. David Orin) contains a concise description of spatial vectors and the most important algorithms for robot dynamics.
• Robot Dynamics: Equations and Algorithms (2000).  This is a survey paper on robot dynamics.  It contains a brief description of spatial vector algebra and the most important algorithms.
• Plücker Basis Vectors (2006).  This paper discusses Plücker coordinates, Plücker basis vectors and rigid-body acceleration using a mathematical tool called a basis mapping.

## Software Package Spatial

This Matlab software package implements most of the algorithms in Rigid Body Dynamics Algorithms.  Version 1 reportedly also works on
GNU Octave (version 3.0.2).  Version 2 includes several tutorial examples using Simulink, more extensive documentation, and greatly improved graphics.