Spatial Vectors and Rigid-Body Dynamics
Spatial vectors are 6D vectors that simplify the task of describing,
analysing, and calculating rigid-body dynamics. This page contains
materials to help you learn about spatial vectors, software to help you
perform dynamics calculations, and links to relevant materials elsewhere.
Materials for the Course at IIT, Nov 28 – Dec 5 2014
- part 1 (slides, notes, question and
- part 2 (question and answer sheets for
- part 3 (slides on articulated-body
algorithm and dynamic models)
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
A Tutorial for Beginners
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superceded by the book below.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).
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).
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
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
This paper discusses Plücker coordinates, Plücker basis
vectors and rigid-body acceleration using a mathematical tool called a
More Stuff on Spatial Vectors
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.
Last modified: Dec 2014
Author: Roy Featherstone