Spatial Vectors and Rigid-Body Dynamics

A Short Course on Spatial Vector Algebra

• slides
• slides (4 per page)
• notes accompanying the slides
• questions sheet
• answers sheet

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  Although it is still worth reading, it has been superceded by the book below.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 (2007).  [link to Amazon].  This is the new book on dynamics algorithms and spatial vectors.  The accompanying software is listed below.
• Robot Dynamics: Equations and Algorithms (2000).  This is a survey paper on robot dynamics.  It contains a brief description of spatial vector algebra and some of the simplest 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.

More Stuff on Spatial Vectors

• a 2-body example using 3D vectors  (shows how much algebra is required to solve a simple problem the traditional way)
• the same 2-body example using spatial vectors  (much easier than using 3D vectors)
• a one-hour seminar on spatial vectors  (predates the short course)

Software

• current matlab software (version 1, Jan 2008).  This software implements most of the algorithms in Rigid Body Dynamics Algorithms.  It reportedly also works on GNU Octave (version 3.0.2).
• source code (zip file)
• documentation  (lets you see the source code as well)
• Python version (subset)  (author: Ralf Grosse-Kunstleve at LBNL CCI)
• old software (undocumented matlab code, pre 2008):
• spatial vector library
• Newton-Euler Algorithm
• Composite Rigid Body Algorithm
• Articulated Body Algorithm
• some code to make planar and spatial robot models