Unicycle maths, physics & robots, a collection of references.

A recent thread on rec.sport.unicycling  titled "How do you turn corners" developed into a discussion of some of the maths & physics behind unicycling.
http://www.unicyclist.com/forums/showthread.php?s=&threadid=20698
The posts in the long thread above that are focused on the physics are:
Gauss: Explains where the non gyroscopic forces come from to enable a unicyclist to make a smooth continuous turn:
http://www.unicyclist.com/forums/showthread.php?s=&postid=81825#post81825

Gauss: Explains the role of gyroscopic forces in relation to a unicyclist making a smooth continuous turn:
http://www.unicyclist.com/forums/showthread.php?s=&postid=82130#post82130

Stay on or fall off -- "Unicycling and Bifurcations" 12 pages of mathematics.
R. C. Johnson, Department of Mathematical Sciences, University of Durham,  England.
http://www.dur.ac.uk/bob.johnson/unicycle/

Postural Stability of a Human Riding a Unicycle and Its Emulation by a Robot
Zaiquan Sheng and Kazuo Yamafuji 

[IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 13, NO. 5, OCTOBER 1997]
http://mike.hinson.unicyclist.com/Unicycle-stability.pdf

These guys built a unicycling robot designed to emulate a human rider.

Picture and (v.short) video
http://www.yama.mce.uec.ac.jp/robot/robo_uni.html


Loony Cycle is a single-wheeled cycling robot
http://www.boltontech.org.uk/loony_cycle.htm

These guys built a single wheeled robot stabilised by the gyroscopic action of the wheel & steered by small fans providing lateral force.


The following thread by Wolfgang Schebeczek references additional literature about the physics of unicycling & unicycling robots, unfortunately I do not know of an on-line copy of any of the references quoted.
http://www.unicyclist.com/forums/showthread.php?s=&threadid=7512&highlight=physics

The following link has further links to good technical explanations of counter steering as related to bicycles: 
http://socrates.berkeley.edu/~fajans/Teaching/bicycles.html

The reference also links to David E. H. Jones' paper on The Stability of The Bicycle. This paper is a good reference for understanding why bicycle stability is fundamentally different to unicycle "stability".


Comments & contributions etc to mike.hinson@unicyclist.com please
Last updated October 22 2002