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