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Bulletin of the London Mathematical Society Advance Access published online on November 1, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp087
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© 2009 London Mathematical Society

Continuous curves from infinite Kempe linkages

John Owen

D-Cubed
Siemens PLM Software
Park House
Castle Park
Cambridge
CB3 ODU
United Kingdom
owen.john.ext@siemens.com

Stephen Power

Department of Mathematics and Statistics
Lancaster University
Lancaster
LA1 4YF
United Kingdom

Received 2 March 2009. Revision received 7 July 2009.

In 1876 Kempe showed that any algebraic curve in the plane may be realised as the locus of one of the joints of a finite bar-joint linkage. An often cited illustration of this is that there is a linkage that can write a person's signature to any particular accuracy. An infinite analogue is established showing that any continuous curve in the plane is the curve of motion of a joint of an infinite bar-joint linkage. This is curious, as continuous curves can be space filling. Moreover, there is a single infinite linkage that simultaneously traces everybody's signature with no error whatsoever.

2000 Mathematics Subject Classification 52C75, 46T20.

Supported by a London Mathematical Society Scheme 7 Grant.


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