**Parametric Cartesian equation: **

*x* = *a*(cos(*t*) + *t* sin(*t*)), *y* = *a*(sin(*t*) - *t* cos(*t*))

**Click below to see one of the Associated curves.**

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

The involute of a circle is the path traced out by a point on a straight line that rolls around a circle.

It was studied by Huygens when he was considering clocks without pendulums that might be used on ships at sea. He used the involute of a circle in his first pendulum clock in an attempt to force the pendulum to swing in the path of a cycloid.

Finding a clock which would keep accurate time at sea was a major problem and many years were spent looking for a solution. The problem was of vital importance since if GMT was known from a clock then, since local time could be easily computed from the Sun, longitude could be easily computed.

The pedal of the involute of a circle, with the centre as pedal point, is a Spiral of Archimedes.

Of course the evolute of an involute of a circle is a circle.

JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Involute.html