# Families of Figure-Eight Curves

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Take a pair of equal short and a pair of equal longer rods. Fix a rod with two nails (here the black points). Let both rods freely rotate around the nails. Hub both free ends together using the remaining fourth rod. Insert a pencil somewhere in this fourth rod (at the cyan point) that will draw the curve.

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Contributed by: Claude Fabre (September 2009)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The linkage, an isosceles trapezoid (called an isosceles trapezium by the British), shows a very simple mechanism hidden behind curves with complicated Cartesian coordinates. A circular motion gives rise to a large family of curves when throttling the length of the rods.

## Permanent Citation

"Families of Figure-Eight Curves"

http://demonstrations.wolfram.com/FamiliesOfFigureEightCurves/

Wolfram Demonstrations Project

Published: September 21 2009