The gear curve is a curve resembling a gear with 
teeth given by the parametric
equations
 |  |  |
(1)
|
 |  |  |
(2)
|
where
![r=a+1/btanh[bsin(nt)],](/images/equations/GearCurve/NumberedEquation1.svg) |
(3)
|
where 
is the hyperbolic
tangent. Plots above show gear curves for 
, 
,
and 
to 12.
Gear Curve
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Cite this as:
Weisstein, Eric W. "Gear Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GearCurve.html