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MATING GEAR PROFILES (CONTINUATION)


 - if  is a cardioid: (hub at the cuspidal point), 
The parametrization of is: 
(d = ka).
Opposite, the case k = 18/5.

The mouth with the heart...
if  is a circle:  (hub on the circle), 
the parametrization of is: 
(d = ka).
Opposite, the case k = -5/3.

 
Schroeder gears dating from 1867, coming from the Musée des Arts et Métiers.
The bottom curve  is a limaçon of Pascal.

See also this link.

When the hub of one of the gears is at infinity, we get a wheel-road couple.
 
 
We saw above that if we attach one of the gears and that we make the other one roll on it, the latter's hub describes a circle. This enables to imagine "Shaddock" vehicles like the one represented opposite... (by Alain Esculier: see at the bottom of this page)

For similar vehicles, but with a linear motion, see the next page.

See also the hyperboloid gears, generalisation to space of this planar notion, at the bottom of this page.
 
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© Robert FERRÉOL , Jean LEFORT, Alain ESCULIER  2017