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LA HIRE LINE
Mechanism studied by Al
Tusi in 1272, Cardan in 1570, and La Hire in 1699.
Other names: gear, La Hire fly. Philippe de La Hire (16401718): French mathematician and astronomer. 
The La Hire line is the hypocycloid with two cusps, obtained when a circle rolls inside a circle with double radius, and that reduces to an ordinary, yet useful, segment of a line.
Here are Shaddocks trucks designed by
Alain
Esculier, using this property:




The points of the plane linked to the moving circle trace ellipses; see the page on glissettes. 

For other linear roulettes,
see wheelroad couple.
This animation uses the La Hire principle, we see it on the right. 

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© Robert FERRÉOL
2019