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 (1640-1718): 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 wheel-road couple.
 
 

This animation uses the La Hire principle, we see it on the right.

 

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© Robert FERRÉOL  2019