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INVERSE EVOLUTOID OF A PLANE CURVE
Notion studied in 1873 by abbé
Aoust (p. 119), in 2010 by Apostol
and Mamikon under the name of tanvolute.
Other names : oblique involute, generalized involute. |
If M0 is
the current point of Solution of this equation : |
The inverse evolutoids under an angle
of a plane curve are the curves of which
is the evolutoid of angle
.
Those are
so the curves crossing
with an angle
the tangents to the curve
.
For ,
we find the involutes of
.
EXAMPLE : INVERSE EVOLUTOID OF CERCLE
Cartezian paramétrization : |
![]() Animation for several values of k |
Oblique involute of a circle under an angle of 45 °. The curve has an asymptote branch to the circle
of radius |
![]() |
Pour proche de 90°, la branche pour t
> 0 commence avec des spires peu ou prou équidistantes, comme pour
une spirale d'Archimède, puis les spires s'écartent, comme
pour une spirale logarithmique.
For |
![]() |
One will find in the article or the book of Apostol/Mamikon, a study on the oblique involutes of cycloidal curves. Opposite, example of the cardioid. |
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© Robert FERRÉOL 2020