Noun:

புறஞ்சுழல் வளை,

epicycloid தமிழ் அர்த்தத்தின் உதாரணம்:

None

epicycloid's Usage Examples:

In both cases the curves are epicycloids; in the first case the radii of the rolling and the fixed circles are a(2n - I) /4n and a/2n, and in the second, an/(2n+ I) and a/(2n4-I), where a is the radius of the mirror and n the number of reflections.

Epicycloid >>an epicycloid in which the radii of the fixed and rolling circles are equal.

Epicycloids also received attention at the hands of Edmund Halley, Sir Isaac Newton and others; spherical epicycloids, in which the moving circle is inclined at a constant angle to the plane of the fixed circle, were studied by the Bernoullis, Pierre Louis M.

The epicycloid shown is termed the "three-cusped epicycloid" or the "epicycloid of Cremona.

"In the particular case when the radii are in the ratio of I to 3 the epicycloid (curve a) will consist of three cusps external to the circle and placed at equal distances along its circumference.

It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.

\Villiss formulae are founded on the following properties of epicycloids Let R be the radius of the pitch-circle; r that of the describing circle; 8 the angle made by the normal TI to the epicycloid at a given point T, with a tangent-to the circle at Ithat is, the obliquity of the action at T.

For an external epicycloid, p 4r sin O~iJThen the radius of curvature of the epicycloid at T is For an internal epicycloid, p 4r sin o~1Nearly Epicycloidal Teeth: Williss Method.

When c a or oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

To facilitate the drawing of epicycloidal teeth in practice, Willis showed how to approximate to their figure by means of two circular arcsone concave, for the flank, and the other convex, for the faceand each having for its radius the mean radius of curvature of the epicycloidal arc.

Therefore any epicycloid or hypocycloid may be represented by the equations p A sin B+,' or p---A cos B,,G, s A sin B11.

Synonyms:

line roulette, cardioid, roulette,

Antonyms:

straight line,