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If a is the radius of a fixed circle and b is the radius of a smaller rotating circle, the parametric equations of the hypocycloid are x = (a - b) cos θ + b cos [(a - b) θ ]/b
y = (a - b) sin θ - b sin [( a - b) θ ]/b.


The plane locus of a point fixed on a circle that rolls on the inside circumference of a fixed circle.


(Mathematics) a curve described by a point on the circumference of a circle as the circle rolls around the inside of a fixed coplanar circle. Compare epicycloid, cycloid4
ˌhypocyˈcloidal adj


(ˌhaɪ pəˈsaɪ klɔɪd)

a curve generated by the motion of a point on the circumference of a circle that rolls internally, without slipping, on a fixed circle.
hy`po•cy•cloi′dal, adj.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.hypocycloid - a line generated by a point on a circle that rolls around inside another circlehypocycloid - a line generated by a point on a circle that rolls around inside another circle
line roulette, roulette - a line generated by a point on one figure rolling around a second figure
References in periodicals archive ?
The three, four-pointed starlike figures within the circle, called hypocycloids for their geometric origin, made it to the NFL in 1962, when Rooney adopted the Steelmark for his football team.
For the achievement of the permanent contact between the peaks of the piston and the inner surface of the carcass, the paths of the peaks must be hypocycloids which are identical with the inner profile of the carcass.
Practically, at the generation of the real surfaces, the cinematic curve C as hypocycloids generated as a generating curve G of the complex surface.
The logo includes three four-pointed figures, called hypocycloids, within a circle, and colored to promote the attributes of steel.
With roots in the steel industry, the Steelers logo is formed with yellow, red and blue hypocycloids sitting atop a football-shaped design created with 32 round diamonds.
Each one of the tools will cut 2 opposite sides of the square, approximated with the elongated hypocycloids, (Popescu, 1998).