(redirected from Hypocycloids)
Also found in: Thesaurus, Encyclopedia.
click for a larger image
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 team had to petition AISI to change the word "Steel" inside the Steelmark to "Steelers." The logo includes three four-pointed figures, called hypocycloids, within a circle, and colored to promote the attributes of steel.
Each one of the tools will cut 2 opposite sides of the square, approximated with the elongated hypocycloids, (Popescu, 1998).
Their topics include the circle's special role in geometry, famous theorems about circles, circle constructions: the problem of Apollonius, Mascheroni constructions: using only compasses, rolling circles: hypocycloids and epicycloids, and spherical geometry: circles on the sphere.
Epicycloids--curves generated by a point on the circumference of a circle (the epicycle)--or hypocycloids (Figure 1)--curves that roll on the inside of the circle--are examples of adding prefixes and suffixes.
PROBLEM: Plot the epicycloids and hypocycloids mentioned above.
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.