Curve traced by a point on a circle rolling within another circle
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The red path is a hypocycloid traced as the smaller black circle rolls around inside the larger black circle (parameters are R=4.0, r=1.0, and so k=4, giving an astroid).
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line.
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the...
In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle...
friction and wear). Their gear tooth profile is based on the epicycloid and hypocycloid curves, which are the curves generated by a circle rolling around the...
{\displaystyle (x_{0},y_{0})} . The special cases of the epicycloid and hypocycloid, generated by tracing the locus of a point on the perimeter of a circle...
R)}{R}}} (where LCM is least common multiple). Special cases include the hypocycloid with d = r and the ellipse with R = 2r and d ≠ r. The eccentricity of...
deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point...
epicycloid or hypocycloid variety. The classic Spirograph toy traces out these curves. Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph [1]...
as a deltoid, a type of quadrilateral A deltoid curve, a three-cusped hypocycloid A leaf shape The deltoid tuberosity, a part of the humerus The deltoid...
along a diameter of the larger circle. The Tusi couple is a 2-cusped hypocycloid. The couple was first proposed by the 13th-century Persian astronomer...
logo. It consists of the word "Steelers" surrounded by three astroids (hypocycloids of four cusps). The original meanings behind the astroids were, "Steel...
the superellipse with n = 2⁄3 and a = b, is a hypocycloid with four cusps. Deltoid curve, the hypocycloid of three cusps. Squircle, the superellipse with...
of the Wankel engine is an epitrochoid. Cycloid Cyclogon Epicycloid Hypocycloid Hypotrochoid Spirograph List of periodic functions Rosetta (orbit) Apsidal...
cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. The smaller generating circles (red and blue) are one quarter the diameter...
In this case the trajectories are called hypocycloids and the equations above reduce to those for a hypocycloid. Cardioid Apsidal precession Cyclograph...
shaft is in the form of a hypocycloid. In the typical case of single-helix rotor and double-helix stator, the hypocycloid is just a straight line. The...
curve may be inside the rolling circle (curtate) or outside (prolate). Hypocycloid: variant of a cycloid in which a circle rolls on the inside of another...
Cycloid Cyclogon Deferent and epicycle Epicyclic gearing Epitrochoid Hypocycloid Hypotrochoid Multibrot set Roulette (curve) Spirograph J. Dennis Lawrence...
epitrochoid) Limaçon (special case of the epitrochoid) Hypotrochoid Hypocycloid (special case of the hypotrochoid) Spirograph (special case of the hypotrochoid)...
significant contributions to hypocycloids - published in De proportionibus, in 1570. The generating circles of these hypocycloids, later named "Cardano circles"...
the inside of a ring, where the main central region of the set is a hypocycloid of ( 1 − d ) {\displaystyle (1-d)} cusps.[citation needed] There is no...
to the time of Archimedes. Beam compass Bourke engine John Farey Jr. Hypocycloid Hypotrochoid Tusi couple Useless machine Scott Russell linkage Schwartzman...
tunnel through a homogeneous earth is a hypocycloid; in the special case of two antipodal points, the hypocycloid degenerates to a straight line. All straight-line...
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