Epicycloid - Wikipedia
In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
Epicycloid -- from Wolfram MathWorld
6 天之前 · The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. Epicycloids are given by the parametric equations x = (a+b)cosphi-bcos((a+b)/bphi) (1) y = (a+b)sinphi-bsin((a+b)/bphi).
Epicycloid - Desmos
Epicycloid: An epicycloid is traced by a fixed point on a circle of radius r rolling around the outside of a circle of radius R. Use the slider to adjust the ratio R/r – this controls the shape of the curve.
Epicycloid - GeeksforGeeks
2024年6月7日 · A curve in geometry known as an epicycloid is created by rolling a point on a circle's circumference around the exterior of another circle. Designing gears, examining planetary motion, and producing visually arresting patterns are just a few of the disciplines in which epicycloids find usage.
Epicycloid - Encyclopedia of Mathematics
2017年12月12日 · When the point is not situated on the rolling circle, but lies in its exterior (or interior) region, then the curve is called an elongated (respectively, shortened) epicycloid or epitrochoid. Epicycloids belong to the so-called cycloidal curves .
EPICYCLOID - MATHCURVE.COM
The epicycloids are the curves described by a point on a circle (C) rolling without slipping on a base circle (C0), the open disks with boundaries (C) and (C0) being disjoint. Therefore, they are special cases of epitrochoids. where a is the radius of the base circle and that of the rolling circle. Cartesian parametrization: .
Epicycloid and Hypocycloid - XahLee.info
Epicycloid and hypocycloid both describe a family of curves. Epicycloid is a special case of epitrochoid, and hypocycloid is a special case of hypotrochoid. Specifically, epi/hypocycloid is the trace of a point on a circle rolling upon another circle without slipping.
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