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. It is a particular kind of roulette.
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 -- from Wolfram MathWorld
4 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 - 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 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.
Deriving the Equations of an Epicycloid - YouTube
2019年5月15日 · In this video, we derive the parametric equations describing an epicycloid - a shape similar to a regular cycloid, but instead of rolling a circle along a plane, we roll along another circle.
Epicycloid - Encyclopedia of Mathematics
2017年12月12日 · Epicycloid. A planar curve given by the trajectory of a point on a circle rolling on the exterior side of another circle. The parametric equations are: $$x= (r+R)\cos\theta-r\cos\left [ (r+R)\frac\theta r\right],$$. $$y= (r+R)\sin\theta-r\sin\left [ (r+R)\frac\theta r\right],$$.
Epicycloids | Teaching Calculus
2014年6月27日 · Curves of this type, with the moving circle smaller or larger than the fixed circle and R = S, are called epicycloids. Epicycloids are a special case of Epitrochoids which will be the subject of the next post in this series. Investigation 3: Determine the value of t for each cusp, of a graph with d cusps.
Equation of Epicycloid - ProofWiki
2022年8月2日 · Theorem. Let a circle C1 of radius b roll without slipping around the outside of a circle C2 of radius a. Let C2 be embedded in a cartesian plane with its center O located at the origin. Let P be a point on the circumference of C1.
EPICYCLOID - Compute, Plot, and Tabulate an Epicycloid Curve
2019年1月9日 · EPICYCLOID is a MATLAB library which computes, plots and tabulates an epicycloid curve. An epicycloid is the curve traced by a point on the perimeter of a circle of radius r1 which is rolling around the perimeter of a a circle of radius r2. Normally, r1 is smaller than r2.