Epicycloid - Wikipedia
网页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 -- from Wolfram MathWorld
网页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
网页The epicycloid is a special case of the epitrochoid. Use the p slider to start tracing out the curve. Special cases are a cardioid when R/r = 1, a nephroid when R/r = 2, and a ranunculoid when R/r = 5.
Deriving the Equations of an Epicycloid - YouTube
网页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
网页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: $$x= (r+R)\cos\theta-r\cos\left [ (r+R)\frac\theta r\right],$$. $$y= (r+R)\sin\theta-r\sin\left [ (r+R)\frac\theta r\right],$$.
EPICYCLOID - MATHCURVE.COM
网页The epicycloids are the curves composed of isometric arcs (the arches) joining at cuspidal points (obtained for ) in a finite number equal to the numerator of q if q is rational, or in an infinite number otherwise. When q is rational, , the …
Epicycloids | Teaching Calculus
网页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.
Epicycloid - Michigan State University
网页1999年5月25日 · Epicycloid. The path traced out by a point on the Edge of a Circle of Radius rolling on the outside of a Circle of Radius . It is given by the equations.
Cycloidal curve - Encyclopedia of Mathematics
网页2023年4月8日 · The plane curve described by a point that is connected to a circle rolling along another circle. If the generating point lies on the circle, then the cycloidal curve is called an epicycloid or a hypocycloid, depending on whether the rolling circle is situated outside or inside the fixed circle.
Epicycloid - MacTutor History of Mathematics
网页Description. There are four curves which are closely related. These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point P P on a circle of radius b b which rolls round a fixed circle of radius a a.