![]() ![]() Special cases include the hypocycloid with d = r is a line or flat ellipse and the ellipse with R = 2 r and d > r or d < r ( d is not equal to r). ![]() This model produces hypotrochoids, curves formed by tracing a point on the radius or extension of the radius of a circle rolling around the inside of another stationary circle. The parametric equations for a hypotrochoid are: x ( θ ) = ( R − r ) cos θ + d cos ( R − r r θ ) where LCM is least common multiple. Hypotrochoids (ca 1900), kinematic model by Martin Schilling, series 24, model 3, number 331, Smithsonian Institution negative number DOR2013-50214. Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. The domain of t has a large effect on what the hypotrochoid will look like. They all belong to a family of curves, which includes other types of trochoids. All hypotrochoids are defined by these parametric equations. The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5, r = 3, d = 5).Ī hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. The title and your entire post use the word hypotrochoid, but both the two equations and the first graphic obviously belong to a hypocycloid known as deltoid, while the latter graphic is clearly that of an epicycloid called cardioid. Title: Graphmatica by kSoft Description: Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features. Hypotrochoids are graphed using the following parametric equations.
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