The ellipse (drawn in red) may be expressed as a special case of the hypotrochoid, with R 2 r ( Tusi couple ) here R 10, r 5, d 1.
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). 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 ).Download Graphmatica 2.4b for Windows 848KB Runs on all modern 32-bit and 64-bit versions of Windows (XP/Vista/7/8.x/10).
GRAPHMATICA EQUATION FOR HYPOTROCHOIDS PLUS
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. Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features. is a powerful, easy-to-use, equation plotter with numerical and calculus features: Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. Consider the envy of your friends, neighbors, and peers.
You can be the first kid on you block with the capability of constructing hypotrochoids with a mere pen.
These equations yield a HYPOCYCLOID when bc and a HYPOTROCHOID when c differs from b. In order to develop the parametric equations for this curve, we need to be able to pinpoint the position of our trace point (P) at any given time. 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. EPICYCLOIDS, HYPOCYLOIDS, EPITROCHOIDS, AND HYPOTROCHOIDS There are four related classic curves which are generated by one circle rolling about the outside or inside of stationary second circle.
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