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The cyclocycloid (in this case an epicycloid) with R = 3, r = 1 and d = 1/2. A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.
Cycloid - curve generated by a rotating point on a wheel Epitrochoid - Wheel rotating around a wheel . In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes.
This is a gallery of curves used in mathematics, by Wikipedia page. ... Epicycloid. Epispiral. Epitrochoid. Hypocycloid. Lissajous curve. Poinsot's spirals. Rose curve.
The red curve is an epicycloid (outside the larger generating circle with diameter D, black) and the blue curve is a hypocycloid. The smaller circles are 1/4 the diameter of the larger circle. The solid curve is the profile of the rotor - half is the epicycloid and half is the hypocycloid.
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nephroid: tangents as chords of a circle, principle nephroid: tangents as chords of a circle. Similar to the generation of a cardioid as envelope of a pencil of lines the following procedure holds: Draw a circle, divide its perimeter into equal spaced parts with points (see diagram) and number them consecutively.
This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like "inner circle" or "circular reasoning" in which the word does not refer literally to the geometric shape.
It would be useful to know the equation(s) for the epicycloid given in polar co:ordinates. I don't know how to do this, but it seems a more natural way to look at it. I am trying to make some plexiglass gears with epicycloidal tooth profiles, and polar co:ordinates for the curve would make it much easier to design and print a template.