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epicycloid
[ep-uh-sahy-kloid]
noun
a curve generated by the motion of a point on the circumference of a circle that rolls externally, without slipping, on a fixed circle. Equation: x = (a +b ) cos(θ) − b cos[(a +b )θ/ b ] and y = (a +b ) sin(θ) − b sin[(a +b )θ/ b ].
epicycloid
/ ˌɛɪˈɪɔɪ /
noun
the curve described by a point on the circumference of a circle as this circle rolls around the outside of another fixed circle, the two circles being coplanar Compare hypocycloid cycloid
epicycloid
The curve described by a point on the circumference of a circle as the circle rolls on the outside of the circumference of a second, fixed circle.
Other 51Թ Forms
- epicycloidal adjective
- ˌ辱ˈǾ岹 adjective
51Թ History and Origins
Origin of epicycloid1
Example Sentences
Suppose b a tracing point on b, then as b rolls on a it will describe the epicycloid a b.
The epicycloid shown is termed the “three-cusped epicycloid” or the “epicycloid of Cremona.”
When c = a or = ∞ the curve reduces to the cardioid or the two cusped epicycloid previously discussed.
They are Involute teeth. in fact epicycloids traced by a rolling circle of infinite radius, i.e. a straight line.
If the generating circle proceeds along the convexity of the periphery, it is called an upper or exterior epicycloid; if along the concavity, a lower or interior epicycloid.
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