Related Curves
Several curves are related to the cycloid.
- Curtate cycloid: Here the point tracing out the curve is inside the circle, which rolls on a line.
- Prolate cycloid: Here the point tracing out the curve is outside the circle, which rolls on a line.
- Trochoid: refers to any of the cycloid, the curtate cycloid and the prolate cycloid.
- Hypocycloid: The point is on the edge of the circle, which rolls not on a line but on the inside of another circle.
- Epicycloid: The point is on the edge of the circle, which rolls not on a line but on the outside of another circle.
- Hypotrochoid: As hypocycloid but the point need not be on the edge of its circle.
- Epitrochoid: As epicycloid but the point need not be on the edge of its circle.
All these curves are roulettes with a circle rolled along a uniform curvature. The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute. If q is the product of that curvature with the circle's radius, signed positive for epi- and negative for hypo-, then the curve:evolute similitude ratio is 1 + 2q.
The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.
Read more about this topic: Cycloid
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