|
Epicycloid and Hypocycloid
|
Main Concept
|
|
An epicycloid is a plane curve created by tracing a chosen point on the edge of a circle of radius r rolling on the outside of a circle of radius R. A hypocycloid is obtained similarly except that the circle of radius r rolls on the inside of the circle of radius R.
The parametric equations for the epicycloid and hypocycloid are:
where  for the epicycloid and  for the hypocycloid.
|
|
Epitrochoid and hypotrochoid
|
|
Two related curves result when we include another parameter, L, which represents the ratio of pen length to the radius of the circle:
When  and  the curve is called an epitrochoid; when  and  , the curve is called a hypotrochoid.
|
|
|
Number of cusps
|
|
Let  .
|
•
|
If k is an integer, the curve has k cusps.
|
|
•
|
If k is a rational number,  and k is expressed in simplest terms, then the curve has a cusps.
|
|
•
|
If k is an irrational number, then the curve never closes.
|
|
|
| |
|
Download Help Document
Was this information helpful?
