Roulette2

Roulette

In the most general case Roulettes are curves generated by rolling a curve a, without slipping, along another curve a. The Roulette is generated by a point rigidly attached to the rolling curve b. The system below illustrates [Roulettes] resulting when a circle of radius b rolls outside a circle of radius a > b. Besides N = a/b is here an integer. Given the radii a and b. The shape of the roulette depends on the distance h of the attached point from the center of the rolling b-circle. For h=b we get the epicycloids with N cusps. For h < b we get the epitrochoids.

To change the shape of the roulette change N or/and the location of the moving point (red) attached to the rolling disc. See the file Roulette.html for the case of a circle rolling inside the big circle.

In the file Hypotrochoid.html it is illustrated the case of circle rolling into a bigger circle. There the point is attached rigidly inside the smaller disc.

http://users.math.uoc.gr/~pamfilos/