Ellipse Rolling inside a Circle

ellipse eccentricity

0.821

generator offset

0.

semimajor axis

0.5

roll the ellipse

9.5

This Demonstration draws the roulette of a generator point on an ellipse that rolls without slipping inside a circle.

Varying the ellipse's semimajor axis or eccentricity changes the circumference ratio

p

q

between the circle and the ellipse. A closed curve can be obtained after

q

complete revolutions inside the circle. By then, the ellipse will have made

p-q

revolutions around its center.

Change the pole offset to create an even greater variety of curves. The bookmarks and snapshots give some examples.