MAT 331

Exercise 5

animations of hypo- and epicycloids

> restart; with(plots): with(plottools):

1. Epicycloid.

Using the code to produce an animation of the cycloid (below) as a guide, produce an animation of the epicycloid (a circle of radius r rolling on the outside a circle of radius R) This should be a procedure which allows the user to vary the inner and outer radius.

sample cycloid code

the guts of the epicycloid animation

2. Hypocycloid.

Modify your answer in (1) to produce the hypocycloid, where the disk rolls on the inside. You will have to rederive the parametric equation. Take care to note which way the rolling wheel turns (clockwise or counter-clockwise).

What happens when ? This should give a rather special hypocycloid.

Sample Hypocycloid animation