A wheel of radius 1 revolves at a constant angular velocity and travels in a
straight line on a level surface. Plot the path traced out by a piint
on the edge of the wheel. You should take in to account the fact that
the wheel is not only revolving but its centre is moving in a
direction opposite to the motion of the edge of the wheel at the point
where it touches the surface. The equation of motion should be a two
coordinate function of the form [*X*(*t*), *Y*(*t*)]. In order to plot the
path of such a function over one complete revolution you can use the
Maple command `plot([X(t), Y(t)],t=0..2*Pi]);`.
Trace the motion of a point which is halfway between the edge and the
hub of the wheel. Calculate the length of the path travelled by such a
point when the wheel has made a quarter revolution.

Next, consider a wheel of radius rotating along the outside rim of a fixed wheel of radius . Trace the motion of a point on the edge of the outer wheel for a few different values of and . What happens if the free wheel travels along the interior rim of the fixed wheel. Calculate the distance travelled by a point on the edge of such a wheel if and and the free wheel makes 2 complete revolutions.

Finally, create an animation which shows both wheels as well as the
point on the edge of the free wheel as they rotate.

Thu Mar 27 17:08:57 EST 1997