Shaping a Road and Finding the Corresponding Wheel

adjust road height

upper limit on wheel integration

roll the wheel

show locators

try to find closed wheel over periods

2

3

4

Integral for wheel closure = 4.

For a given road shape, the corresponding wheel (given in polar form centered at the origin) might not close up. This Demonstration lets you vary the shape of the periodic road using locators. You can then raise or lower the road to see how the wheel can become closed, which is when the integral above the plot is an integer. Choosing

n

to be 2, 3, or 4 in the setter bar causes the height of the road to be changed so that the wheel is automatically closed, with one revolution taking

n

periods of the road.