The trace of reflectors as a roulette
When a bicycle is illuminated by a headlight in the dark, the track of the reflectors on the spokes and pedals becomes visible as a curve.
Task
Use the checkbox to show the cycloids.
Play the animation for the parameter t.
Change the value of parameter a. What is the meaning of this parameter?
When a circle rolls on a straight line, a point on the circle creates a special roulette, a so-called cycloid.
Parameter representation of the cycloids
x(t) = r·t - a·sin(t)
y(t) = r - a·cos(t)
In this case, the parameter t represents the angle of rotation.
Task
Change the parameter a and the radius r of the wheel.