Spirals: Polar, Parametric Equations [RESOLVED]

[Phenix]

I am trying to come up with the equation(s) that would describe the curve that would be the result of the following actions.

Say we have a wheel spinning at a constant rotational rate. In this example, let's use 1 revolution per second. Now I overlay a cartesian coordinate system with the origin at the center of the wheel. If I had a marker moving at constant linear velocity from position (0, rMax) along the y axis toward the origin to position (0, rMin). What would be the equation of the resulting curve drawn on the wheel? Let us take the constant linear velocity of my marker as (rMax-rMin) per 0.5 seconds. At this point you can mentally stop the wheel from spinning to examine the resulting curve (i.e. some type of spiral).

I'm guessing that in this case, the curve is like a half circle or half sine wave, but I would also like to know a general form if say the linear velocity or the angular velocity were to be varied. An image is attached. Or at least for a constant linear acceleration of the marker (instead of the constant linear velocity).

I was thinking that this graphical approach could be programmed, so then I thought of VB and the Math forum.

Thanks.