Ok, here's the situation:
I'm imagining a circle of radius A, and a circle of (a smaller) radius B. Circle A is centred at the point (0,0) and circle B starts centred at the point (b, 0). On circle B is a point P, which starts at (a+b, 0). The centre of circle B then travels along the circumference of circle A at a given rate (the rate itself is unimportant); simultaneously, P travels along the circumference of circle B, again at some arbitrary rate.
Now for the problem: given A, B, their respective rates of rotation, and the time elapsed, how do I calculate the new x and y coordinates for P? I've tried drawing countless diagrams, yet I just can't crack it. I suspect there's something missing in my intuition, or else I'm just overthinking everything. In any case, any help would be welcome.
Here's a rough diagram of what I'm trying to do:
You can ignore the bottom circle, as that was just me trying to figure something else out.