need to get 2 angles: MOTOR1 spins BLACK PLATE, MOTOR2 spins yellow plate

[batata003]

I already spent the last 4 hours trying to work out this solution which probably is very very simple but I cant find it.
I am building a 2D printer which works like this image:

MOTOR1 spins the BLACK PLATE and the MOTOR2 spins the yellow plate in precise angles. I have the point (1,1) in the BLACK PLATE and I need to rotate both motors in order to get the BLUE DOT to touch this coordinate (1,1).
Considering that the yellow bar is initially all perfectly vertically and the black plate is in the "standard" position, how much must I rotate the BLACK PLATE (in radians or degrees) and how much must I rotate the YELLOW BAR (in radians or degrees) in order to get this to work?

 

[RalphD]

I've solved this problem in a graphical environment called Desmos here: https://www.desmos.com/calculator/gu4wjdfm1o. I've used the equations and other information at Wolfram's entry on circle-circle intersections: http://mathworld.wolfram.com/Circle-CircleIntersection.html. The eventual angles by which you must rotate are given in the Desmos environment; you merely need to insert the correct value for \(\displaystyle B\) and set \(\displaystyle R\) to \(\displaystyle 1\) (which is the case as it is, right now).

In summary, the formulas for the angles by which you need to rotate your disks are as follows:
\(\displaystyle
\theta = \arccos \left(\frac{d^2-r^2+R^2}{2dR}\right) \\
\phi = \arccos \left(\frac{d^2-r^2+R^2}{2dr}\right)
\)
where \(\displaystyle \theta\) is the angle of the black plate and \(\displaystyle \phi\) is the angle of rotation of the yellow plate relative to the positive x-axis. To then get the angle of rotation for the two objects, simply subtract their current angle from the above angles correspondingly.

Hopefully that helps. Make sure to let me know if anything isn't clear as it is!