[Max Lobovsky]

I susepct you can do it using some linear algebra. If you know any linear algebra, this would be the process. Create a transform matrx that transforms angles of the two joints to x-y coordinates. It looks you already have this part of it done in that diagram you posted. Then, you need to solve for the inverse of this matrix and that will give you the transform matrix to do the same operation in reverse.

If you don't know linear algebra, learn it, or find someone who does. I may try this problem just because it sounds like fun. This exact problem can probably be found online somewhere, so you may not have to do anything at all.