The diagram of my kinematics problem is as of above. I am having trouble finding the proper relation between the length $\overline{CD}$ and the angle $\varrho $. Note that the radius need not be 2 a shown in the image, but can be arbitrary. Using some trigonometry I did however come to a solution, which seems too complicated since this is a kinematics problem, and the focus is not too much on mathematics: $$\overline{CD}=\frac{R}{2}\left | \cos\varrho \right |+R\sqrt{1-\frac{1}{4}sin^{2}\varrho }$$ Anyone else have a simpler solution?