I do not have Atomstack parts, but I hope to get you started on the road to success.
Position the Rotary parallel to the Xaxis so the Xmotion makes it travel the length of the rotary.
This will orientate the direction of travel to be the same as the Xaxis. So X travels in X and Y rotates in X. Do you see how this is not going to work?
Pretend there is a ruler laying on top of the rotary chuck. When the rotary turns, the ruler will travel back and forth in the Y direction. Now imagine the rotary as being flattened out. That is your Yaxis travel.
Here are links to help get you going: