Moving a group of rotating objects. I have some objects that rotate around a common center, the formula I use to calculate their rotation is something like:
Math.cos(angle) * radius;
Math.sin(angle) * radius;
in every frame I update their position, and everything works ok.
Now, I need to also move the entire group of elements like if they were attached to something. Think of them as numbers in a wheel of fortune, and the wheel is moving to the right, at a constant speed.
So I have to mathematically calculate how much I should increase the X of each rotating element so they appear to move together as a group of objects.
If I just simply add a static increment after I assign the new position, it ends up having a sort of deformation, the circle is gone. I assume I would need to use he sin, but my tests fail.
Group of rotating elements:

What happens when I add a static amount in the X axis every frame:


If you attach radially with length along radius $r,$ no problem. If you have a radial component $c$ as well, then you need to consider $ \sqrt { c^2 + r^2 }$ as new radius.
EDIT 1/2
You superimposed rotary motion ( unintentionally ) with linear motion. Not adding to both $X,Y $ but only adding to $X$ created an imbalanced  $ prolate-cycloid $ situation. The static amount should be added for $Y$ also.
The speeds at top and bottom should not be  different.They should be made same with same offset of circle center.
prolate cycloid
