Parented Object follow different path? so my aim is to imitate a radial engine. 

this is what I have done so far


On the left its already working. The big cylinder moves only on the Z axes based on the location of the small cylinder below who follows the cycle path on and on again. I did this by giving the upper cylinder the "Child of" constraint.

Unfortunately this is not working when I start to rotate the whole construction like on the right. 

My question is. how can I parent the small cylinder to the big one and let the small one move on the circle while the big cylinder can only follow the linear path which he is putted on?

I would try to parent the small cylinder to the big one and then make a follow path for the big cylinder on the line. but this is not working properly, maybe I did something wrong.
A possibility is to set a copy location to the big cylinder with the small one as target. This copy is set on Z only and the space is set to local. 

So the big cylinder does not follow a path here, but follows the Z of the small one.