How to make something move in a linear straight motion?

I would draw the cylinder perfectly horizontal. I would group all the artwork layers under a root "+MyFunkyPart" layer. I would draw the rod as a separate layer and put a "+" at the start of the layer name ("+Rod"). I would then add a "Transform" behavior to the Rod layer in the rigging panel. Because its horizontal, use keyframes etc to adjust the Position X value of the Rod - I think that will move it relative to the rest of the device. You can apply a root transform to the overall cylinder to put it on an angle and the Rod should rotate with it all fine.

+MyFunkyPart

   Cylinder

   +Rod -- add Transform behavior to move it relative to rest of part.

If you need to add tubes or something for fluids, I would use say 4 layers showing movement along the pipe. You put the 4 stages of animation in a group and add a Cycle Layers behavior to the group. That will how the 4 frames, animating movement along the pipe. You could make the pipes a part of the cylinder part if you want to, so they join on. You could put draggers on the end of the pipe (or use a Transform behavior on the ends of the pipe) to position them. Not sure what the full story you are trying to achieve is.