I've been practising with cycling objects and familiarising myself with motion paths; I now need to combine the two but I can't figure out how.
My application is an oscillating jig saw blade cutting a ply panel along a line.
Can anyone help?
The trick with motion paths is that they 'take over' the transformations of the object that is assigned to them. This removes the animator's freedom to tweak the motion, or--as in your case--layer another type of motion atop it.
In general, any time you as an animator need extra control, the trick is usually to add an extra transform node. This is true of many cases, such as when you want to be able to move smoothly in one direction while rotating in another, or animate some high-frequency bobbing or swaying while also controlling a longer overall path of motion, etc.
In this case what you want to do is animate the oscillations on the saw blade itself, then attach one of its parents (either an empty transform node or the main body of the saw, if that exists) to the motion path. The oscillating motion will then be relative to the overall movement, which is what you want.