Here's a very simple head band kind of rig I made.
To make this I basically made something to move the head band up and down. But Because the shape of the head isnt exactly a quare I got geo penetration without doing anything. The tip here is to sculpt some blendshapes to correct the problem areas.
So I made four blendshapes (down, mid, up, and a default). I hooked these up before I edited them via set driven keys. A custom slide attribute was driving the weights for all the blendshapes and the ty for headband. After editing the blendshapes with the slide looking okay I moved on to making the slide have an animator mover.
The slide had its own range (here -10, to 10 with 0 default), but I wanted an animator control to be used instead of the channel editor. The problem was after lining up the animator control at its topmost and lower most points and setting its ty limit information to those, the middle was a 0.2.
Using a remap straight off connected to the slide would think a zero value was not the default. To fix this I moved the control to 0.2 , then point constrained it maintain offset to the real animator mover which is at 0. I then hooked up the remap to the thing the real animator mover was constraining.
Now I hooked up the remaps outcolor r, to the slide attribute because the remap had made a (-0.8,1.2) range fit in with what the slide attribute wants (-10,10). And because of the offset stuff a zero on our mover would be a zero on the slide too.
Hope these tips were helpful.