Definitely not a duplicated question to this one... Rather a much more specific question...
The situation arises when there are bolted anchors at foot level on the edge of the cliff:
The issue is that if you have set up the anchor off a cordelette (or a sling) as in...
and you clip a dynamic rope to this anchor, and then set up the rappelling device (extended ATC with Prusik knot)
you may very well find yourself hanging from some 4 to 5 feet of slack.
If you can't set up a static rope in the back of the ledge (say, off a tree or boulder) to lower yourself smoothly until the rappel device comes under tension, I only see two solutions to avoid downclimbing on a slack rappel setup with a possible nasty slip:
Set up a static rope off one of the bolts (using one of the locking biners already in use for the main anchor), and use a grigri to lower yourself until the Prusik engages the ATC and makes the rappel device taut. This would entail connecting a dynamic system and the static rope to a single biner, which is probably not a good idea.
Perhaps using a personal anchor system. And this is the question. Good idea? Can the Petzl device below (with progressive lengthening options) avoid a bad fall with a huge fall factor? How can the PAS be disengaged after placing the rappel system under tension?
... using the Petzl personal anchor system:
Here is a way of lowering oneself to make the rappel device taut below the bolted anchors using the Petzl PAS (biner to one of the anchoring biners). In this case, the system is tied to the bolts via a figure 8 bunny-ears knot, leaving two strands of a static rope to rappel down, or lowering oneself using one strand and a GriGri.