Knock-Down is one of my favorite feats in 3.5, letting you make a trip attempt after dealing enough damage with a melee attack. But does that work if you're using, say, a glaive? You can't trip with a glaive, so presumably the touch attack part of the trip attempt would have to be made unarmed (with your foot or something). But such an opponent would be out of unarmed reach, since the glaive is a reach weapon. So can you make the free trip attempt, or are you forced to forgo it?
This is interesting—I have never seen this question. Generally, everyone just assumes you’re using a trip weapon with Knock-Down, because why wouldn’t you?
But you’re totally right—this is a confusing situation. I would say you definitely don’t get to move in to make the trip as an unarmed attack—Knock-Down definitely isn’t granting free movement. If you haven’t moved this round, you would be able to take a 5-ft. step in between your initial attack and your Knock-Down trip attack, since the trip is a separate free action, but not otherwise (and it would count as your 5-ft. step for the round). But do you have to? Arguably, Knock-Down is saying you can make a trip attack—does that override your usual inability to make a trip attack with that weapon? It’s unclear.
Unfortunately, as far as I know, the rules text of Knock-Down itself is the beginning and end of information we have here. So I do not think any answer is really possible aside from “ask your DM.”
Specific trumps general. You normally can't trip with a glaive, but since Knock-Down says you can attempt to trip under certain conditions, it would allow you to trip with a glaive. The flavor supports this as well; you're not just tripping them, hitting them so hard that they get knocked down.