... mir ist Derartiges unter dem Begriff 'Laufgeschirr' bekannt . . .

... das ist ein Brustgeschirr, das Kleinkindern umgelegt wird und das eine Führungsleine in Form eines Zügels hat . . .

http://lh4.ggpht.com/_rxtOI7A6yqY/S1DJGicdDII... . . .

I believe the hyphen is obsolete, and that it's actually used in the plural in English. Do you have any citations with just the singular?

I would also be inclined to mark at least the English side historic; I have the feeling there's a discussion in the forum archive (Suche in allen Foren) about what the equivalent for modern toddlers is and it's something different, though I can't remember what.

LMH, while you're being so busy, would you like to fill out your profile a little, at least whether your native language is German or English or something else, and mention if you're interested in history or whatever? It helps others to know what kinds of comments are most helpful to you, and what you might be able to help someone else with.

In the OED the word has a hyphen and is indeed plural:
1. Strings with which children used to be guided and supported when learning to walk. to be in leading-strings : to be still a child; fig. to be in a state of dependence or pupilage.
Quelle: www.oed.com

Edit: Das OED sagt: "Chiefly pl.", also auch Sg. möglich.

"Wir waren schon vom Führband an / Die unzertrennlichsten Gespielen"
(Wieland)

#2: hm-us: Denkst Du vielleicht an diesen Faden?

Siehe auch: Use of reins / child harness for toddlers