A fun look at the meaning of "erledigen", how to say "Never mind!" and what all that has to do with body parts, memberships and a certain Goethe.
erledigen, das Glied, das Mitglied, gliedern, die Gliederung, ledig, lediglich
The core idea of this root was:
With the ge-prefix it became Glied, the German word for limb/body part with the core idea of “what bends”.
The sense of ledig (unbound) comes from the notion of being flexible.
In English, the word limb is the only offspring I could find mentioned in etymological sources.