An Etymological Dictionary of the German Language/Gelenk
Gelenk, n., ‘joint, articulation, wrist, link,’ from MidHG. gelęnke, n., ‘waist, bend, bow,’ akin to ModHG. gelenk, gelenkig, adj. formed from MidHG. gelęnke, ‘pliant, skilful’ (see lenken). While the MidHG. gelenke, as a collective of MidHG. lanke, signifies the ‘pliable narrow part of the body between the hips and breast,’ and hence, as it were, the joint of the entire body, the word in ModHG. is applied to each limb; akin to OHG. lancha, hlancha, ‘hip, loins’ (whence also the Romance cognates — Ital. fianco, from which ModHG. Flanke is borrowed), likewise OIc. hlekkr, ‘link of a chain.’