An Etymological Dictionary of the German Language/Annotated/Gelenk
Gelenk, neuter, ‘joint, articulation, wrist, link,’ from Middle High German gelęnke, neuter, ‘waist, bend, bow,’ akin to Modern High German gelenk, gelenkig, adjective formed from Middle High German gelęnke, ‘pliant, skilful’ (see lenken). While the Middle High German gelenke, as a collective of Middle High German 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 Modern High German is applied to each limb; akin to Old High German lancha, hlancha, ‘hip, loins’ (whence also the Romance cognates — Italian fianco, from which Modern High German Flanke is borrowed), likewise Old Icelandic hlekkr, ‘link of a chain.’