An Etymological Dictionary of the German Language/Annotated/walken
walken, verb, ‘to full, mill (cloth); tread (skins); thrash, cudgel,’ from Middle High German walken, Old High German walchan, strong verb, ‘to strike, thrash, full, mill (cloth)’; compare Dutch walken, ‘to press,’ Anglo-Saxon wealcan, Old Icelandic valka, ‘to roll, move to and fro.’ From Teutonic walkan are also derived Italian gualcare, ‘to calender or press cloth,’ gualchiera, ‘fulling-mill.’ The Teutonic root walk, from Aryan walg, seems to coincide with Sanscrit valg, ‘to hop or skip along.’ — From Middle High German walker, węlker, ‘fuller,’ is derived the proper name Welker.