Old English sceacan "to vibrate, make vibrate, move away" (class VI strong verb; past tense scoc, past participle scacen), from Proto-Germanic *skakanan (cf. Old Norse, Swedish skaka, Danish skage "to shift, turn, veer").
No certain cognates outside Germanic, but some suggest a possible connection to Sanskrit khaj "to agitate, churn, stir about," Old Church Slavonic skoku "a leap, bound," Welsh ysgogi "move," and ultimately to PIE *(s)keg-. To shake hands dates from 1530s. Shake a leg "hurry up" first recorded 1904; shake a heel (sometimes foot) was an old way to say "to dance" (1660s). Phrase more _____ than you can shake a stick at is attested from 1818, American English. To shake (one's) head as a sign of disapproval is recorded from c.1300.
late 14c., from shake (v.). As a type of instantaneous action, it is recorded from 1816. Phrase fair shake "honest deal" is attested from 1830, American English. The shakes "nervous agitation" is from 1620s. Shakeout "business upheaval" is from 1895; shake-up "reorganization" is from 1899. Dismissive phrase no great shakes (1816) perhaps is from dicing.