1530s, "pitchfork," from Old North French croche "shepherd's crook," variant of croc "hook," from Old Norse krokr "hook," which is of obscure origin but perhaps related to the widespread group of Germanic kr- words meaning "bent, hooked."
From 1570s as "any fork or forking," especially "a parting of branches of a tree;" meaning "region where the body forks" is attested from 1590s. Hence crotchcutter "women's bathing suit with leg openings which reach above the hips" (by 1997).
early 14c., "small hook;" mid-15c. "a staff with a hook at the end," from Old French crochet (pronounced "crotchet") "small hook; canine tooth" (12c.), diminutive of croc "hook," from Old Norse krokr "hook," which is of obscure origin but perhaps related to the widespread group of Germanic kr- words meaning "bent, hooked."
As a curved surgical instrument with a sharp hook, from 1750. Figurative use in musical notation for "quarter note" is from mid-15c., from the shape of the notes. Also from 1670s in now-obsolete sense "one of the pair of marks now called 'brackets.'"
Meaning "whimsical fancy, singular opinion," especially one held by someone who has no competency to form a sound one, is from 1570s; the sense is uncertain, perhaps it is the same mechanical image in extended senses of crank; but other authorities link it to the musical notation one (think: "too many notes").