prefix of reversal, deprivation, or removal (as in unhand, undo, unbutton), Old English on-, un-, from Proto-Germanic *andi- (source also of Old Saxon ant-, Old Norse and-, Dutch ont-, Old High German ant-, German ent-, Gothic and- "against"), from PIE *anti "facing opposite, near, in front of, before, against" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before").
More or less confused with un- (1) through similarity in the notions of "negation" and "reversal;" an adjective such as unlocked might represent "not locked" (un- (1)) or the past tense of unlock (un- (2)).
1610s, "to wind, gather into rings one above the other" (trans.), from French coillir "to gather, pick," from Latin colligere "to gather together" from assimilated form of com "together" (see co-) + legere "to gather," from PIE root *leg- (1) "to collect, gather." Intransitive sense "to form rings or spirals" is by 1798. Related: Coiled; coiling.
<a href="https://www.etymonline.com/word/uncoil">Etymology of uncoil by etymonline</a>
Harper, D. (n.d.). Etymology of uncoil. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/uncoil