Etymology
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twisted (adj.)
late 15c., "intertwined, past-participle adjective from twist (v.). Meaning "perverted, mentally strange" (1900) probably is from twist (n.) in a sense of "mental peculiarity, perversion" attested by 1811.
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twist (v.)
c. 1200 (implied in past tense form twaste), "to wring," from twist (n.). Sense of "to spin two or more strands of yarn into thread" is attested from late 15c. Meaning "to move in a winding fashion" is recorded from 1630s. To twist the lion's tail was U.S. slang (1895) for "to provoke British feeling" (the lion being the symbol of Britain). To twist (someone's) arm in the figurative sense of "pressure (to do something)" is from 1945. Related: Twisted; twisting.
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torque (v.)
1570s (implied in torqued "twisted"), from torque (n.).
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strepto- 
word-forming element used in science to mean "twisted," from Latinized combining form of Greek streptos "twisted, easy to bend, pliant," verbal adjective of strephein "to turn, twist," from PIE root *streb(h)- "to wind, turn."
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twine (n.)
"strong thread made from twisted strands," Old English twin "double thread," from Proto-Germanic *twiznaz "double thread, twisted thread" (source also of Dutch twijn, Low German twern, German zwirn "twine, thread"), from PIE root *dwo- "two."
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coir (n.)

also coire, "prepared coconut fiber" (used for making ropes, mats, etc.), 1580s, from Malayalam (Dravidian) kayar "cord," from kayaru "to be twisted."

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awry (adv.)
late 14c., "crooked, askew, turned or twisted to one side," from a- (1) "on" + wry (adj.).
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spiro- 
word-forming element meaning "twisted, spiraled, whorled," from combining form of Latin spira "a coil, twist," from Greek speira (see spiral (adj.)).
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withe (n.)

Old English wiððe "twisted cord, tough, flexible twig used for binding, especially a willow twig," from PIE *withjon-, from root *wei- "to turn, twist."

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worsted (n.)
woolen fabric made from twisted yarn, late 13c., from Worstead (Old English Wurðestede), town in Norfolk where the cloth originally was made.
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