Words related to draw
c. 1300 (mid-13c. in surnames), "to move or try to move forcibly by pulling, to drag forcibly or with effort," from Old English pullian "to pluck off (wool), to draw out," a word of unknown origin, perhaps related to Low German pulen "remove the shell or husk," Frisian pûlje "to shell, husk," Middle Dutch polen "to peel, strip," Icelandic pula "work hard." Related: Pulled; pulling.
From early 14c. as "to pick, pull off, gather by hand" (fruit, flowers, berries, leaves, petals, etc.); mid-14c. as "to extract, uproot" (of teeth, weeds, etc.).
Sense of "to draw (to oneself), attract" is from c. 1400; sense of "to pluck at with the fingers" is from c. 1400; meaning "tear to pieces" is mid-15c. By late 16c. it had replaced draw (v.) in these senses. From mid-14c. as "to deprive (someone of something)."
Common in slang terms 19c.-20c.; Bartlett (1859) has to pull foot "walk fast; run;" pull it "to run." To pull (someone's) chain in the figurative sense is from 1974, perhaps on the notion of a captive animal; the expression was also used for "to contact" (someone), on the notion of the chain that operates a signaling mechanism. To pull (someone's) leg is from 1882, perhaps on notion of "playfully tripping" (compare pull the long bow "exaggerate," 1830, and pulling someone's leg also sometimes was described as a way to awaken a sleeping person in a railway compartment, ship's berth, etc.). Thornton's "American Glossary" (1912) has pull (n.) "a jest" (to have a pull at (someone)), which it identifies as "local" and illustrates with an example from the Massachusetts Spy of May 21, 1817, which identifies it as "a Georgian phrase."
To pull (one's) punches is from 1920 in pugilism, from 1921 figuratively. To pull in "arrive" (1892) and pull out "depart" (1868) are from the railroads. To pull for someone or something, "exert influence or root for" is by 1903.
To pull (something) off "accomplish, succeed at" is originally in sporting, "to win the prize money" (1870). To pull (something) on (someone) is from 1916; to pull (something) out of one's ass is Army slang from 1970s. To pull rank is from 1919; to pull the rug from under (someone) figuratively is from 1946.
"cashbox," mid-15c., from Anglo-French tylle "compartment," Old French tille "compartment, shelter on a ship," probably from Old Norse þilja "plank, floorboard," from Proto-Germanic *theljon. The other theory [Klein, Century Dictionary] is that the word is from Middle English tillen "to draw," from Old English -tyllan (see toll (v.)), with a sense evolution as in drawer (see draw (v.)).