rote n.

c. 1200, "a way, a road, space for passage," from Old French rute "road, way, path" (12c.), from Latin rupta (via) "(a road) opened by force," broken or cut through a forest, etc., from rupta, fem. past participle of rumpere "to break" (see rupture (n.)).

The sense of "fixed or regular course for carrying things" (originally and for long especially postal, as in mail route) is from 1792, an extension of the meaning "customary path of animals" (early 15c.) itself later extended to sales, collections, delivery of milk or newspapers, etc. OED says the pronunciation that rhymes with "stout" appeared early 19c.

1731, from Medieval Latin rotarius "pertaining to wheels," from Latin rota "a wheel, a potter's wheel; wheel for torture," from PIE root *ret- "to run, to turn, to roll" (source also of Sanskrit rathah "car, chariot;" Avestan ratho; Lithuanian ratas "wheel," ritu "I roll;" Old Irish roth, Welsh rhod "carriage wheel"). The root also forms the common West Germanic word for "wheel" (originally "spoked wheel"): Old High German rad, German Rad, Dutch rad, Old Frisian reth, Old Saxon rath.

The international service club (founded by Paul P. Harris in Chicago in 1905) is so called from the practice of clubs entertaining in rotation. Hence Rotarian (1911).