"small wheel or roller," late 14c., from Anglo-French trocle, from Latin trochlea "a small wheel, sheaf of a pulley," from Greek trokhileia "a pulley," from trokhos "wheel," from trekhein "to run," from PIE root *dhregh- "to run" (cf. Old Irish droch "wheel," Lithuanian pa-drosti "to run fast"). Truckle bed "small bed on wheels that can be stowed under a larger bed" is from mid-15c.
"give up or submit tamely," 1610s, "sleep in a truckle bed" (see truckle (n.)). Meaning "give precedence, assume a submissive position" (1650s, implied in truckling) is perhaps in reference to that type of bed being used by servants and inferiors, or from it simply occupying the lower position. Related: Truckled; truckling.