"prickly seed vessel of some plants," c.1300, burre, from a Scandinavian source (cf. Danish borre, Swedish hard-borre, Old Norse burst "bristle"), from PIE *bhars- (see bristle (n.)). Transferred 1610s to "rough edge on metal," which might be the source of the sense "rough sound of the letter -r-" (see burr).
bur or burr (bûr)
n.
A rotary cutting instrument used in dentistry for excavating decay, shaping cavity forms, and reducing tooth structure.
A drilling tool for enlarging a trephine hole in the cranium.