The origin of the term ‘Bracelet’ is from the Greek branchile meaning of the arm from the Old French bracchiale or armlet.
Dictionary.com – mid-15c., from O.Fr. bracelet (14c.), dim. of bracel, from L. bracchiale “armlet,” from bracchium
The etymology is also tied to the word ‘Brace’
“early 14c., “armor for the arms,” from O.Fr. brace, braz “arms,” also “length measured by two arms” (12c., Mod.Fr. bras “arm, power;” brasse “fathom, armful, breaststroke”), from L. bracchia pl. of bracchium “an arm, a forearm,” from Gk. brakhion “arm” (see brachio-). Applied to various devices for fastening and tightening, on notion of clasping arms. The verb “to render firm or steady by tensing” is mid-15c., with figurative extension to tonics, etc. that “brace” the nerves (cf. bracer “stiff drink”). Related: Braced; bracing.” [From Online Etymology Dictionary]