arm (n.1)

"upper limb of the human body," Old English earm, from Proto-Germanic *armaz (source also of Old Saxon, Danish, Swedish, Middle Dutch, German arm, Old Norse armr, Old Frisian erm), from PIE root *ar- "to fit together" (source also of Sanskrit irmah "arm," Greek arthron "a joint," Latin armus "shoulder"). Arm of the sea was in Old English. Arm-twister "powerful persuader" is from 1915. Arm-wrestling is from 1899.

They wenten arme in arme yfere Into the gardyn [Chaucer]

arm (n.2)

"weapon," c. 1300, armes (plural) "weapons of a warrior," from Old French armes (plural), "arms, weapons; war, warfare" (11c.), from Latin arma "weapons" (including armor), literally "tools, implements (of war)," from PIE *ar(ə)mo-, suffixed form of root *ar- "to fit together." The notion seems to be "that which is fitted together."

Meaning "branch of military service" is from 1798, hence "branch of any organization" (by 1952). Meaning "heraldic insignia" (in coat of arms, etc.) is early 14c., from Old French; originally they were borne on shields of fully armed knights or barons. To be up in arms figuratively is from 1704; to bear arms "do military service" is by 1640s.

arm (v.)

"to furnish with weapons," c. 1200, from Old French armer "provide weapons to; take up arms," or directly from Latin armare "furnish with arms," from arma "weapons," literally "tools, implements" of war (see arm (n.2)). Intransitive sense "provide oneself with weapons" in English is from c. 1400. Related: Armed; arming.

Definitions of arm
arm (n.)
a human limb; technically the part of the superior limb between the shoulder and the elbow but commonly used to refer to the whole superior limb;
arm (n.)
any projection that is thought to resemble a human arm;
an arm of the sea
the arm of the record player
Synonyms: branch / limb
arm (n.)
any instrument or instrumentality used in fighting or hunting;
Synonyms: weapon / weapon system
arm (n.)
the part of an armchair or sofa that supports the elbow and forearm of a seated person;
arm (n.)
a division of some larger or more complex organization;
Synonyms: branch / subdivision
arm (n.)
the part of a garment that is attached at the armhole and that provides a cloth covering for the arm;
Synonyms: sleeve
arm (v.)
prepare oneself for a military confrontation;
Synonyms: build up / fortify / gird
arm (v.)
supply with arms;
The U.S. armed the freedom fighters in Afghanistan