armchair n.

[upper limb of the human body], Middle English arm, from 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]

"a seat with a back, intended for one person," early 13c., chaere, from Old French chaiere "chair, seat, throne" (12c.; Modern French chaire "pulpit, throne;" the humbler sense having gone since 16c. with the variant form chaise), from Latin cathedra "seat" (see cathedral).

The figurative sense of "seat of office or authority" (c. 1300) originally was in reference to bishops and professors. The meaning "office of a professor" (1816) is extended from the seat from which a professor lectures (mid-15c.). The meaning "seat of a person presiding at meeting" is from 1640s. As short for electric chair from 1900. Chair-rail "strip or board of wood fastened to a wall at such a height as to prevent the plaster from being scraped by the backs of chairs" is from 1822.