A robot arm assembly includes a first robot arm and a second robot arm rotatably connected to the first. The first robot arm includes a first input shaft and a second input shaft. The second robot arm includes a sleeve and an output shaft partially received in the sleeve. The sleeve of the second robot arm is rotated relative to the first robot arm via a pair of bevel gears. The output shaft is rotated relative to the sleeve via a plurality of bevel gears which cooperatively form a polygon.