A robot arm mechanism includes a housing, upper and lower arms rotatably mounted on the housing, a respective substrate-supporting blade connected to each upper arm, and first, second, third and fourth driving units for rotating the housing, the upper and lower arms and the blade independently of one another. Thus, positions of the blades are readily controlled so that the blades and/or the substrates supported by the blades can be prevented from colliding against the inner wall of the chambers into and from which the substrates are transferred by the robot arm mechanism.