When regarding plate mail, it seems that rivets would limit the range of motion for a wearer too much, especially for a sword arm. How were the individual segments of the armor held together?
Rivets, properly placed in well-designed joints, can allow full range of motion. Beyond that, pieces of armor can be attached to leather straps, or attached over the top of a base layer of mail, leather, or heavy fabric. Also, different pieces can slide over the top of other components. For example, a gauntlet cuff may be sized to allow freedom of movement over the top of forearm armor.