A substrate-transporting robot apparatus is disclosed. The robot apparatus may include an upper arm, a forearm independently rotatable relative to the upper arm, a wrist member independently rotatable relative to the forearm, and an end effector adapted to carry a substrate. In some aspects, the independent rotation is provided by a robot drive assembly having a second driving pulley mounted for rotation on a first driving pulley. In another aspect, robot drive assemblies including base-mounted and web-mounted pulleys are disclosed. Robot drive assemblies and operational methods are provided, as are numerous other aspects.