A transporter or transport robot especially for transporting workpieces between presses has a cantilever arm swingable about a vertical first axis on a stationary base and a horizontal second axis in a common plane. A linear positioner is swingable at a free end of this cantilever arm about a vertical third axis and carries a gripper head on which the gripper is mounted for rotation about further axes. The workpiece can thus be swung across the first vertical axis to maintain its position along a line between the presses if the linear positioner and cantilever arm will swing in opposite senses. The actuator for the angular displacement may be electrical or hydraulic and a linear motor can be provided for the linear positioner.