In this paper, a globally stabilising PID-type control scheme with a generalised saturating structure for robot manipulators under input constraints is proposed. It gives rise to various families of bounded PID-type controllers whose implementation is released from the exact knowledge of the system parameters and model structure. Compared to previous approaches of the kind, the proposed scheme is not only characterised by its generalised structure but also by its very simple tuning criterion, the simplest hitherto obtained in the considered analytical framework. Experimental results on a 3-degree-of-freedom direct-drive manipulator corroborate the efficiency of the proposed approach.