The objective of this paper is two-fold. Firstly, we extend the applications of the control scheme, proposed by Ailon (1996, Automatica, 32(10), 1455-1461), which is based on the contraction mapping theorem, to a full model of a robot manipulator (Tomei, 1991, IEEE Transactions on Automatic Control, 36(10), 1208-1213). Next, we present relaxed sufficient conditions on the gains involved in the control scheme that ensure convergence of the system trajectory to the desired neighborhood of the equilibrium point. Simulation results demonstrate the contribution of this note.