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In this work, two globally stabilizing bounded control schemes for the tracking control of robot manipulators with saturating inputs are proposed. They may be seen as extensions of the so-called PD+ algorithm to the bounded input case. With respect to previous works on the topic, the proposed approaches give a global solution to the problem through static feedback. Moreover, they are not defined using a specific sigmoidal function, but any one on a set of saturation functions. Consequently, each of the proposed schemes actually constitutes a family of globally stabilizing bounded controllers. Furthermore, the bound of such saturation functions is explicitly considered in their definition. Hence, the control gains are not tied to satisfy any saturation-avoidance inequality and may consequently take any positive value, which may be considered beneficial for performance-adjustment/improvement purposes. Further, a class of desired trajectories that may be globally tracked avoiding input saturation is completely characterized. For both proposed control laws, global uniform asymptotic stabilization of the closed-loop system solutions towards the prespecified desired trajectory is proved through a strict Lyapunov function. The efficiency of the proposed schemes is corroborated through experimental results.