We present a methodology based on the energy shaping framework to derive strict Lyapunov functions for a class of global regulators for robot manipulators. The class of controllers is described by control laws composed by the gradient of an artificial potential energy plus a linear velocity feedback. We provide explicit sufficient conditions on the artificial potential energy that allow to obtain in a straightforward manner strict Lyapunov functions ensuring directly global asymptotic stability of the closed-loop system. As an important consequence of this methodology, we also establish a framework for designing adaptive versions for this class of regulators. An explicit update law is proposed that guarantees closed-loop stability and global positioning. Finally, we characterize a class of tracking controllers for which global uniform asymptotic stability is ensured via strict Lyapunov functions.