We consider the problem of perfect cancellation of gravity effects in the dynamics of robot manipulators having flexible transmissions at the joints. Based on the feedback equivalence principle, we aim at designing feedback control laws that let the system outputs behave as those of a desired model where gravity is absent. The cases of constant stiffness (elastic joints), nonlinear flexible, and variable nonlinear flexible transmissions with antagonistic actuation are analyzed. In all these situations, viable solutions are obtained either in closed algebraic form or by a simple numerical technique. The compensated system can then be controlled without taking into account the gravity bias, which is particularly relevant for safe physical human-robot interaction tasks where such compliant manipulators are commonly used. Simulation results are reported illustrating the obtained performance.