In this paper a novel approach to the global trajectory tracking control problem for manipulators is presented. The generalised coordinates of such mechanical systems include the link angles, that makes it possible to consider the trajectory tracking control problem in a cylindrical phase space. We propose a design procedure for nonlinear controller with computed feedforward of robot manipulators. Stability proof of the closed-loop system is given by constructing the Lyapunov function which is periodic in angular coordinates with a semi-definite time derivative and using the quasi-invariance principle for non-autonomous systems of ordinary differential equations. We illustrate the implementation of the controller using simulation example.