Based on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multi‐link flexible joint robots is considered in this paper. The resulting externally linearized and input‐output decoupled closed‐loop system describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, there still exists a nonlinear joint deformation subsystem causing perturbations in the nominal trajectory. To rapidly damp out the elastic vibrations and to render the complete closed‐loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the perturbed stage control. The tracking errors of the end effector caused by joint deflections due to gravity and inertia force can be compensated for by taking into account the nominal deflections in both the trajectory planning and LQ regulation. A three‐link PUMA type arm is tested via simulation.