This paper deals with a new control scheme for parallel kinematic manipulators (PKMs) based on the L 1 adaptive control theory. The original L 1 adaptive controller is extended by including an adaptive loop based on the dynamics of the PKM. The additional model-based term is in charge of the compensation of the modeled non-linear dynamics in the aim of improving the tracking performance. Moreover, the proposed controller is enhanced to reduce the internal forces, which may appear in the case of redundantly actuated PKMs (RA-PKMs). The generated control inputs are first regulated through a projection mechanism that reduces the antagonistic internal forces, before being applied to the manipulator. To validate the proposed controller and to show its effectiveness, real-time experiments are conducted on a new four degrees-of-freedom (4-DOFs) RA-PKM developed in our laboratory.