Redundantly actuated parallel manipulator (RAPM) has been proved to have comparative advantages of higher rigidity and higher payload over other parallel manipulators. This paper is to quantitatively reveal the effect of redundancy on rigidity enhancement of a previously invented 2UPR&1RPS&1RPU RAPM. For this purpose, three critical issues are clarified, i.e. establishing a sufficient accurate stiffness model, constructing a reasonable index frame for evaluating rigidity performance and quantifying the effect of redundancy on the rigidity enhancement. Firstly, drawing on the screw theory, a hierarchical method is presented to establish a semi-analytic stiffness model at joint level for the proposed RAPM. Secondly, based on the stiffness matrix, a set of local and global stiffness indices are constructed to evaluate the rigidity of parallel manipulators. Finally, the stiffness indices of the 2UPR&1RPS&1RPU RAPM and its non-redundantly actuated forms are predicted and compared to reveal the effort of redundancy. The present work is expected to provide a useful frame for quantitatively assessing redundancy induced rigidity enhancement in redundantly actuated parallel manipulators.