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.　First,　drawing　on　the　screw　theory,　a　hierarchical　method　is　presented　to　establish　a　semi-analytic　stiffness　model　at　the　joint　level　for　the　proposed　RAPM.　Subsequently,　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.　Copyright　©　2022　by　ASME.