Redundantly　actuated　parallel　manipulators　(RAPMs)　receive　growing　interest　due　to　their　enlarged　dexterous　workspace,　higher　stiffness　and　improved　force　distribution.　The　results　of　dimensional　synthesis　have　an　important　influence　on　the　comprehensive　performance　of　RAPMs.　Usually,　dexterity　index　is　one　of　the　performance　indices,　which　should　be　took　into　consideration.　The　dexterity　index　is　based　on　the　algebraic　characteristics　of　the　Jacobian　matrix.　However,　for　an　RAPM　with　combined　motilities　of　rotation　and　translation,　its　Jacobian　matrix　has　inconsistent　element　units　and　un-clear　physical　meaning.　This　paper　establishes　a　set　of　dexterity　indices　based　on　the　dimensionally　homogeneous　Jacobian　(DHJ)　matrix　of　a　2UPR-2RPS　RAPM　for　dimensional　synthesis.　Firstly,　a　local　dexterity　index　is　established　to　evaluate　the　dexterity　of　the　2UPR-2RPS　RAPM　at　a　certain　posture.　Meanwhile,　a　global　dexterity　index　is　determined　in　accordance　with　the　local　dexterity　index.　Secondly,　a　dimensional　design　method　based　on　the　parameter-finiteness　normalization　method　(PFNM)　is　proposed　to　optimize　the　dimensional　parameters　of　the　2UPR-2RPS　RAPM.　Finally,　a　set　of　dimensional　parameters　is　optimized　and　a　laboratory　prototype　of　the　2UPR-2RPS　RAPM　is　fabricated.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.