The　unified　analysis　of　omni-directional　wheeled　mobile　manipulator(OWMM)　through　the　dimensionally　nonhomogeneous　Jacobian　matrix　may　lead　to　unreliable　results.　The　existing　researches　focus　on　the　integrated　performance　evaluation　of　OWMM,　without　taking　the　influence　of　velocity　difference　into　consideration.　This　paper　presents　a　new　approach　to　formulate　the　dimensionally　homogeneous　Jacobian　matrix　and　a　new　index　for　OWMM.　First,　the　universal　transformational　matrix　of　the　link　coordinate　frame　is　derived　based　on　double　quaternion.　The　degree　of　locomotion　of　a　mobile　platform　and　the　degrees　of　manipulation　of　a　manipulator　are　treated　equally　as　the　joints　of　a　redundant　composite　robot.　Then　the　integrated　modeling　of　OWMM　is　established,　and　the　non-dimensional　Jacobian　matrix　is　obtained　from　the　above　matrix.　Next,　by　examining　the　concept　of　directional　manipulability,　a　new　index　is　proposed　to　evaluate　the　directional　manipulability　of　OWMM　along　the　specified　task　direction.　Furthermore,　for　the　same　task　and　the　time　of　simulation,　the　kinematic　performance　of　the　fixed　base　operation　of　the　manipulator　and　the　operation　of　OWMM　are　analyzed　by　numerical　simulation.　The　results　suggest　that　the　proposed　approach　is　equivalent　to　the　method　of　traditional　kinematic　modeling,　with　the　error　of　numerical　solution　being　10-7,　and　the　varying　frequency　of　DMTR　is　higher　than　that　of　the　condition　number.　This　indicates　that　DMTR　is　more　effective　to　reflect　the　variation　of　the　task　direction.　The　proposed　method　can　be　used　to　analyze　the　manipulating　capability　of　OWMM,　and　has　a　simple　structure　and　generality　in　the　unified　analysis　of　OWMM.