In　view　of　the　fact　that　the　dexterity　evaluation　on　robots　cannot　be　made　due　to　the　dimensional　inhomogeneity　of　Jacobian,　a　new　approach　to　formulation　of　the　dimensional　homogeneous　Jacobian　and　kinematic　dexterity　measure　for　the　robot　with　mixed　joints　is　proposed.　According　to　the　double　quaternion,　the　rotation　and　translation　in　three-dimensional　Euclidean　spaces　are　converted　to　the　pure　rotation　in　four-dimensional　Euclidean　spaces.　The　universal　transformational　expression　of　the　link　coordinate　system　is　derived　based　on　double　quaternion.　Then　the　kinematics　model　of　robot　is　developed　and　the　non-dimensional　Jacobian　is　obtained　by　this　approach.　Furthermore,　a　new　performance　index　is　proposed.　The　new　approach　can　solve　the　dimensional　inhomogeneity　of　Jacobian　which　occurs　for　robots　with　mixed　joints.　Finally,　the　kinematic　dexterity　of　spatial　3R　and　the　spatial　RPR　robot　is　analyzed　by　numerical　simulation.　The　results　show　that　this　approach　is　not　only　applicable　to　the　robot　with　same　joints,　but　also　to　the　robot　with　mixed　joints.