Since　singularity　is　the　inherent　characteristic　of　parallel　mechanism　and　has　bad　effects　on　manipulator＇s　working　performance,　for　a　certain　mechanism,　its　singular　configures　should　be　found　out.　The　paper　chooses　the　Tricept　parallel　mechanism,　analyzing　the　singularity　in　three　different　actuator　dispositions,　including　a　prismatic　pair　and　two　revolute　pairs　of　the　universal　joint,　of　the　Tricept.　First,　the　systems　of　twists　and　reciprocal　screws　of　the　limbs　of　the　Tricept　are　deduced　based　on　the　screws　theory.　Second,　the　constraint　sub-matrix　and　actuation　sub-matrix　are　obtained　through　the　orthogonal　product,　and　the　complete　Jacobian　matrix　of　the　Tricept　is　obtained.　Finally,　the　singular　conditions　of　the　parallel　mechanism　are　analyzed　by　investigating　the　rank　of　the　Jacobian　matrices　and　the　theory　of　Grassmann　line　geometry,　and　the　singular　configures　of　three　actuator　dispositions　of　the　Tricept　and　their　kinematic　characteriscs　are　obtained.