Abstract: 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 scerws 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.