The 6-UPS mechanism posture matrix is described by using quaternion,and both the rotation matrix and the coordinates of the vectors are expanded to 4dimensions,and the kinematical equations is obtained.Through derivation,the new type of Jacobi matrix JAand JBof mechanism motion are obtained,and JAis described by using quaternion and do not contain beyond variables.According to the nature of the quaternion,the JAis translated into 8dimensions square matrix,and make it applicable to the analysis of singular position and posture singular.The expansion of a determinant JAand JB is respectively carried out,the trajectory equation of first kind of singularity and the second kind of singularity are obtained,and their three-dimensional trajectory surfaces are obtained by using MATLAB when the location of the mechanism is given.The advantages of solving convenient of using the matrix obtained by this method is proved.