This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Scho¨nflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The study is developed through the singularity analysis of the 4-RUU parallel manipulator. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity, namely, two constraint moments, among its six Plu¨cker lines. The Grassmann-Cayley Algebra is used to obtain geometric singularity conditions. However, due to the presence of lines at infinity, the rank deficiency of the Jacobian matrix for the singularity conditions is not easy to grasp. Therefore, a wrench graph representation for some singularity conditions emphasizes the linear dependence of the Plu¨cker lines of the Jacobian matrix and highlights the correspondence between Grassmann-Cayley algebra and Grassmann geometry.