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This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower mobility parallel manipulators and parallel manipulators, of which some legs have no spherical joint, are such manipulators. The geometric conditions associated with the dependency of six PlUumlcker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra (GCA). Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.