This paper presents a generic approach to analyze the singularity of robots with an articulated nacelle like the H4 robot. Using screw theory, the concept of equivalent twist graph is introduced in order to characterize the constraint wrenches and the actuation wrenches applied to the moving platform. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plücker vectors of finite and infinite lines in the projective space P3 are reformulated in the superbracket decomposition in order to characterize geometrically the parallel singularities of the robot.