The singularity locus analysis of the Stewart mechanism is one of the main concerns in the analysis and design of the parallel manipulators. Based on the new singularity kinematics theory we propose a singularity-equivalent-mechanism, thus the complex singularity analysis of the parallel Stewart mechanism is transformed into a simpler position analysis of the singularity-equivalent-mechanism. Using this method, the singularity locus equation of an analytical polynomial expression of degree three is transformed into a simpler equation and has finally been resolved into a plane equation and a hyperbola for all of the possible orientations of the moving platform.