In general case the singularity locus of a parallel manipulator of stewart gough type is a cubic surface on the surface on the space of translation. In the present study many objective to find all the stewart gough platform which possess only a linear or quadratic singularity surface. This manipulator has the advantage, that their singularity surface can be easily visualized because it is a plane or a quadric for any orientation of the platform, I am also aiming to give a geometric interpretation of this manipulator.