Characterization and parameterization of the singular manifold of a   simple 6-6 Stewart platform
  This paper presents a study of the characterization of the singular manifold of the six-degree-of-freedom parallel manipulator commonly known as the Stewart platform. We consider a platform with base vertices in a circle and for which the bottom and top plates are related by a rotation and a contraction. It is shown that in this case the platform is always in a singular configuration and that the singular manifold can be parameterized by a scalar parameter. 
T. Charters and P. Freitas