Abstract: A general symbolic expression for representing the three-dimensional orientation-singularity locus of the Gough-Stewart parallel mechanism for a given position was obtained and the three-dimensional view of the orientation-singularity locus was described by using the unit quaternion as the orientation parameters. The orientation-singularity locus property of the mechanism was analyzed. Conception of the orientation-singularity-free void was advanced and the necessity of existence of the orientation-singularity-free void was illustrated. The orientation capability that was the singularity-free ball with regular shape was defined and used as an important performance index for measuring the volume of the orientation-singularity-free void. The influence of the geometry parameters and the position parameters of the mechanism on the orientation-capability was further explored and the atlases were constructed. Investigation shows that the unit quaternion can be efficiently used to represent the orientation-singularity and orientation-capability the class of the parallel mechanisms.