Abstract: Unit quaternion is used to represent the orientation of rigid body,orientation-singularity expression of the Stewart platform at a given position is deduced,and the singularities caused by Euler angles are avoided.The concept and algorithm for nonsingular orientation-workspace of the platform at a certain position are proposed.The minimum inscribed sphere of the boundary surface of nonsingular orientation-workspace is represented as the practical orientation-workspace,and the sphere radius is used as the performance index of the platform's practical orientation-capability at the given position.Specific structural parameters of the platform are given,and the nonsingular orientation-workspace of the platform at a certain position is described.Furthermore,the practical orientation-capability changing with the variation of positions in the position-workspace of "initial orientation" is described.