In this paper, we study the singularity loci of a special class of spherical three-degree-of-freedom parallel manipulators. The concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the direct and inverse kinematic solutions of these manipulators, respectively. As mentioned elsewhere, there are three different types of singularities for parallel manipulators, each having a different physical interpretation. These types are considered and it is shown that, for the manipulators considered here, the three types of singularities coincide. Moreover, for the two types of manipulators studied here, there are only four singular configurations in the Cartesian space. In addition, the three-dimensional graphical representations of the singularity loci in the joint and in the Cartesian spaces are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.
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