|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.