Singularity Analysis and Representation of Spatial Six-Dof Parallel Manipulators

In this paper, the singularity loci of general six-degree-of-freedom spatial parallel manipulators are studied and a graphical representation of these loci in the manipulator’s workspace is obtained. The algorithm presented is based on analytical expressions of the determinant of the Jacobian matrix. As mentioned elsewhere, two different types of singularities can occur when parallel manipulators are actuated. Both types are considered here and it is shown that one of the two types leads to a trivial description while the second type is more challenging. Moreover, it is shown that, for a given orientation of the platform, the singularity locus in the Cartesian space is represented by a polynomial of degree four. Examples illustrating these results are given. A graphical representation in the Cartesian space is also obtained.