Singularity Analysis of Limited-dof Parallel Manipulators using Grassmann-Cayley Algebra

This paper characterizes geometrically the singularities of limited DOF parallel manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra. Manipulators under consideration do not need to have a passive spherical joint somewhere in each leg. This study is illustrated with three example robots