Singularity Analysis of the 4-RUU Parallel Manipulator Using Grassmann-Cayley Algebra”. Transactions of the canadian society for mechanical engineering

This paper deals with the singularity analysis of 4-DOF parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6×6 Jacobian matrix of such manipulators contains two lines at infinity among its six Plücker lines. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manip-ulator