Singularity Analysis of the 4-RUU Parallel Manipulator using Grassmann-Cayley Algebra

International audienceThis 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 6x6 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-\underline RUU parallel manipulator