Local analysis of singular configurations of open and closed loop manipulators

The paper gives a general approach to the local analysis of singular configurations of both serial and parallel manipulators. For all possible cases the maximum rank deficiency of the manipulator Jacobian is given and shown never to exceed 4. This is the equivalent to the maximum number of linear dependent constraint equations for kinematic loops. Singular configurations of serial/parallel manipulators are roughly classified with respect to the active and passive joints. An algorithm is presented which determines the singular motion of a mechanism. This algorithm is purely algebraic and involves at maximum three steps. It is based on the instantaneous screw system of the considered mechanism. It is shown that fourth order analysis is always sufficient to locally characterize the configuration space manifold in singular points. Thus the singular set can locally be approximated by a hypersurface of maximum degree 4. The approach can easily be implemented in existing simulation tools. Finally the minimum number of joints is given that a serial manipulator must activate in order to escape from a singular configuration.