Analysis of Kinematic Singularities for a Serial Redundant Manipulator with 7 DOF

In this work, the kinematic singularities of serial manipulators with 7 rotational joints are analyzed and their effects on the possible end effector movement are studied. We obtain the numerical kinematic singularities through algebraic varieties and demonstrate this on the kinematically redundant serial manipulator KUKA LBR iiwa. The algebraic equations for determining the variety are derived by taking the determinant of the 6-by-6 submatrix of the Jacobian matrix of the forward kinematics. By using the primary decomposition, the singularities can be decomposed and classified. Further analysis of the kinematic singularities including the inverse kinematics of the redundant manipulator provide us valuable insights. Firstly, there are kinematic singularities where the inverse kinematics has no effect on the self-motion and cannot be used to avoid obstacles. Secondly, there are kinematic singularities, which lead to a single closed-loop connection with the serial redundant manipulator, so that a kinematotropic mechanism is achieved.