Kinematics Analysis of 7-DOF Collaborative Robotic Manipulators with Offsets at Shoulder and Wrist

In this paper, the inverse kinematics of a 7-DOF redundant manipulator with offsets at shoulder and wrist is presented based on the Jacobian matrix. Three Euler angles of roll-pitch-yaw are used for parameterization of the orientation of the end-effector. Then the linear relationship between joint velocities and Cartesian velocity is given for the inverse kinematic problem at velocity level. The null space of the Jacobian matrix is also used to exploit the advantages of the redundancy of the manipulator. The effectiveness of the proposed approach is verified by some numerical simulations.