An analytical solution for inverse kinematic of 7-DOF redundant manipulators with offset-wrist

A valid analytical inverse kinematics computation for seven-degree-of- freedom (7-DOF) redundant manipulators with offset-wrist is proposed. The method uses a virtual joint to replace the join offset from the wrist, and forms a virtual manipulator with a sphere-wrist. Assuming that the virtual manipulator and the real manipulator's joint angles keep the same all the time, the virtual manipulator seems to be driven by the real manipulator; meanwhile, the real manipulator seems to be driven by the virtual manipulator. There is an interesting relationship between these two manipulators: the pose of the virtual manipulator can be calculated if the pose and the 7th joint's angle of the real manipulator are given. It means that the virtual manipulator is driven to the calculated pose when the real manipulator moves to the given pose with the given 7th joint angle, meanwhile, the real manipulator will be driven to the to the given pose when the virtual manipulator moves to the calculated pose with the given 7th joint angle. Then the inverse kinematic solutions of real manipulator can be obtained through solving the inverse kinematic problems of virtual manipulator with a known 7th joint angle. They share the same solutions. In this paper, the manipulators' configuration is analyzed and the virtual joint method and its detailed solution processes were given. Lastly the method is verified by kinematic simulations. The results show that the virtual joint method behaves high precision in solving the inverse kinematic of 7-DOF redundant manipulator with offset-wrist.