This paper presents an efficient inverse kinematics solution for redundant robotic arms. The proposed method combines the principles of continuation methods, improves the instability of the computation time by increasing the convergence of the kinematics function, and improves the efficiency of traditional numerical methods. The effectiveness and efficient performance of the method are demonstrated through comparative experiments. The computational speed of the method is twice as fast as the Newton–Raphson method under joint limit constraints and equal solution accuracy.