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It is still a challenge to accurately and efficiently solve inverse kinematics (IK) using six-degrees-of-freedom (DOF) serial manipulators with offset or reduced wrists, which is mainly due to the complex, highly nonlinear, and coupled IK equations. In order to solve this problem, an efficient IK algorithm called hierarchical iterative inverse kinematic algorithm (HIIKA) is proposed in this paper. This novel IK solution algorithm consists of two-level iterations. The first-level iteration can achieve accurate initial estimates through an extended heuristic iterative method that proposed in this paper. The second-level iteration calculates all joint angles based on the results of the first-level iteration. To evaluate the performance of the HIIKA, experiments were carried out with a six-DOF manipulator with a two-DOF reduced wrist. The results obtained demonstrate the advancement and excellence of the HIIKA in terms of its convergence, accuracy, computational efficiency, and multiple solutions. The HIIKA provides a new tool for the analysis and application of manipulators with offset or reduced wrists.