<p>This paper presents a novel numerical algorithm for inverse kinematics (IK) in robotic arms with offset wrists to address the challenges in IK solutions caused by biased parameters. Initially, the problem is simplified by categorizing robotic arms into two standard types and applying rotation or translation transformations to the terminal link. This approach is used for a robotic arm with a biased wrist, allowing for the acquisition of joint angles that approximate the desired solution. Subsequently, the initial Hessian matrix is corrected by incorporating the Jacobian matrix and regularization terms. Furthermore, the step size of the scaled memoryless augmented Broyden-Fletcher-Goldfarb-Shanno (SMABFGS) algorithm is dynamically adjusted to avoid convergence to local optima by integrating a momentum-based gradient descent (GD) method. The joint angles are iteratively refined to facilitate the convergence of the robotic arm’s end effector toward the desired pose. Finally, the algorithm’s accuracy in solving discrete end-effector poses is validated through a simulation experiment of IK with randomly sampled end poses. Additionally, a trajectory-tracking experiment is conducted on a physical robotic arm with an offset wrist to demonstrate its effectiveness and real-time performance in practical robotic operations.</p>