Kinematic Study of Non-Spherical Wrists in Industrial Robots

Serial 6DOF robots with non-spherical wrists are widely used in applications requiring high flexibility and large workspaces, such as painting and welding. A key challenge is the lack of analytical solutions for their inverse kinematics. This study investigates the kinematics of three common non-spherical wrists. Using their kinematic equations, the complete workspace of each wrist is analyzed. We propose the Generalized Reduced Gradient (GRG) numerical method to solve the inverse kinematics problem. Validation results demonstrate that the GRG method achieves high accuracy with minimal errors, outperforming existing approaches. This approach offers a robust and efficient solution for kinematic analysis and control of non-spherical wrist robots, with significant potential for industrial applications.