This paper presents a closed-form kinematic pipeline suitable for deployment on the ABB IRB 1520ID welding robot and more generally on other 6-DoF spherical-wrist manipulators. Built on the standard Denavit–Hartenberg framework and Pieper’s analytical decoupling, our Python implementation provides both forward and inverse kinematics. The forward model returns the tool center point pose from joint variables with orientation expressed using intrinsic Euler ZYX angles, while the inverse kinematics explicitly enumerates the eight admissible configurations induced by the shoulder–elbow–wrist couplings and enforces manufacturer-specified joint-limit bounds to ensure physically feasible solutions. Cross-checks in RoboDK show agreement within numerical precision between analytic results and simulator outputs under the stated settings. Benchmarking over repeated trials indicates per-pose runtimes of \(52.45~\mu s\) for forward kinematics, \(117.18~\mu s\) for inverse kinematics, and an end-to-end (including verification) cost of \(\approx 1.37~ms\) , supporting real-time use. Thanks to its generic structure, the methodology can be readily adapted to other six-revolute industrial robots with spherical wrists and can support practical deployment in robot programming and control, and research on welding-path optimization and motion planning.