Abstract
This paper presents a comprehensive mathematical model of the ABB IRB 2400 industrial robot, developed to support simulation, control design, and digital twin applications. The model includes both kinematic and dynamic descriptions of the manipulator. Kinematic modelling is based on a modified Denavit-Hartenberg convention and includes transformation matrices and the Jacobian matrix. The dynamic model was derived using both the Euler-Lagrange and Newton-Euler formalisms, enabling validation through independent formulations. Physical parameters such as link masses, centres of mass, and moments of inertia, were estimated through CAD analysis. Friction coefficients were determined by experimental testing. Model validation was performed by comparing simulated joint torques with measurements on the real robot for representative trajectories. The results show agreement: for Joints 2–3 the RMSE relative to the average actuator torque is ≈ 3.4–3.7%, while for Joints 4–6 it remains below 10% (Joint 1 reaches 11.6%). Compared with typical kinematics-only simulation in offline-programming tools, the proposed model captures dynamic effects. The equation set is computationally light and amenable to real-time use within standard control cycles, facilitating integration into digital-twin workflows. The approach is also transferable to other six-axis manipulators of comparable architecture by updating link inertias and friction coefficients. Limitations include the rigid-body assumption (no link/joint compliance or backlash) and reliance on controller-reported actuator torques whose proprietary accuracy is not disclosed; these aspects motivate future extensions with elastic joints, external-force observers and uncertainty tracking.