FORWARD KINEMATICS MODELING OF A 5-DOF GANTRY ROBOT USING THE DENAVIT–HARTENBERG METHOD

О. О. Баранов, М. П. Ковальов, А. О. Бреус

Abstract


This paper presents an analytical solution to the forward kinematics problem for a prospective gantry robotic manipulator with five degrees of freedom, intended for typical industrial automation tasks such as packaging, sorting, and precise object positioning. The manipulator’s design includes one translational and four rotational actuators, providing high flexibility in controlling the end-effector’s movement in space. To develop the mathematical model, the classical Denavit–Hartenberg (D-H) method was employed, allowing for a compact representation of the kinematic chain using four parameters for each joint. Local coordinate systems were sequentially constructed on each link, and parameters for offset, rotation, link length, and displacement were identified. Homogeneous transformation matrices were generated, leading to the final transformation matrix representing the end-effector’s position and orientation relative to the base frame. To validate the model, a simulation of sequential joint movements was carried out, covering five characteristic manipulator poses. The results are presented as graphs showing changes in the end-effector’s center coordinates and direction cosines, which reflect the orientation of the local coordinate axes. The visualization enabled tracking the influence of each degree of freedom individually and assessing the model’s precision. The developed model is universal and may serve as a foundation for digital twin generation, motion control software development, pre-deployment testing in CAD/CAE environments, and integration into flexible manufacturing systems. The proposed approach enables efficient resolution of the forward kinematics problem and is easily adaptable to other gantry robot architectures with varying numbers of degrees of freedom. As such, this study contributes to improving the accuracy, repeatability, and reliability of robotic systems operating in complex production environments.


Keywords


gantry robot, forward kinematics, Denavit–Hartenberg method, manipulator.

References


Gantry Robot for Mobile Observation / H. Jamaludin, M. N. Mansor, A. K. Junoh, A. Idris // Applied Mechanics and Materials. – 2015. – Vol. 798. – p. 70 74.

Development of multi-axis gantry type welding robot system using a PC based controller / J. Lee, J.Kim, H. Kim, I. Park. – IEEE International Symposium on Industrial Electronics Proceedings. – 2001. – Vol.3. – p. 1536-1541.

Diagnostics Laboratory Automation – Archiving Vacuum Tubes Using a Low-Cost Gantry Robot / R. P. Badiger; V. N. Patil; S. Marathe; N. Ananya. – International Conference on Control, Automation and Robotics (ICCAR) : Orchard District, Singapore. – 2024. – p. 159-165.

Linear Gantry Robot Control System / S. Date, S. Makwana, D. Mewada, S. D. Degadwala. – 4th National Conference on Advances in Engineering and Applied Science : Maharashtra, India. – 2020. – Vol. 5, Iss. 7. – p. 30-38.

Development of multi-axis gantry type welding robot system using a PC-based controller / J. Lee, J. Kim, H. Kim, I. Park. – IEEE International Symposium on Industrial Electronics Proceedings : Pusan, Korea (South). – 2001. – Vol. 3. – p. 1536 1541.

Dynamic Scheduling of Gantry Robots using Simulation and Reinforcement Learning / H. Zisgen, R. Miltenberger, M. Hochhaus, N. Stöhr. – Winter Simulation Conference : San Antonio, USA. – 2023. – p. 3026-3034.

Mobile Gantry Robot for Pick & Place Application / L. P. Chandak, A. Junghare, T. Naik, N. Ukani, S. Chakole. – IEEE International Students' Conference on Electrical, Electronics and Computer Science : Bhopal, India. – 2020. – p. 1-5.

Ranaganathan, S. A Customised Gantry Pick and Place System for Forging Industries / S. Ranaganathan., M. Saravanabalaji, V. Athappan. – International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation : Coimbatore, India. – 2021. – p. 1-4.

Černohorský, J. Laboratory gantry robot design and control / J. Černohorský, D. Lindr. – Proceedings of the 13th International Carpathian Control Conference : High Tatras, Slovakia, 2012, pp. 86-90.

Application of Denavit Hartenberg Method in Service Robotics / E. Prada, S. Murali, L. Miková, J. Ligusova // Acta Mechatronica. – 2020. – Vol. 5, Iss. 4. – p. 47 52.

Research on the Relationship between Classic Denavit-Hartenberg and Modified Denavit-Hartenberg / H. Wang, H. Qi, M. Xu, Y. Tang, J. Yao, X. Yan. –Seventh International Symposium on Computational Intelligence and Design : Hangzhou, China. – 2014. – p. 26-29.

Asif, S. Kinematics Analysis of 6-DoF Articulated Robot with Spherical Wrist / S. Asif, P. Webb // Mathematical Problems in Engineering. – 2021. – Vol. 2021, Iss. 1. – Article No. 6647035. – p. 1-11.

Ciuccio, R. Comparison of Modified D-H Notation with Standard D-H for and all of Direct Kinematics of Industrial Robotic manipulators / R. Ciuccio // Engineering and Technology Journal. – 2022. – Vol. 07, Iss. 07. – 2022. – p. 1419 1421.

Villalobos, J. Statistical comparison of Denavit-Hartenberg based inverse kinematic solutions of the UR5 robotic manipulator / J. Villalobos, I. Y. Sanchez, F. Martell, //International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME). – Mauritius, Mauritius. – 2021. – p. 1-6.

Brodtmann, N. Kinematics of Serial Robotics - Algorithms for simplified calculation of Direct & Inverse Kinematics in a Consistent Coordinate Reference sys¬tem / N. Brodtmann, D. Schilberg. – Emerging Technologies and Future of Work. AHFE (2023) International Conference : New York, USA. – 2023. – Vol. 117. – p. 34 38.

Corke, P. I. A Simple and Systematic Approach to Assigning Denavit–Hartenberg Parameters / P. I. Corke // IEEE Transactions on Robotics. – 2007. – Vol. 23, Iss. 3. – pp. 590-594.

Martínez, O. Comparing Methods Using Homogeneous Transformation Matrices for Kinematics Modeling of Robot Manipulators / O. Martínez, R. Campa. – Multibody Mechatronic Systems : Springer, Cham. – 2021. – Vol 94. – p. 127-136.

Industrial robot calibration method using Denavit - Hartenberg parameters / J. -W. Lee, G. -T. Park, J. -S. Shin and J. -W. Woo. – 17th International Conference on Control, Automation and Systems : Jeju, Korea (South). – 2017. – p. 1834-1837.

Baločková, L. The Method for Solving Kinematics of an Industrial Robot / L. Baločková // Applied Mechanics and Materials. – 2013. – Vol. 282. – P. 274-281.

Robot control and kinematic analysis with 6DoF manipulator using direct kinematic method / K. S. Gaeid, A. F. Nashee, I. A. Ahmed, M. H. Dekheel // Bulletin of Electrical Engineering and Informatics. – Vol.10, Iss.1. – 2021. – p. 70-78

Denavit, J. A kinematic notation for lower-pair mechanisms / J. Denavit, R. S. Hartenberg // Journal of Applied Mechanics. – 1955. – Vol. 22, Iss. 2. – p. 215 221.




DOI: https://doi.org/10.32620/oikit.2025.104.10

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