Dynamic Modelling of the Spring Attached Two-Link Planar Manipulator

Year 2023, , 133 - 140, 30.06.2023

Onur Denizhan

https://doi.org/10.22399/ijcesen.1307444

Abstract

Robot dynamics is required for simulation, control, analysis of robot motion planners and controllers. There are a number of dynamic modelling investigations of robots with the different approaches and these investigations mostly focus on the link flexibility, joint friction or actuator dynamics. In addition to that these studies present dynamic model without any attached linear or torsion springs. In this study, the dynamic modelling of a two-link rigid manipulator with attached torsion springs is presented using the Lagrangian approach. The Lagrangian approach is a variational method that relies on the potential and kinetic energy of the mechanism, making it well-suited for the analysis of the two-link planar manipulator considered in this study. Initially, the two-link mechanism equations of motion are derived without any attached torsion springs. Subsequently, two torsion springs are attached to the joints of the mechanism, and the existing equations of motion are modified accordingly. The study also presents the kinetic, potential and total energies of the two link-manipulator, angular positions of the links and their velocities. By considering the dynamic modelling of the torsion spring attached two-link rigid manipulator, this study contributes to understanding and analysis of the two-link manipulators and the dynamic effects of the attached springs.

Keywords

Two-link planar manipulator, Dynamic modelling, Lagrangian, Torsion springs

References

• [1] Khairudin, M., Mohamed, Z., Husain, A. R., & Ahmad, M. A. (2010). Dynamic modeling and characterization of a two-link flexible robot manipulator. Journal of Low Frequency Noise, Vibration and Active Control, 29(3); 207-219. https://doi.org/10.1260/0263-0923.29.3.207
• [2] Subudhi, B., & Morris, A. S. (2002). Dynamic modelling, simulation and control of a manipulator with flexible links and joints. Robotics and Autonomous Systems, 41(4); 257-270. https://doi.org/10.1016/S0921-8890(02)00295-6
• [3] Chen, W. (2001). Dynamic modeling of multi-link flexible robotic manipulators. Computers and Structures, 79(2); 183-195. https://doi.org/10.1016/S0045-7949(00)00129-2.
• [4] Subedi, D., Tyapin, I., & Hovland, G. (2021). Dynamic modeling of planar multi-link flexible manipulators. Robotics, 10(2); 70. https://doi.org/10.3390/robotics10020070.
• [5] Morris, A.S., & Madani, A. (1996). Static and dynamic modelling of a two-flexible-link robot manipulator. Robotica, 14; 289-300 doi:10.1017/S0263574700019603.
• [6] Nicosia, S., Valigi, P., & Zaccarian, L. (1996). Dynamic modelling of a two link flexible robot and experimental validation, Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, 3, 1953-1958. doi: 10.1109/ROBOT.1996.506158.
• [7] Mayeda, H., Yoshida, K., & Osuka, K., (June, 1990). Base parameters of manipulator dynamic models. IEEE Transactions on Robotics and Automation, 6(3); 312-321, doi: 10.1109/70.56663.
• [8] Thomas, M., & Tesar, D. (1982) Dynamic modeling of serial manipulator arms. J. Dyn. Sys. Meas. Control. 104(3); 218-228. https://doi.org/10.1115/1.3139701
• [9] Mehrjooee, O., Dehkordi, S. F., & Korayem, M. H. (2020). Dynamic modeling and extended bifurcation analysis of flexible-link manipulator, Mechanics Based Design of Structures and Machines, 48(1); 87-110, doi: 10.1080/15397734.2019.1665542
• [10] Gamarra-Rosado, V. & Yuhara, E. (1999). Dynamic modeling and simulation of a flexible robotic manipulator. Robotica, 17(5); 523-528. doi: 10.1017/S0263574799001721
• [11] Vakil, M., Fotouhi, R., & Nikiforuk, P. N. (December 28, 2011). A new method for dynamic modeling of flexible-link flexible-joint manipulators. ASME J. Vib. Acoust. 134(1); 014503. https://doi.org/10.1115/1.4004677.
• [12] De Luca, A., & Siciliano, B. (1990). Explicit dynamic modeling of a planar two-link flexible manipulator, 29th IEEE Conference on Decision and Control, Honolulu, HI, USA, 2, 528-530. doi: 10.1109/CDC.1990.203652.
• [13] Lochan, K., Roy, B. K., & Subudhi, B. (2016). A review on two-link flexible manipulators, Annual Reviews in Control, 42; 346-367. https://doi.org/10.1016/j.arcontrol.2016.09.019.
• [14] Hastings, G., & Book, W. (February, 1987). A linear dynamic model for flexible robotic manipulator, IEEE Control Systems Magazine, 7(1); 61-64, doi: 10.1109/MCS.1987.1105233.
• [15] Arteaga, M. A. (March 1, 1998). On the properties of a dynamic model of flexible robot manipulators, ASME J. Dyn. Sys. Meas., Control., 120(1); 8-14. https://doi.org/10.1115/1.2801326