Journal of Intelligent & Robotic Systems

, Volume 94, Issue 2, pp 327–338 | Cite as

Robust Backstepping Control for a Four-Bar Linkage Mechanism Driven by a DC Motor

  • Mohammad SalahEmail author
  • Ahmad Al-Jarrah
  • Enver Tatlicioglu
  • Suleiman Banihani


Four-bar linkage mechanisms have dragged the attention of many specialists due to its importance in the academic and industrial sectors. Hence, a lot of research work has been conducted to understand their complex behavior and explore various control techniques. In fact, such mechanisms possess highly nonlinear dynamics that require advanced nonlinear control methods. In addition, the four-bar linkage mechanism is exposed to significant dynamic fluctuations at high speeds due to the system inertias. In this paper, a backstepping control algorithm with a robust scheme is designed and applied on the four-bar linkage mechanism to investigate and explore its dynamical performance under various operating conditions and without a priori knowledge of the model parameters. Five operating conditions are introduced and tested in numerical simulations to show that the proposed nonlinear controller successfully regulates and tracks the speed of the driving link of the mechanism and shows a satisfactory performance.


Nonlinear system Robust backstepping control Four-bar mechanism Mechatronics 

Nomenclature List


vicious damping at motor bearing


torsional damping coefficient


center of mass of the ith link


motor armature current


moment of inertia of the motor rotor and gear


moment of inertia of the ith link


torsional spring constant


motor electromotive force voltage constant


positive control gain


motor torque constant


positive control gain


positive control gain


motor armature inductance


length of inertia of the ith link


mass of inertia of the ith link


gear ratio


motor rotor armature resistor


location of the center of mass of the ith link


total applied torque on the leading link (i.e., link 2)


mechanical load torque


motor output torque


applied armature voltage


arbitrary small positive constant


arbitrary small positive constant


arbitrary small positive constant


arbitrary small positive constant


positive constant


positive constant


positive constant


small positive constant

\(\ddot {{\phi }}_{i}\)

angular acceleration of the ith link

\(\dot {{\phi }}_{i}\)

angular velocity of the ith link


angular displacement of the ith link


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Work of E. Tatlicioglu is partially supported by The Scientific and Technological Research Council of Turkey via grant number 116M272.


  1. 1.
    Al-Jarrah, A., Salah, M., Banihani, S., Al-Widyan, K., Ahmad, A.: Applications of various control schemes on a Four–Bar linkage mechanism driven by a geared DC motor. WSEAS Trans. Syst. Control 10, 584–597 (2015)Google Scholar
  2. 2.
    Boscariol, P., Gasparetto, A., Zanotto, V.: Model predictive control of a flexible links mechanism. J. Intell. Robot. Syst. 58(2), 125–147 (2010)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bulatovic, R., Dordevic, S.: On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations. Mech. Mach. Theory 44(1), 235–246 (2009)CrossRefzbMATHGoogle Scholar
  4. 4.
    Choudhary, V.B., Singh, V.K., Dutta, A.: Design of an optimal 4-bar mechanism based gravity balanced leg orthosis. J. Intell. Robot. Syst. 86(3-4), 485–494 (2017)CrossRefGoogle Scholar
  5. 5.
    Diken, H.: Trajectory control of mass balanced manipulator. Mech. Mach. Theory 32(3), 313–322 (1997)CrossRefGoogle Scholar
  6. 6.
    Ebrahimi, S., Payvandy, P.: Efficient constrained synthesis of path generating four bar mechanisms based on the heuristic optimization algorithms. Mech. Mach. Theory 85, 189–204 (2015)CrossRefGoogle Scholar
  7. 7.
    Erentürk, K.: Hybrid control of a mechatronic system: fuzzy logic and grey system modeling approach. IEEE/ASME Trans. Mechatronics 12(6), 703–710 (2007)CrossRefGoogle Scholar
  8. 8.
    Ge, Z., Li, X., Ren, Z., Yang, F.: Research on the Hybrid Cam-Linkage Mechanism Realizing Trajectory. In: International Technology and Innovation Conference (ITIC), Hangzhou, China, pp 2012–2016 (2006)Google Scholar
  9. 9.
    Gündoğdu, Ö., Erentürk, K.: Fuzzy control of a dc motor driven four-bar mechanism. Mechatronics 15(4), 423–438 (2005)CrossRefGoogle Scholar
  10. 10.
    Hassan, A., Abomoharam, M.: Design of a Single DOF Gripper Based on Four-Bar and Slider-Crank Mechanism for Educational Purposes. In: 24th CIRP Design Conference, Procedia CIRP, vol. 21, pp 379–384 (2014)Google Scholar
  11. 11.
    Huang, T.-H., Huang, H.-P., Kuan, J.-Y.: Mechanism and control of Continuous-State coupled elastic actuation. J. Intell. Robot. Syst. 74(3-4), 571–587 (2014)CrossRefGoogle Scholar
  12. 12.
    Khalil, H.: Nonlinear Systems. 3rd Ed. Prentice Hall (2002)Google Scholar
  13. 13.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)zbMATHGoogle Scholar
  14. 14.
    Liaw, H.-C., Shirinzadeh, B.: Enhanced adaptive motion tracking control of piezoactuated flexure-based four-bar mechanisms for micro/nano manipulation. Sensors Actuators A Phys. 147(1), 254–262 (2008)CrossRefGoogle Scholar
  15. 15.
    Lin, M.-C., Chen, J.-S.: Experiments toward MRAC design for linkage system. Mechatronics 6(8), 933–953 (1996)CrossRefGoogle Scholar
  16. 16.
    Liu, Y.-H.: Saturated robust adaptive control for uncertain non-linear systems using a new approximate model. IET Control Theory Appl. 11(6), 870–876 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Lungu, R., Sepcu, L., Lungu, M.: Four-bar mechanism’s proportional-derivative and neural adaptive control for the thorax of the micromechanical flying insects. ASME J Dyn. Syst., Measurement, and Control 137(5), 051005–0510017 (2015)CrossRefGoogle Scholar
  18. 18.
    Maeda, Y., De Figueiredo, R.J.B.: Learning rules for neuro-controller via simultaneous perturbation. IEEE Trans. Neural Netw. 8(5), 1119–1130 (1997)CrossRefGoogle Scholar
  19. 19.
    Marquez, H.: Nonlinear Control Systems – Analysis and Design. Wiley, New York (2003)zbMATHGoogle Scholar
  20. 20.
    Nariman-Zadeh, N., Felezi, M., Jamali, A., Ganji, M.: Pareto optimal synthesis of four-bar mechanisms for path generation. Mech. Mach. Theory 44(1), 180–191 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    Qu, Z.: Robust Control of Nonlinear Uncertain Systems. Wiley, New York (1998)zbMATHGoogle Scholar
  22. 22.
    Rajesh Kanna, G., Ashik, M.: Design and development of a rope climbing robot using four bar mechanism with wireless control using TX2/RX2 RF Module. In: IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems (SPICES), Kozhikode, India, pp 1–6 (2015)Google Scholar
  23. 23.
    Ren, Q., Bigras, P.: A highly accurate model-free motion control system with a Mamdani fuzzy feedback controller Combined with a TSK fuzzy feed-forward controller. J. Intell. Robot. Syst. 86(3–4), 367–379 (2017)CrossRefGoogle Scholar
  24. 24.
    Sánchez-Márquez, Á., Vega-Alvarado, E., Alfredo Portilla-Flores, E., Mezura-Montes, E.: Synthesis of a Planar Four-Bar Mechanism for Position Control Using the Harmony Search Algorithm. In: 11Th International Conference on Electrical Engineering, Computing Science, and Automatic Control (CCE), Campeche, Mexico, pp 1–6 (2014)Google Scholar
  25. 25.
    Ting, C.-S., Chang, Y.-N., Shi, B.-W., Lieu, J.-F.: Adaptive backstepping control for permanent magnet linear synchronous motor servo drive. IET Electr. Power Appl. 9(3), 265–279 (2015)CrossRefGoogle Scholar
  26. 26.
    Yan, H.-S., Yan, G.-J.: Integrated control and mechanism design for the variable input-speed servo four-bar linkages. Mehcatronics 19(2), 274–285 (2009)CrossRefGoogle Scholar
  27. 27.
    Youcef-Toumi, K.: Analysis, Design and Control of Direct Drive Manipulators PhD Dissertation. Mechanical Engineering Department, Massachusetts Institute of Technology (1985)Google Scholar
  28. 28.
    Youcef-Toumi, K., Kuo, A.: High-speed trajectory control of a direct-drive manipulator. IEEE Trans. Robot. Autom. 9(1), 102–108 (1993)CrossRefGoogle Scholar
  29. 29.
    Zhang, W., Chen, X.: Mechatronics design for a programmable closed-loop mechanism. Proc. IME C J Mech. Eng. Sci. 215(3), 365–375 (2001)CrossRefGoogle Scholar
  30. 30.
    Zhang, K.: Research on high precision control system of a hybrid five-bar actuator. In: International Technology and Innovation Conference (ITIC), Hangzhou, China, pp 2149–2154 (2006)Google Scholar
  31. 31.
    Zhang, W.J., Li, Q., Guo, L.S.: Integrated design of mechanical structure and control algorithm for a programmable four-bar linkage. IEEE/ASME Trans. Mechatron. 4(4), 354–362 (1999)CrossRefGoogle Scholar
  32. 32.
    Zhang, Z., Park, J.H., Shao, H., Qi, Z.: Exact tracking control of uncertain non-linear systems with additive disturbance. IET Control Theory Appl. 9(5), 736–744 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhao, H.: Application of robust adaptive backstepping control in a class of uncertain nonlinear system. In: International Conference on Automatic Control and Artificial Intelligence (ACAI), Xiamen, China, pp 558–560 (2012)Google Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechatronics Engineering DepartmentThe Hashemite UniversityZarqaJordan
  2. 2.Electrical and Electronics Engineering DepartmentIzmir Institute of TechnologyIzmirTurkey

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