Calculated Torque Control of a Planar Parallel Robot 2-RR

Eugenio Yime Rodríguez, Javier Roldán Mckinley, José Villa Ramírez


This paper introduces the design, structure and control method of a five-bar planar mechanism with five revolute joints and two degrees of freedom. The control is realized by calculating the torque in the joint space to obtain the required trajectory. The direct and inverse kinematics of position and velocity are proposed, and the inverse kinematics of acceleration is taken as the parameter required by the control law. The method selected for this parallel robot is advantageous because it allows to obtain the dynamic equations similar to the traditional series robot modeling, which is helpful to the realization of nonlinear control technology. The effectiveness of the method and the functionality of the controller are verified by experiments, and a circular trajectory is generated by the actuator. Although the simulation results are consistent with the experimental results, it is suggested that the future work is to change the control strategy to compensate for the influence of the unmodeled system.


CTC; Parallel Dynamics; Robot Control; 5-Bar Mechanism; Planar Robot 2-RR

Full Text:



Vinogradov O. Fundamentals of kinematics and dy-namics of machines and mechanisms. U.S.A: CRC Press; 2000.

Uicker J, Pennock G, Shigley J. Theory of machines and mechanisms. U.S.A: Oxford University Press; 2010.

Norton R. Design of machinery: An introduction to the synthesis and analysis of mechanisms and machines. New York: McGraw-Hill; 2011.

Stanisic M. Mechanisms and machines: Kinematics, dynamics and synthesis. U.S.A: Cengage Learning; 2014.

Seth B, Vaddi S. Programmable function generator—I: Base five-bar mechanism. Mechanism and Machine Theory 2003; 38(4): 321–330. doi: 10.1016/S0094-114X(02)00121-0.

Zhou H, Ting KL. Path generation with singularity avoidance for five-bar slider-crank parallel manipulators. Mechanism and Machine Theory 2005; 40(3): 371–384. doi: 10.1016/j.mechmachtheory.2004.07.007.

Kim JY. Task based kinematic design of a two DOF manipulator with a parallelogram five-bar link mecha-nism. Mechatronics 2006; 16(6): 323–329. doi: 10.1016/j.mechatronics.2006.01.004.

Ouyang PR, Li Q, Zhang WJ, et al. Design, modeling and control of a hybrid machine system. Mechatronics 2004; 14(10): 1197–1217. doi: 10.1016/j.mechatronics.2004.06.004.

Nahavandi S, Uddin MJ, Saadat M, et al. Heavy tools manipulation by low powered direct-drive five-bar par-allel robot. Mechanism and Machine Theory 2008; 43(11): 1450–1461. doi: 10.1016/j.mechmachtheory.2007.11.004.

Giberti H, Cinkemani S, Ambrosetti S. 5R 2-DOF par-allel kinematic manipulator: A multidisciplinary test case in mechatronics. Mechatronics 2013; 23(8): 949–959. doi: 10.1016/j.mechatronics.2012.09.006.

Krebs H, Ferraro M, Buerger S, et al. Rehabilitation robotics: Pilot trial of a spatial extension for MIT-Manus. Journal of NeuroEngineering and Rehabil-itation 2004; 1(5): 1–15. doi: 10.1186/1743-0003-1-5.

Villarreal-Cervantes M, Cruz-Villar C, Alvarez-Gallegos J, et al. Differential evolution techniques for the struc-ture-control design of a five-bar parallel robot. Engi-neering Optimization 2010; 42(6): 535–565. doi: 10.1080/03052150903325557.

Joubair A, Slamani M, Bonev I. Kinematic calibration of a five-bar planar parallel robot using all working modes. Robotics and Computer-Integrated Manufacturing 2013; 29(4): 15–25. doi: 10.1016/j.rcim.2012.10.002.

Qunser. Two DOF robot [Online]. 2014 [Cited 2015 July 7]. Available from:

Figielski A, Bonev I,Bigras P. Towards development of a 2-DOF planar parallel robot with optimal workspace use. 2007 IEEE International Conference on Systems, Man and Cybernetics; 2007 Oct 7–10; Montreal. 2008. p. 1562–1566.

Campos L,Bourbonnais L, Bonev I,et al. Devel-opment of five-bar parallel robot with large workspace. ASME International Design Engineering Technology Conference; 2010 Aug 15–18; Montreal. 2010.

Bourbonnais F, Bigras P, Bonev I. Minimum time tra-jectory planning and control of a pick-and-place five-bar parallel robot. IEEE/ASME Transactions on Mechatronics 2015; 20(2): 740–749. doi: 10.1109/TMECH.2014.2318999.

Wu FX, Zhang WJ, Li Q, et al. Control of hybrid ma-chines with 2-DOF for trajectory tracking problems. IEEE Transactions on Control Systems Technology 2005; 13(2): 338–342. doi: 10.1109/TCST.2004.839580.

Cheng L, Lin Y, Hou ZG, et al. Adaptive tracking con-trol of hybrid machines: A closed-chain five-bar mech-anism case. IEEE/ASME Transactions on Mechatronics 2011; 16(6): 1155–1163. doi: 10.1109/TMECH.2010.2083680.

Cheng L, Hou ZG, Tan M, et al. Tracking control of a closed-chain five-bar robot with two DOF by integration of an approximation-based approach and mechanical design. IEEE Transactions on Systems, Man, and Cy-bernetics 2012; 42(5): 1470–1479. doi: 10.1109/TSMCB.2012.2192270.

Zi B, Cao J, Zhu Z. Dynamic simulation of hy-brid-driven planar five-bar parallel mechanism based on SimMechanics and tracking control. International Journal of Advanced Robotic Systems 2011; 8(4): 28–33. doi: 10.5772/45683.

Yu H. Modeling and control of hybrid machine sys-tems—A five-bar mechanism case. International Journal of Automation and Computing 2006; 3(3): 235–243.

Peidró A, Gil A, Marín JM, et al. A web-based tool to analyze the kinematics and singularities of parallel ro-bots. Journal of Intelligent & Robotic Systems 2015; 81(1): 145–163.

Karande S, Paluri N, Gandhi P, et al. Control of parallel flexible five-bar manipulator using QFT. IEEE Interna-tional Conference on Industrial Technology; 2009 Feb; Gippsland. IEEE International; 2009.

Stacella K, Schreiber F, Schumacher W. Modeling, con-trol, and evaluation of an experimental adaptronic five-bar robot. In: Schutz D, Wahl F (editors). Robotic systems for handling and assembly. Berlin: Springer Tracts in Advanced Robotics; 2001. p.125–142.

Yime E, Saltaren R, Diaz J. (June 2010). Robust adap-tive control of the Stewart-Gough robot in the task space. Proceedings of the 2010 American Control Conference; 2010 Jun; Baltimore. 2010. p. 5248–5253.

Yime E, Saltaren R, García C, et al. Robot based on task-space dynamical model. IET Control Theory and Applications 2011; 5(18): 2111–2119. doi: 10.1049/iet-cta.2010.0622.

Slotine JJE, Li WP. Applied nonlinear control. U.S.A: Prentice Hall; 1991.

Siciliano B, Khatib O (editors). Springer handbook of Robotics. U.S.A: Springer International Press; 2008.

Pengutronix. Real time kernel: Linux community dis-tribution [Online]. 2016. [Cited 2016 Jun 28]. Available from:

Fu L, Schwebel R. RT-preempt patch [Online] 2014. [Cited 2016 Jun 28]. Available from: PREEMPT HOWTO.



  • There are currently no refbacks.

Copyright (c) 2022 Eugenio Yime Rodríguez, Javier Roldán Mckinley, José Villa Ramírez

License URL: