Skip to main content

The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy

  • Yao Jiang (a1), Tiemin Li (a1) and Liping Wang (a1)

This paper discusses a planar 2-DOF (degrees of freedom) parallel kinematic machine with actuation redundancy. Its inverse dynamic model is constructed by utilizing the Newton–Euler method based on the kinematic analysis. However, the dynamic model cannot be solved directly because the number of equations is less than the number of unknowns, which is due to the redundant force. In order to solve this problem, the relationship between the deformations of the links and the position errors of the moving platform are further explored. Then a novel method, which aims at minimizing the position errors of the machine, is proposed to optimize the redundant force. It also enables to solve the dynamic model. Finally, the dynamic performance analyses of this machine and its non-redundant counterpart are provided by numerical examples. Besides, another optimization method proposed for minimizing the constraint forces is also applied for comparison. The results show the effectiveness of the novel methods in improving the position precision of the machine.

Corresponding author
*Corresponding author. E-mail:
Hide All
1.Merlet J. P., Parallel Robots, 2nd ed. (Kluwer Academic Publishers, Dordrecht, 2005).
2.Ebrahimi I., Carretero J. A. and Boudreau R., “3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses,” Mech. Mach. Theory 42 (8), 10071016 (2007).
3.Zhao Y. J., Gao F., Li W. M. and Zhao X. C., “Development of a 6-DOF parallel seismic simulator with novel redundant actuation,” Mechatronics 19 (3), 422427 (2009).
4.Zhao Y. J. and Gao F., Dynamic formulation and performance evaluation of the redundant parallel manipulator,” Robot. Comput.-Integr. Manuf. 25 (4–5), 770781 (2009).
5.Kim J., Park F. C., Ryu S. J., “Design and analysis of a redundantly actuated parallel mechanism for rapid machining,” IEEE Trans. Robot. Autom. 17 (4), 423434 (2001).
6.Müller A. and Hufnagel T.Model-based control of redundantly actuated parallel manipulators in redundant coordinates,” Robot. Auton. Syst. 60 (4), 563571 (2012).
7.Cheng H., Yiu Y. K. and Li Z. X.Dynamics and control of redundantly actuated parallel manipulators,” IEEE-ASME Trans. Mechatronics 8 (4), 483491 (2003).
8.Zhao Y. J. and Gao F.Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart-the 6PSS parallel manipulator,” Mech. Mach. Theory 44 (5), 9911008 (2009).
9.Nokleby S. B., Fisher R., Podhorodeski R. P. and Firmani F., “Force capabilities of redundantly actuated parallel manipulators,” Mech. Mach. Theory 40 (5), 578599 (2005).
10.Zibil A., Firmani F., Nokleby S. B., Podhorodeski R. P., “An explicit method for determining the force-moment capabilities of redundantly actuated planar parallel manipulators,” J. Mech. Des. 129 (10), 10461055 (2007).
11.Müller A., “Internal preload control of redundantly actuated parallel manipulators–-It's application to backlash avoiding control,” IEEE Trans. Robot. 21 (4), 668677 (2005).
12.Fattah A. and Kasaei G.Kinematics and dynamics of a parallel manipulator with a new architecture,” Robotica 18, 535543 (2000).
13.Dasgupta B. and Choudhury P.A general strategy based on the Newton–Euler approach for the dynamic formation of parallel manipulators,” Mech. Mach. Theory 34 (6), 801824 (1999).
14.Carvalho J. and Ceccarelli M., “A closed-form formulation for the inverse dynamics of a Cassino parallel manipulator,” Multibody Syst. Dyn. 5 (2), 185210 (2001).
15.Khalil W. and Guegan S., “Inverse and direct dynamic modeling of Gough-Stewart robots,” IEEE Trans. Robot. Autom. 20 (4), 754762 (2004).
16.Abdellatif H. and Heimann B., “Computational efficient inverse dynamic of 6-DOF fully parallel manipulators by using the Lagrangian formalism,” Mech. Mach. Theory 44 (1), 192207 (2009).
17.Di Gregorio R. and Parenti-Castelli V., “Dynamics of a class of parallel wrists,” J. Mech. Des. 126 (3), 436441 (2004).
18.Callegari M., Palpacelli M. C. and Principi M., “Dynamics modelling and control of the 3-RCC translational platform,” Mechatronics 16 (10), 589605 (2006).
19.Tsai L. W., “Solving the inverse dynamics of a Stewart–Gough manipulator by the principle of virtual work,” J. Mech. Des. 122 (1), 39 (2000).
20.Liu M. J., Li C. X. and Li C. N., “Dynamics analysis of the Gough-Stewart platform manipulator,” IEEE Trans. Robot. Autom. 16 (1), 9498 (2000).
21.Cheng G. and Shan X. L., “Dynamic analysis of a parallel hip joint simulator with four degree of freedoms (3R1T),” Nonlinear Dyn. 70 (4), 24752486 (2012).
22.Gallardo J., Rico J. M., Frisoli A., Checcacci D. and Bergamasco M., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38 (11), 11131131 (2003).
23.Zheng Y. F. and Luh J. Y. S., “Optimal load distribution for two industrial robots handling a single object,” Trans. ASME, J. Dyn. Syst. Meas. Control 111 (2), 232237 (1989).
24.Tao J. M., Luh J. Y. S., “Coordination of Two Redundant Manipulators,” Proceedings of the 1989 IEEE International Conference on Robotics and Automation, Scottsdale, USA (May 14–19, 1989) pp. 425430.
25.Nahon M. and Angeles J., “Optimization of dynamic forces in mechanical hands,” J. Mech. Des. 113 (2), 167173 (1991).
26.Merlet J. P., “Redundant parallel manipulators,” Lab. Robot. Autom. 8 (1), 1724 (1996).
27.Garg V., Nokleby S. B. and Carretero J. A., “Wrench capability analysis of redundantly actuated spatial parallel manipulators,” Mech. Mach. Theory 44 (5), 10701081 (2009).
28.Lee S. H., Lee J. H., Yi B. J., Kim S. H. and Kwak Y. K., “Optimization and experimental verification for the antagonistic stiffness in redundantly actuated mechanisms: a five-bar example,” Mechatronics 15 (2), 213238 (2005).
29.Wang X. Y. and Mills J. K., “Dynamic modeling of a flexible-link planar parallel platform using a substructuring approach,” Mech. Mach. Theory 41 (6), 671687 (2006).
30.Tzafestas S., Kotsis M. and Pimenides T., “Observer-based optimal control of flexible Stewart parallel robots,” J. Intell. Robot. Syst. 34 (4), 489503 (2001).
31.Taghirad H. D. and Nahon M. A., “Dynamic analysis of a macro-micro redundantly actuated parallel manipulator,” Adv. Robot. 22 (9), 949981 (2008).
32.Wu J., Wang J. S., Li T. M. and Wang L. P., “Dynamic analysis of the 2-DOF planar parallel manipulator of a heavy duty hybrid machine tool,” Int. J. Adv. Manuf. Technol. 34 (3–4), 413420 (2007).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 37 *
Loading metrics...

Abstract views

Total abstract views: 178 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th February 2018. This data will be updated every 24 hours.