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

Published online by Cambridge University Press:  27 February 2014

Yao Jiang ,
Tiemin Li  and
Liping Wang
Yao Jiang
Affiliation:
Department of Mechanical Engineering, Manufacturing Engineering Institute, Tsinghua University, Beijing 100084, China
Tiemin Li*
Affiliation:
Department of Mechanical Engineering, Manufacturing Engineering Institute, Tsinghua University, Beijing 100084, China
Liping Wang
Affiliation:
Department of Mechanical Engineering, Manufacturing Engineering Institute, Tsinghua University, Beijing 100084, China
*
*Corresponding author. E-mail: [email protected]
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Summary

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.

Keywords

Parallel kinematic machineActuation redundancyDynamic modelingRedundant-force optimizationDynamic performance analysis
Type
Articles
Information
Robotica , Volume 33 , Issue 2 , February 2015 , pp. 241 - 263
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Merlet, J. P., Parallel Robots, 2nd ed. (Kluwer Academic Publishers, Dordrecht, 2005).Google Scholar
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), 1007–1016 (2007).Google Scholar
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), 422–427 (2009).Google Scholar
4.Zhao, Y. J. and Gao, F., Dynamic formulation and performance evaluation of the redundant parallel manipulator,” Robot. Comput.-Integr. Manuf. 25 (4–5), 770–781 (2009).Google Scholar
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), 423–434 (2001).CrossRefGoogle Scholar
6.Müller, A. and Hufnagel, T. “Model-based control of redundantly actuated parallel manipulators in redundant coordinates,” Robot. Auton. Syst. 60 (4), 563–571 (2012).Google Scholar
7.Cheng, H., Yiu, Y. K. and Li, Z. X. “Dynamics and control of redundantly actuated parallel manipulators,” IEEE-ASME Trans. Mechatronics 8 (4), 483–491 (2003).CrossRefGoogle Scholar
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), 991–1008 (2009).Google Scholar
9.Nokleby, S. B., Fisher, R., Podhorodeski, R. P. and Firmani, F., “Force capabilities of redundantly actuated parallel manipulators,” Mech. Mach. Theory 40 (5), 578–599 (2005).CrossRefGoogle Scholar
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), 1046–1055 (2007).Google Scholar
11.Müller, A., “Internal preload control of redundantly actuated parallel manipulators–-It's application to backlash avoiding control,” IEEE Trans. Robot. 21 (4), 668–677 (2005).Google Scholar
12.Fattah, A. and Kasaei, G. “Kinematics and dynamics of a parallel manipulator with a new architecture,” Robotica 18, 535–543 (2000).Google Scholar
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), 801–824 (1999).Google Scholar
14.Carvalho, J. and Ceccarelli, M., “A closed-form formulation for the inverse dynamics of a Cassino parallel manipulator,” Multibody Syst. Dyn. 5 (2), 185–210 (2001).CrossRefGoogle Scholar
15.Khalil, W. and Guegan, S., “Inverse and direct dynamic modeling of Gough-Stewart robots,” IEEE Trans. Robot. Autom. 20 (4), 754–762 (2004).Google Scholar
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), 192–207 (2009).Google Scholar
17.Di Gregorio, R. and Parenti-Castelli, V., “Dynamics of a class of parallel wrists,” J. Mech. Des. 126 (3), 436–441 (2004).Google Scholar
18.Callegari, M., Palpacelli, M. C. and Principi, M., “Dynamics modelling and control of the 3-RCC translational platform,” Mechatronics 16 (10), 589–605 (2006).CrossRefGoogle Scholar
19.Tsai, L. W., “Solving the inverse dynamics of a Stewart–Gough manipulator by the principle of virtual work,” J. Mech. Des. 122 (1), 3–9 (2000).Google Scholar
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), 94–98 (2000).Google Scholar
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), 2475–2486 (2012).CrossRefGoogle Scholar
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), 1113–1131 (2003).Google Scholar
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), 232–237 (1989).Google Scholar
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. 425–430.Google Scholar
25.Nahon, M. and Angeles, J., “Optimization of dynamic forces in mechanical hands,” J. Mech. Des. 113 (2), 167–173 (1991).Google Scholar
26.Merlet, J. P., “Redundant parallel manipulators,” Lab. Robot. Autom. 8 (1), 17–24 (1996).Google Scholar
27.Garg, V., Nokleby, S. B. and Carretero, J. A., “Wrench capability analysis of redundantly actuated spatial parallel manipulators,” Mech. Mach. Theory 44 (5), 1070–1081 (2009).Google Scholar
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), 213–238 (2005).Google Scholar
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), 671–687 (2006).CrossRefGoogle Scholar
30.Tzafestas, S., Kotsis, M. and Pimenides, T., “Observer-based optimal control of flexible Stewart parallel robots,” J. Intell. Robot. Syst. 34 (4), 489–503 (2001).Google Scholar
31.Taghirad, H. D. and Nahon, M. A., “Dynamic analysis of a macro-micro redundantly actuated parallel manipulator,” Adv. Robot. 22 (9), 949–981 (2008).Google Scholar
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), 413–420 (2007).Google Scholar