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Modal space decoupled optimal design for a class of symmetric spatial parallel mechanisms with consideration of passive joint damping

Published online by Cambridge University Press:  17 March 2014

Tian Ti-Xian ,
Jiang Hong-Zhou ,
Tong Zhi-Zhong  and
He Jing-Feng
Tian Ti-Xian
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, P.R. China
Jiang Hong-Zhou*
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, P.R. China
Tong Zhi-Zhong
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, P.R. China
He Jing-Feng
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, P.R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

In this study, we analyze the influence of passive joint viscous friction (PJVF) on modal space decoupling for a class of symmetric spatial parallel mechanisms (SSPM). The Jacobian matrix relating the platform movements to each passive joint velocity is first gained by vector analysis and the passive joint damping matrix is then derived by applying the Kane method. Next, an analytic formula index measuring the degree of coupling effects between the damping terms in the modal coordinates is proposed using classical modal analysis of dynamic equations in task space. Based on the index, a new optimal design method is found which establishes the kinematics parameters for minimizing the coupling degree of damping and achieves optimal fault tolerance for modal space decoupling when all struts have identical damping and stiffness coefficients in their axial directions. To illustrate the effectiveness of the theory, the new method was used to redesign two configurations of a specific manipulator.

Keywords

Passive jointsKane methodCouplingOptimal design methodModal space decoupling
Type
Articles
Information
Robotica , Volume 33 , Issue 4 , May 2015 , pp. 828 - 847
Copyright
Copyright © Cambridge University Press 2014 

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References

1. Stewart, D., “A platform with six degrees of freedom,” Proceedings of the IMechE (UK) 180 (15), 371–385 (1965).CrossRefGoogle Scholar
2. Dasgupta, B. and Mruthyunjaya, T. S., “The Stewart Platform Manipulator: a Review,” Mech. Mach. Theory 35 (1), 15–40 (2000).CrossRefGoogle Scholar
3. Merlet, J.-P., Parallel Robots (Kluwer Academic Publishers, Netherlands, 2000).CrossRefGoogle Scholar
4. McInroy, J. E. and Hamann, J. C., “Design and control of flexure jointed hexapods,” IEEE Trans. Robot. Automat., 16, 372–381 (Aug. 2000).CrossRefGoogle Scholar
5. Chen, Y. and McInroy, J. E., “Decoupled Control of Flexure-Jointed Hexapods using Estimated Joint-Space Mass-Inertia Matrix,” IEEE Transactions on Control Systems Technology 12 (3), 413–421 (2004).CrossRefGoogle Scholar
6. McInroy, J. E., O'Brien, J. F. and Allais, A., “Designing dynamics and control of isotropic Gough-Stewart micromanipulators, Robotics and Automation (ICRA),” 2013 IEEE International Conference on, Karlsruhe, Germany, (May 6–10, 2013) pp. 1458–1464.Google Scholar
7. Plummer, A. R. and Guinzio, P. S., “Modal Control of an Electrohydrostatic Flight Simulator Motion System,” ASME 2009 Dynamic Systems and Control Conference, Volume 2, Hollywood, California, USA (October 12–14, 2009).Google Scholar
8. Plummer, A. R., “Modal control for a class of multi-axis vibration table,” Control 2004, Bath, UK (Sep. 2004).Google Scholar
9. Plummer, A. R., “Motion control for parallel overconstrained servohydraulic mechanisms,” The Tenth Scandinavian International Conference on Fluid Power, SICFP'07, Tampere, Finland.Google Scholar
10. Plummer, A. R., “High bandwidth motion control for multiaxis servohydraulic mechanisms,” ASME International Mechanical Engineering Congress and Exposition, Seattle, USA (Nov. 13–16, 2007) (Paper IMECE2007–41240).Google Scholar
11. Foss, K. A., “Co-ordinates which uncouple the equations of motion of damped linear dynamic systems,” ASME Journal of Applied Mechanics 25, 361–364 (1958).CrossRefGoogle Scholar
12. Velestos, A. S. and Ventura, C. E., “Modal analysis of non-classically damped linear systems,” Earthquake Engineering and Structural Dynamics 14, 217–243 (1986).Google Scholar
13. Vigneron, F. R., “An atural mode model and modal identities for damped linear dynamic structures,” ASME Journal of Applied Mechanics 53, 33–38 (1986).CrossRefGoogle Scholar
14. Harib, K. and Srinivasan, K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21 (5), 541–554 (2003).CrossRefGoogle Scholar
15. Oftadeh, Reza, Aref, Mohammad M. and Hamid, D., “Taghirad, Explicit Dynamics Formulation of Stewart–Gough Platform: A Newton–Euler Approach,” The 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan (Oct. 18–22, 2010)Google Scholar
16. Abdellatif, H. and Heimann, B., “Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism,” Mech. Mach. Theory 44, 192–207 (2009).CrossRefGoogle Scholar
17. Lebret, G., Liu, K. and Lewis, F. L., “Dynamic analysis and control of a Stewart platform manipulator,” J. Robot. Syst. 10 (5), 629–655 (1993).CrossRefGoogle Scholar
18. Liu, M., Li, C. and Li, C., “Dynamics analysis of the Gough-Stewart platform manipulator,” IEEE Transactions on Robotics and Automation 16 (1), 94–98 (2000).Google Scholar
19. Koekebakker, S. H., Model based control of a flight simulator motion system PhD thesis (Delft, Netherlands: Delft University of Technology, 2001).Google Scholar
20. Cronin, D. L., “Approximation for determining harmonically excited response of nonclassically damped systems,” ASME Journal of Engineering for Industry 98, 43–47 (1976).CrossRefGoogle Scholar
21. Chung, K. R. and Lee, C. W., “Dynamic reanalysis of weakly non-proportionally damped systems,” Journal of Sound and Vibration 111 (1), 37–50 (1986).CrossRefGoogle Scholar
22. Shahruz, S. M. and Ma, F., “Approximate decoupling of the equations of motion of linear underdamped systems,” ASME Journal of Applied Mechanics 55, 716–720 (1988).CrossRefGoogle Scholar
23. Prater, G. and Singh, R., “Quantification of the extent of non-proportional viscous damping in discrete vibratory systems,” Journal of Sound and Vibration 104 (1), 109–125 (1986).CrossRefGoogle Scholar
24. Bellos, J. and Inman, D. J., “Frequency response of nonproportionally damped, lumped parameter, linear dynamic systems,” ASME Journal of Vibration and Acoustics 112, 194–201 (1990).CrossRefGoogle Scholar
25. Tong, M., Liang, Z. and Lee, G. C., “An index of damping non-proportionality for discrete vibratory systems,” Journal of Sound and Vibration 174 (1), 37–55 (1994).CrossRefGoogle Scholar
26. Liu, K., Kujath, M. R. and Zheng, W., “Evaluation of damping non-proportionality using identified modal information,” Mechanical Systems and Signal Processing 15 (1), 227–242 (2001).CrossRefGoogle Scholar
27. Jiang, H. Z., He, J. F. and Tong, Z. Z., “Characteristics analysis of joint space inverse mass matrix for the optimal design of a 6-DOF parallel manipulator,” Mechanism and Machine Theory 45 (5), 722–739 (2010).CrossRefGoogle Scholar
28. He, J. F., Jiang, H. Z., Tong, Z. Z., Li, B. P. and Han, J. W., “Study on dynamic isotropy of a class of symmetric spatial parallel mechanisms with actuation redundancy,” Journal of Vibration and Control 18 (8), 1156–1164 (2012).CrossRefGoogle Scholar
29. Tong, Z. Z., He, J. F., Jiang, H. Z. and Duan, G. R., “Optimal design of a class of generalized symmetric Gough–Stewart parallel manipulators with dynamic isotropy and singularity-free workspace,” Robotica 30 (2), 305–314 (2012).CrossRefGoogle Scholar