Optimal Force Distribution Based on Slack Rope Model in the Incompletely Constrained Cable-Driven Parallel Mechanism of FAST Telescope

  • Hui Li
  • Xinyu Zhang
  • Rui Yao
  • Jinghai Sun
  • Gaofeng Pan
  • Wenbai Zhu
Chapter
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 12)

Abstract

This paper addressed the determination of the tension distribution in the slack steel wires of the incompletely constrained cable-driven parallel mechanism of FAST telescope. Slack rope hung with piecewise uniform mass is specially investigated. First, the general formulation based on the wrench matrix was derived. Then the analytical model of slack rope was built to give the quantized relation between direction and amplitude of tension vector. The wrench matrix is not only platform pose dependent but influenced by rope geometry. Finally, a performance index based on minimal tension variance is selected to optimize the tension distribution among steel wires. Levenberg-Marquardt method is applied to solve the quadratic program and a discrete-mesh plan is proposed for the whole focal surface. An example of computation is given to verify the effect of the resolution.

Keywords

Steel Wire Mobile Platform Base Frame Tension Distribution Focal Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The author would like to acknowledge the financial support of the National Natural Science Foundation (NNSF) under grant No. 10973023.

References

  1. 1.
    Nan, R.D.: Five-hundred-meter aperture spherical radio telescope (FAST). Sci. China Ser. G Phys. Mech. Astron. 49(2), 129–148 (2006).Google Scholar
  2. 2.
    Li, H., Zhu, W., Pan, G.: Equilibrium analysis of FAST rope-drive parallel manipulator based on rope force optimization. Eng. Mech. 28(4), 185–193 (2010) (in Chinese).Google Scholar
  3. 3.
    Barrette, G., Gosselin, C.: Determination of the dynamic workspace of cable-driven planar parallel mechanisms. ASME J. Mech. Des. 127(2), 242–248 (2005)CrossRefGoogle Scholar
  4. 4.
    Bosscher, P., Ebert-Uphoff, I.: Wrench-based analysis of cable-driven robots. In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, pp. 4950–4955, New Orleans, LA, USA (2004).Google Scholar
  5. 5.
    Verhoeven, R., Hiller, M.: Estimating the controllable workspace of tendon-based Stewart platforms. In: Lenarcic, J., Stanisic, M.M. (eds.) Advances in Robot Kinematics, pp. 277–284. Kluwer Academic, Dordrech (2000)CrossRefGoogle Scholar
  6. 6.
    Riechel, A.T., Ebert-Uphoff, I.: Force-feasible workspace analysis for underconstrained point-mass cable robots. In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, pp. 4956–4962, New Orleans, LA, USA (2004).Google Scholar
  7. 7.
    Li, H., Nan, R., Kärcher, H., et al.: Working space analysis and optimization of the main positioning system of FAST cabin suspension. In: Proceedings of SPIE, Astronomical Instrumentation, Ground-Based and Airborne Telescopes II, Marseille, vol. 70120T(1–11) (2008).Google Scholar
  8. 8.
    Levenberg, K.: A method for the solution of certain non-linear problems in least squares. . Q. Appl. Math. 2(2), 164–168 (1944)MathSciNetMATHGoogle Scholar
  9. 9.
    Marquardt, D.W.: An algorithm for the least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11(2), 431–441 (1963)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hui Li
    • 1
  • Xinyu Zhang
    • 1
  • Rui Yao
    • 1
  • Jinghai Sun
    • 1
  • Gaofeng Pan
    • 1
  • Wenbai Zhu
    • 1
  1. 1.National Astronomical ObservatoriesChinese Academy of SciencesBeijingChina

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