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Stiffness Analysis of a Semi-symmetrical Three-Translation Delta-CU Parallel Robot

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Robotics and Mechatronics (ISRM 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 78))

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Abstract

The Delta-CU parallel mechanism is a semi-symmetrical 3-DOF translational parallel mechanism designed by the author based on the topological structure design theory of POC equation. Compared with the Delta mechanism, the structure is more simple, and the kinematics performance is consistent. The stiffness modeling and characteristics of Delta-CU mechanism are studied in this paper. First, the stiffness model of the limb is established by using the virtual spring method, and the equilibrium equation of the limb is given. Then, the differential mapping from the deflection of the virtual joint to the end-effector is obtained by the Screw theory, and the Cartesian stiffness matrix of the mechanism is obtained by the equilibrium equation; Finally, through the Virtual Work based stiffness index, the Delta-CU mechanism under given parameters is analyzed and compared with the Delta mechanism.

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References

  1. Corradini, C., Fauroux, J.C., Krut, S. and Company, O.: Evaluation of a 4-degree of freedom parallel manipulator stiffness. In: Proceedings of the 11th World Congress in Mechanism and Machine Science, IFTOMM, Tianjin, China (2004)

    Google Scholar 

  2. Fernández-Bustos, I., Agirrebeitia, J., Ajuria, G., Angulo, C.: A new finite element to represent prismatic joint constraints in mechanisms. Finite Elements Anal. Des. 43(1), 36–50 (2006)

    Article  MathSciNet  Google Scholar 

  3. Long, C.S., Snyman, J.A., Groenwold, A.A.: Optimal structural design of a planar parallel platform for machining. Appl. Math. Model. 27(8), 581–609 (2003)

    Article  Google Scholar 

  4. Wu, G., Zou, P.: Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms. Robotica 35(6), 1310–1326 (2017)

    Article  MathSciNet  Google Scholar 

  5. Martin, H.C.: Introduction to Matrix Methods of Structural Analysis. McGraw-Hill Book Company, Montreal (1966)

    Google Scholar 

  6. Deblaise, D., Hernot, X., Maurine, P.: A systematic analytical method for PKM stiffness matrix calculation. In: Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, America, pp. 4213–4219 (2006)

    Google Scholar 

  7. Ecorchard, G., Neugebauer, R., Maurine, P.: Elasto-geometrical modeling and calibration of redundantly actuated PKMs Original Research Article. Mech. Mach. Theory 45(5), 795–810 (2010)

    Article  Google Scholar 

  8. Gosselin, C.M.: Stiffness mapping for parallel manipulators. IEEE Trans. Robot. Autom. 6(3), 377–382 (1990)

    Article  Google Scholar 

  9. Majou, F., Gosselin, C., Wenger, P., Chablat, D.: Parametric stiffness analysis of the Orthoglide. Mech. Mach. Theory 42(3), 296–311 (2007)

    Article  Google Scholar 

  10. Quennouelle, C., Gosselin, C.M.: Stiffness matrix of compliant parallel mechanisms. In: Lenarčič, J., Wenger, P. (eds.) Advances in Robot Kinematics: Analysis and Design, pp. 331–341. Springer, Dordrecht (2008)

    Chapter  Google Scholar 

  11. Pashkevich, A., Chablat, D., Wenger, P.: Stiffness analysis of overconstrained parallel manipulators. Mech. Mach. Theory 44, 966–982 (2010)

    Article  Google Scholar 

  12. Wu, G., Bai, S., Kepler, J.: Mobile platform center shift in spherical parallel manipulators with flexible limbs. Mech. Mach. Theory 75, 12–26 (2014)

    Article  Google Scholar 

  13. Yan, S.J., Ong, S.K., Nee, A.Y.C.: Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method. Robot. Comput. Integr. Manuf. 37, 13–22 (2016)

    Article  Google Scholar 

  14. Wu, G., Bai, S., Preben, H.: On the stiffness of three/four degree-of-freedom parallel pick-and-place robots with four identical limbs. In: IEEE International Conference on Robotics and Automation, Stockholm, Sweden, pp. 861–866 (2016)

    Google Scholar 

  15. Vu, L.N., Kuo, C.H.: An analytical stiffness method for spring-articulated planar serial or quasiserial manipulators under gravity and an arbitrary load. Mech. Mach. Theory 137, 108–126 (2019)

    Article  Google Scholar 

  16. Yang, K., Yang, W., Cheng, G., Lu, B.: A new methodology for joint stiffness identification of heavy duty industrial robots with the counterbalancing system. Robot. Comput. Integr. Manuf. 53, 58–71 (2018)

    Article  Google Scholar 

  17. Li, J.Y., Shen, H.P., Meng, Q.M., Deng, J.M.: A Delta-CU – kinematic analysis and dimension design. In: International Conference on Intelligent Robotics and Applications, pp. 371–382. Springer, Heidelberg (2017)

    Chapter  Google Scholar 

  18. Li, J.Y., Shen, H.P., Meng, Q.M., Deng, J.M., Zhang, Z.: A Delta deflection mechanism and its scale design based on workspace analysis. Mech. Des. 35(07), 92–98 (2018)

    Google Scholar 

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Acknowledgments

NSFC No. 51375062 and No. 51475050 is greatly appreciated.

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Authors and Affiliations

  1. Modern Institutional Research Center, Changzhou University, Changzhou, 213016, China

    Huiping Shen, Yixi Wang & Qingmei Meng

  2. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Guanglei Wu

Authors
  1. Huiping Shen
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  2. Yixi Wang
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  3. Guanglei Wu
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  4. Qingmei Meng
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Corresponding author

Correspondence to Guanglei Wu .

Editor information

Editors and Affiliations

  1. School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW, Australia

    Chin-Hsing Kuo

  2. Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan

    Pei-Chun Lin

  3. Department of Mechanical Engineering, National Central University, Taoyuan City, Taiwan

    Terence Essomba

  4. Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, New Taipei City, Taiwan

    Guan-Chen Chen

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Shen, H., Wang, Y., Wu, G., Meng, Q. (2020). Stiffness Analysis of a Semi-symmetrical Three-Translation Delta-CU Parallel Robot. In: Kuo, CH., Lin, PC., Essomba, T., Chen, GC. (eds) Robotics and Mechatronics. ISRM 2019. Mechanisms and Machine Science, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-030-30036-4_1

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