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Computation Time Efficient Stiffness Analysis of the Modified R-CUBE Mechanism

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Book cover Advances in Italian Mechanism Science (IFToMM ITALY 2018)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 68))

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Abstract

Parallel manipulators are known to be more stiff than the serial manipulators. However, modeling the stiffness for parallel manipulators are difficult compared to serial manipulators due to the constrained structure and passive joints. In addition, computation of the stiffness model for parallel manipulators are exhausting since it requires an iterative solution algorithm due requirement of force-position convergence of all serial chains connecting to the same mobile platform. Direct solutions are faster however, they lack in accuracy. In this study, direct solution is preferred for real-time application and analytic stiffness model of the modified R-CUBE mechanism is obtained by using Virtual Joint Method (VJM). The finite element (FE) model is constructed and simulated to validate the analytical model. Then, a combination of external wrenches \(\pm 5\) N in various directions are applied on the mobile platform in both FE and VJM in some critical poses. Finally, the computed numerical results are listed and compared along with their computation times.

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References

  1. Connor, J.J.: Analysis of Structural Member Systems. Ronald Press Co., New York (1976)

    Google Scholar 

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

    Article  Google Scholar 

  3. Kern, T.A.: Engineering Haptic Devices: A Beginner’s Guide for Engineers. Springer (2009)

    Google Scholar 

  4. Li, W., Gao, F., Zhang, J.: R-CUBE, a decoupled parallel manipulator only with revolute joints. Mech. Mach. Theory 40(4), 467–473 (2005)

    Article  Google Scholar 

  5. McGuire, W., Gallagher, R.H., Ziemian, R.D.: Matrix structural analysis (2000)

    Google Scholar 

  6. Pashkevich, A., Klimchik, A., Chablat, D.: Enhanced stiffness modeling of manipulators with passive joints. Mech. Mach. Theory 46(5), 662–679 (2011)

    Article  Google Scholar 

  7. Salisbury, J.K., Craig, J.J.: Articulated hands: force control and kinematic issues. Int. J. Robot. Res. 1(1), 4–17 (1982)

    Article  Google Scholar 

  8. 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 

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Acknowledgements

This work is supported in part by The Scientific and Technological Research Council of Turkey via grant number 117M405.

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Correspondence to İ. Görgülü .

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Görgülü, İ., Dede, M.İ.C. (2019). Computation Time Efficient Stiffness Analysis of the Modified R-CUBE Mechanism. In: Carbone, G., Gasparetto, A. (eds) Advances in Italian Mechanism Science. IFToMM ITALY 2018. Mechanisms and Machine Science, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-030-03320-0_25

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  • DOI: https://doi.org/10.1007/978-3-030-03320-0_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03319-4

  • Online ISBN: 978-3-030-03320-0

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