Skip to main content

Rigid finite elements and multibody modeling in analyses of a robot shaped elastic/plastic deformations of a beam

  • Conference paper
  • First Online:
Advances in Mechanism and Machine Science (IFToMM WC 2019)

Abstract

Dynamics analysis of a system composed of a parallel manipulator and of an elastic beam is presented in the paper. Classic 3RRR parallel manipulator is considered and used to deform the beam. Elasto-plastic deformations are investigated. Rigid-finite-elements technique is employed to deal with dynamics of the beam. A multibody structure is associated with the introduced hybrid system in order to model its dynamics. Idea of the corresponding numerical model is presented. Then numerical tests are performed in order to observe behaviour of the tested system. The tests have validated that the parallel manipulator can be successfully used for plastic deformations of beams in order to form them into the industry required shapes. The tests proved that resistances of the beam deformations are the dominant loads for such application. Influence of the platform dynamics is of the secondary order. Longitudinal slip at the platform’s gripper is significant during such processes and should not be locked.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Merlet, J.P.: Parallerl Robots. 2nd edn. Springer, Netherlands (2006)

    Google Scholar 

  2. Staicu S.: Dynamics of Parallel Robots. Springer Internat. Publishing, Switzerland (2019)

    Google Scholar 

  3. Notash, L., Huang, L.: On the design of fault tolerant parallel manipulators. Mechanism and Machine Theory 38, 85–101 (2003)

    Google Scholar 

  4. Lipinski, K.: Modeling and Control of a Redundantly Actuated Variable Mass 3RRR Planar Manipulator Controlled by a Model-Based Feedforward and a Model-Based-Proportional-Derivative Feedforward–Feedback Controller. Mechatronics 37, 42–53 (2016).

    Google Scholar 

  5. Lipinski, K.: Redundant Actuation of 3RRR over-actuated Planar Parallel Manipulator. Acta Technica Napocensis-Series Applied Mathematics and Mechanics 52(3), 137-142 (2009).

    Google Scholar 

  6. Germain, C., Briot, S., Caro, S., Wegner Ph.: Natural Frequency Computation of Parallel Robots. Journal of Computational and Nonlinear Dynamics 10(2), (2015).

    Google Scholar 

  7. Kruszewski J., Gawroński W., Wittbrodt E., Najbar F., Grabowski S.: Metoda sztywnych elementów skończonych, Arkady, (in Polish), Warszawa, Poland (1975).

    Google Scholar 

  8. Kruszewski J., Sawiak S. and Wittbrodt E.: Metoda sztywnych elementów skończonych w dynamice konstrukcji, WNT, (in Polish), Warszawa, Poland (1999).

    Google Scholar 

  9. Wittbrodt E., Adamiec-Wójcik I. and Wojciech S.: Dynamics of flexible multibody systems, Springer (2006).

    Google Scholar 

  10. Wojciech S.: Dynamika płaskich mechanizmów dźwigniowych z uwzględnieniem podatności ogniw oraz tarcia i luzów w węzłach, Wydawnictwo Politechniki Łódzkiej, rozprawy naukowe nr 66, (in Polish), Łódz, Poland (1984).

    Google Scholar 

  11. Lipinski, K.: Rigid finite elements and multibody modelling used in estimation and reduction of rod vibrations. The Archive of Mechanical Engineering LX (3), 369–388 (2013).

    Google Scholar 

  12. Lipiński K., Wittbrodt E.: Nelder-Mead optimization in dynamical balancing of planar four bar mechanism and rigid finite elements’ modeling in an analysis of its deformations, Proceedings, 7th World Congress on Structural and Multidisciplinary Optimization, WCSMO-7, 21–25 May 2007, ISSMO – international society of structural and multidisciplinary optimization, Seul, Korea, 1908–1917 (2007).

    Google Scholar 

  13. Fisette, P., Lipinski, K., Samin, J.C.: Modelling for the Simulation Control and Optimization of Multibody System. Advances in Multib. Sys. and Mechat., Gratz(Austria), 139-174 (1999).

    Google Scholar 

  14. Fisette, P., Samin, J.C.: Symbolic Modeling of Multibody System. Kluwer Acad. Publ., Netherlands (2003).

    Google Scholar 

  15. Lipiński, K.: Multibody Systems with Unilateral Constr. in Application to Modelling of Complex Mechanical Systems. Monografie 123, Wydaw.P.G., Gdańsk (2012) (in Polish).

    Google Scholar 

  16. Haug, E.J. Yen, J.: Generalized Coord. Partitioning Meth. for Num. Integ., Real-Time Integ. Meth. for Mech. Sys. Simul.. NATO ASI Series 69, 97-114 (1990).

    Google Scholar 

  17. Stok, B., Halilovic, M.: Analytical solutions in elasto-plastic bending of beams with rectangular cross section. Applied mathematical Modelling 33(3), 1749-1760 (2009)

    Google Scholar 

  18. Rimovskis, S., Sabaliauskas, A.: Analysis of Rectangular and Circular Cross-section Power Hardening Elements under Pure Bending. International Journal of Materials Engineering 2(6), 84-89 (2012).

    Google Scholar 

  19. Rees, D. W.: Descriptions of Reversed Yielding in Bending. Journal of Mechanical Engineering Science 221, 981-991 (2007).

    Google Scholar 

  20. Jakubowicz, A., Orłoś, Z.: Wytrzymałość materiałów, WNT, Warszawa, Poland,(1984).

    Google Scholar 

  21. Information on http://www.mathworks.com/

  22. Wittbrodt E., Szczotka M., Maczyński W., Wojciech S. : Rigid Finite Elerment Method in Analysis of Dynamics of Offshore Structures. Springer (2013).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Krzysztof Lipinski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lipinski, K., Bobrowski, K., Wittbrodt, E. (2019). Rigid finite elements and multibody modeling in analyses of a robot shaped elastic/plastic deformations of a beam. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_270

Download citation

Publish with us

Policies and ethics