Skip to main content
SpringerLink
Log in

Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this study, the researchers try to examine nonlinear dynamic analysis and determine Dynamic load carrying capacity (DLCC) in flexible manipulators. Manipulator modeling is based on Timoshenko beam theory (TBT) considering the effects of shear and rotational inertia. To get rid of the risk of shear locking, a new procedure is presented based on mixed finite element formulation. In the method proposed, shear deformation is free from the risk of shear locking and independent of the number of integration points along the element axis. Dynamic modeling of manipulators will be done by taking into account small and large deformation models and using extended Hamilton method. System motion equations are obtained by using nonlinear relationship between displacements-strain and 2nd PiolaKirchoff stress tensor. In addition, a comprehensive formulation will be developed to calculate DLCC of the flexible manipulators during the path determined considering the constraints end effector accuracy, maximum torque in motors and maximum stress in manipulators. Simulation studies are conducted to evaluate the efficiency of the method proposed taking two-link flexible and fixed base manipulators for linear and circular paths into consideration. Experimental results are also provided to validate the theoretical model. The findings represent the efficiency and appropriate performance of the method proposed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. B. da Veiga, C. Lovadina and A. Reali, Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods, Comput. Methods Appl. Mech. Engrg., 241–244 (2012) 38–51.

    Article  Google Scholar 

  2. B. O. Al-Bedoor and M. N. Hamdan, Geometrically nonlinear dynamic model of a rotating flexible arm, Journal of Sound and Vibration, 240 (1) (2001) 59–72.

    Article  MATH  Google Scholar 

  3. A. Meghdari, A variational approach for modeling flexibility effects in manipulator arms, Robotica, 9 (1991) 213–217.

    Article  Google Scholar 

  4. R. G. K. M. Aarts and J. B. Jonker, Dynamic simulation of planar flexible link manipulators using adaptive modal integration, Multibody System Dynamics, 7 (2002) 31–50.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Pratiher and S. K. Dwivedy, Non-linear dynamics of a flexible single link Cartesian manipulator, International Journal of Non-Linear Mechanics, 42 (2007) 1062–1073.

    Article  Google Scholar 

  6. J. B. Jonker and R. G. K. M. Aarts, A perturbation method for dynamic analysis and simulation of flexible manipulators, Multibody System Dynamics (2001) 245–266.

    Google Scholar 

  7. R. Fotouhi, Dynamic analysis of very flexible beams, Journal of Sound and Vibration (2007) 521–533.

    Google Scholar 

  8. E. Bayo, Timoshenko versus Bernoulli-Euler beam theories for inverse dynamics of flexible robots, International Journal of Robotics and Automation, 4 (1) (1989) 53–56.

    Google Scholar 

  9. P. Salehi, H. Yaghoobi and M. Torabi, Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load, Journal of Mechanical Science and Technology, 26 (9) (2012) 2879–2887.

    Article  Google Scholar 

  10. M. E. Erguven and A. Gedikli, A mixed finite element formulation for timoshenko beam on winkler foundation, Computational Mechanics, 31 (2003) 229–237.

    Google Scholar 

  11. K. D. Hjelmstad and E. Taciroglu, Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli-Euler beams, Commun. Numer. Meth. Engng., 19 (2003) 809–832.

    Article  MATH  Google Scholar 

  12. R. L. Taylor, F. C. Filippou, A. Saritas and F. Auricchio, A mixed finite element method for beam and frame problems, Computational Mechanics, 31 (2003) 192–203.

    Article  MATH  Google Scholar 

  13. C. Sharma, Displacement / Mixed finite element formulation for beam and frame problems, Europen school of advanced studies in reduction of seismic, Master Thesis, October (2007).

    Google Scholar 

  14. R. Ranjan, Nonlinear finite element analysis of bending of straight beams using hp-spectral approximations, Journal of Solid Mechanics, 3 (1) (2011) 96–113.

    Google Scholar 

  15. Q. H. Nguyen, M. Hjiaj, B. Uy and S. Guezouli, A class of finite elements for nonlinear analysis of composite beams, Composite Construction in Steel and Concrete VI (2011) 566–577.

    Chapter  Google Scholar 

  16. A. Ayoub and F. C. Filippou, Mixed formulation of nonlinear steel-concrete beam element, Journal of Structural Engineering (2000) 371–381.

    Google Scholar 

  17. R. Grimaldi, D. Addessi and V. Ciampi, Mixed finite elements for modeling non-linear structural responses, European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS (2004).

    Google Scholar 

  18. R. Grimaldi, D. Addessi and V. Ciampi, Mixed finite elements for non-linear material problems, European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS (2004) 1–20.

    Google Scholar 

  19. S. Abid, M. Taktak, F. Dammak and M. Haddar, An accurate two-node finite element for the pre-twisted beam modeling, Journal of Mechanical Engineering (2008) 135–150.

    Google Scholar 

  20. M. Thomas, H. C. Yuan-Chou and D. Tesar, Optimal actuator sizing for robotic manipulators based on local dynamic criteria, Journal of Mechanisms, Transmissions and Automation in Design, 107 (1985) 163–169.

    Article  Google Scholar 

  21. L. T. Wang and B. Ravani, Dynamic load carrying capacity of mechanical manipulators. Part 2: computational procedure and applications, J. Dyn. Sys. Meas. Control, 110 (1988) 53–61.

    Article  Google Scholar 

  22. D. R. Da and E. Papadopoulos, Online automatic tip-over presentation for mobile and redundant manipulators, Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS’97) (1997) 1273–1278.

    Google Scholar 

  23. E. Papadopoulos and Y. Gonthier, A frame force for large force task planning of mobile and redundant manipulators, J. Robot Sys., 16 (3) (1999) 151–162.

    Article  MATH  Google Scholar 

  24. M. H. Korayem and H. Ghariblu, The effect of base replacement on load carrying capacity of robotic manipulators, Int. J. Adv. Manufact. Technol., 23 (1) (2004) 28–38.

    Article  Google Scholar 

  25. M. H. Korayem and H. Ghariblu, Maximum allowable load on wheeled mobile manipulators imposing redundancy constraints, Robotics Autonomous Syst., 44 (2003) 151–159.

    Article  Google Scholar 

  26. Y. Maddahi, Calculation of load carrying capacity on a redundant manipulator, 2nd WSEAS Int. Conf. on Circuits, Systems, Signal and Telecommunications (CISST'08), Acapulco, Mexico (2008) 25–27.

    Google Scholar 

  27. M. H. Korayem and H. Ghariblu, Maximum allowable load on wheeled mobile manipulators, IJE Transactions A: Basics, 16 (3) (2003) 279–292.

    Google Scholar 

  28. S. Yue, S. K. Tso and W. L. Xu, Maximum dynamic payload trajectory for flexible robot manipulators with kinematic redundancy, Mech. Mach. Theory, 36 (2001) 785–800.

    Article  MATH  Google Scholar 

  29. M. H. Korayem, M. Haghpanahi and H. R. Heidari, Maximum allowable dynamic load of flexible manipulators undergoing large deformation, Transaction B: Mechanical Engineering, Sharif University of Technology, February, 17 (1) (2010) 61–74.

    MATH  Google Scholar 

  30. M. H. Korayem and A. Heidari, Maximum allowable dynamic load of flexible mobile manipulators using finite element approach, Adv. Manuf. and Tech., 36 (2007) 606–617.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Habib Esfandiar & Moharam Habibnejad Korayem

  2. Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    Moharam Habibnejad Korayem

Authors
  1. Habib Esfandiar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Moharam Habibnejad Korayem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moharam Habibnejad Korayem.

Additional information

Recommended by Associate Editor Kyoungchul Kong

Moharam Habibnejad Korayem was born in Tehran, Iran in 1961. He received his B.S. (Hon) and M.S. degrees in Mechanical Engineering from Amirkabir University of Technology in 1985 and 1987, respectively. He obtained his Ph.D. degree in Mechanical Engineering from the University of Wollongong, Australia in 1994. He is now a Professor of Mechanical Engineering at Iran University of Science and Technology. His research interests include dynamics of elastic mechanical manipulators, trajectory optimization, symbolic modeling, robotic multimedia software, mobile robots, industrial robotics standard, robot vision, soccer robot, and the analysis of mechanical manipulator with maximum load carrying capacity.

Habib Esfandiar was born in Iran in 1984. He is currently a Ph.D. degree student in Mechanical Engineering at Science and Research Branch, IAU, Tehran, Iran. His research has focused on dynamic modeling of flexible robotic manipulators, mobile robots, trajectory optimization, and game theory in engineering problems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Esfandiar, H., Korayem, M.H. Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load. J Mech Sci Technol 29, 3971–3982 (2015). https://doi.org/10.1007/s12206-015-0842-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-015-0842-2

Keywords

Search

Navigation