Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Closed-Form Dynamic Formulation of a General 6-P US Robot

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

The 6-P US parallel manipulator can be used as a good alternative for the 6-UP S manipulator, known as Stewart platform. 6-P US parallel robots may be designed and manufactured in various architectures with different attributes. In this paper, to assess all the possible architectures of the 6-P US with respect to both workspace and dynamic performance, a general geometry is first defined. Using Newton-Euler method, the dynamic model of the general 6-P US robot is derived and its closed-form dynamic equations are presented. More accurate formulation is obtained by considering all robot’s component inertia as well as including the angular velocity and acceleration vectors of the robot’s legs. Moreover, the effect of neglecting link inertia of the 6-P US robot is studied for different payload to link mass ratios. The closed-form model includes dynamic matrices of the robot which can conveniently be used for model based control techniques. Two trajectories are considered and the derived dynamic formulation is verified using a commercial multibody dynamics software. Finally, four case studies covering the well-known architectures of the 6-P US manipulator, including the Hexaglide and the HexaM, are compared based on the robot workspace and forces of the actuators. The results indicates that amongst the studied designs of the 6-P US robot, the architecture with rails leaning outside provides the best performance and therefore can be considered as a competitor for the conventional Stewart platforms.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Dasgupta, B., Mruthyunjaya, T.: Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach. Mech. Mach. Theory 33, 993–1012 (1998)

    Article  MathSciNet  Google Scholar 

  2. Leroy, N., Kokosy, A., Perruquetti, W.: Dynamic modeling of a parallel robot. Application to a surgical simulator. In: 2003 Proceedings. ICRA’03. IEEE international conference on robotics and automation, pp. 4330–4335 (2003)

  3. Kalani, H., Rezaei, A., Akbarzadeh, A.: Improved general solution for the dynamic modeling of Gough–Stewart platform based on principle of virtual work. Nonlinear Dyn. 83, 2393–2418 (2016)

    Article  MathSciNet  Google Scholar 

  4. Akbarzadeh, A., Enferadi, J.: A virtual work based algorithm for solving direct dynamics problem of a 3-RRP spherical parallel manipulator. J. Intell. Robot. Syst. 63, 25–49 (2011)

    Article  Google Scholar 

  5. Enferadi, J., Tootoonchi, A.A.: Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work. Nonlinear Dyn. 61, 419–434 (2010)

    Article  Google Scholar 

  6. Yamane, K., Nakamura, Y., Okada, M., Komine, N., Yoshimoto, K.I.: Parallel dynamics computation and H8 acceleration control of parallel manipulators for acceleration display. J. Dyn. Syst. Meas. Control. 127, 185–191 (2005)

    Article  Google Scholar 

  7. Wang, J., Wu, J., Wang, L., Li, T.: Simplified strategy of the dynamic model of a 6-UPS parallel kinematic machine for real-time control. Mech. Mach. Theory 42, 1119–1140 (2007)

    Article  Google Scholar 

  8. Blajer, W., Koodziejczyk, K.: Improved DAE formulation for inverse dynamics simulation of cranes. Multibody Sys. Dyn. 25, 131–143 (2011)

    Article  Google Scholar 

  9. Lebret, G., Liu, K., Lewis, F.L.: Dynamic analysis and control of a Stewart platform manipulator. J. Robot. Syst. 10, 629–655 (1993)

    Article  Google Scholar 

  10. Khalil, W., Ibrahim, O.: General solution for the dynamic modeling of parallel robots. J. Intell. Robot. Syst. 49, 19–37 (2007)

    Article  Google Scholar 

  11. Dasgupta, B., Choudhury, P.: A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators. Mech. Mach. Theory 34, 801–824 (1999)

    Article  MathSciNet  Google Scholar 

  12. Abedloo, E., Molaei, A., Taghirad, H.D.: Closed-form dynamic formulation of spherical parallel manipulators by Gibbs-Appell method. In: 2014 2nd RSI/ISM international conference on robotics and mechatronics (ICRoM), pp. 576–581 (2014)

  13. Nabavi, S.N., Akbarzadeh, A., Enferadi, J.: A Study on Kinematics and Workspace Determination of a General 6-P US Robot, Journal of Intelligent & Robotic Systems, pp. 1–12 (2017)

  14. Narayanan, M.S., Chakravarty, S., Shah, H., Krovi, V. N.: Kinematic-, static-and workspace analysis of a 6-PUS parallel manipulator. In: 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference ASME , pp. 1456–1456.8 (2010)

  15. Ferrari, D., Giberti, H.: A genetic algorithm approach to the kinematic synthesis of a 6-DoF parallel manipulator. In: 2014 IEEE conference on control applications (CCA), pp. 222–227 (2014)

  16. Zhao, Y., Gao, F.: Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work. Robotica 27, 259–268 (2009)

    Article  Google Scholar 

  17. Wang, H., Chen, G., Lin, Z.: Forward dynamics analysis of the 6-PUS mechanism based on platform-legs composite simulation. Chinese Journal of Mechanical Engineering, pp. 496 (2009)

    Article  Google Scholar 

  18. Rao, A.K., Saha, S., Rao, P.: Dynamics modelling of hexaslides using the decoupled natural orthogonal complement matrices. Multibody Sys. Dyn. 15, 159–180 (2006)

    Article  MathSciNet  Google Scholar 

  19. Lopes, A.M.: Complete dynamic modelling of a moving base 6-dof parallel manipulator. Robotica 28, 781–793 (2010)

    Article  Google Scholar 

  20. Honegger, M., Codourey, A., Burdet, E.: Adaptive control of the hexaglide, a 6 dof parallel manipulator. In: 1997 IEEE international conference on robotics and automation, 1997. Proceedings, pp. 543–548 (1997)

  21. Najafi, A., Movahhedy, M., Zohoor, H., Alasty, A.: Dynamic stability of a Hexaglide machine tool for milling processes. Int. J. Adv. Manuf. Technol. 86, 1753–1762 (2016)

    Article  Google Scholar 

  22. Bonev, I.A., Ryu, J.: A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators. Mech. Mach. Theory 36, 1–13 (2001)

    Article  Google Scholar 

  23. Harib, K., Srinivasan, K.: Kinematic and dynamic analysis of Stewart platform-based machine tool structures. Robotica 21, 541–554 (2003)

    Article  Google Scholar 

  24. Nabavi, N., Akbarzadeh Tootoonchi, A., Enferadi, J.: Mass and inertia effect of the links on simplification of the 6-PUS robot dynamic equations for different payload ratio. Modares Mech. Eng. 17, 108–116 (2017)

    Google Scholar 

  25. Lopes, A., Almeida, F.: A force–impedance controlled industrial robot using an active robotic auxiliary device. Robot. Comput. Integr. Manuf. 24, 299–309 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Center of Excellence on Soft Computing and Intelligent Information Processing, (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran

    S. Nader Nabavi & Alireza Akbarzadeh

  2. Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Javad Enferadi

Authors
  1. S. Nader Nabavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alireza Akbarzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javad Enferadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Akbarzadeh.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nabavi, S.N., Akbarzadeh, A. & Enferadi, J. Closed-Form Dynamic Formulation of a General 6-P US Robot. J Intell Robot Syst 96, 317–330 (2019). https://doi.org/10.1007/s10846-019-00990-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-019-00990-7

Keywords

Search

Navigation