Skip to main content

Dynamic analysis of Hexarot: axis-symmetric parallel manipulator

  • Siamak Pedrammehr (a1), Behzad Danaei (a2), Hamid Abdi (a1), Mehdi Tale Masouleh (a2) and Saeid Nahavandi (a1)...

In this study, the kinematics and dynamics of a six-degree-of-freedom parallel manipulator, known as Hexarot, are evaluated. Hexarot is classified under axis-symmetric robotic mechanisms. The manipulator comprises a cylindrical base column and six actuated upper arms, which are connected to a platform through passive joints and six lower arms. The actuators of the mechanism are located inside a cylindrical-shaped base, which allows the mechanism to rotate infinitely about the axes of the latter column. In the context of kinematics, the inverse-kinematic problem is solved using positions, velocities, and accelerations of the actuated joints with respect to the position, orientation, and motion of the platform. Accordingly, the main objective of this study is to dynamically model the manipulator using the Newton–Euler approach. For validation, the obtained dynamic model of the Hexarot manipulator is simulated in MATLAB based on the formulations presented in this paper. The kinematic and dynamic models of the manipulator are simulated for a given motion scenario using MATLAB and ADAMS. The results of the mathematical model obtained using MATLAB are in good agreement with that using the ADAMS model, confirming the effectiveness of the proposed mathematical model.

Corresponding author
*Corresponding author. E-mail:
Hide All
1. Stewart D., “A platform with six degrees of freedom,” Proc. Inst. Mech. Eng. 180, 371386 (1965).
2. Isaksson M., Brogårdh T., Watson M., Nahavandi S., and Crothers P., “The octahedral Hexarot—a novel 6-DOF parallel manipulator,” Mech. Mach. Theory 55, 91102 (2012).
3. Isaksson M., Brogårdh T. and Nahavandi S., “Parallel manipulators with a rotation-symmetric arm system,” J. Mech. Des. 134, 114503 (2012).
4. Qazani M. R. C. et al., “Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system,” Robotica 33, 16861703 (2015).
5. Qazani M. R. C., Pedrammehr S., Rahmani A., Shahryari M., Rajab A. K. S. and Ettefagh M. M., “An experimental study on motion error of hexarot parallel manipulator,” Int. J. Adv. Manuf. Technol. 72, 13611376 (2014).
6. Isaksson M. and Watson M., “Workspace analysis of a novel six-degrees-of-freedom parallel manipulator with coaxial actuated arms,” J. Mech. Des. 135, 104501 (2013).
7. Tsai L.-W., “Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work,” J. Mech. Des. 122, 39 (2000).
8. Staicu S., Liu X.-J. and Wang J., “Inverse dynamics of the HALF parallel manipulator with revolute actuators,” Nonlinear Dyn. 50, 112 (2007).
9. Zhao Y. and Gao F., “Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work,” Robotica 27, 259268 (2009).
10. Abedinnasab M. H. and Vossoughi G., “Analysis of a 6-DOF redundantly actuated 4-legged parallel mechanism,” Nonlinear Dyn. 58, 611622 (2009).
11. Liu M.-J., Li C.-X. and Li C.-N., “Dynamics analysis of the Gough-Stewart platform manipulator,” IEEE Trans. Robot. Autom. 16, 9498 (2000).
12. You W., Kong M.-X., Du Z.-J. and Sun L.-N., “High efficient inverse dynamic calculation approach for a haptic device with pantograph parallel platform,” Multibody Syst. Dyn. 21, 233247 (2009).
13. Wu P., Xiong H. and Kong J., “Dynamic analysis of 6-SPS parallel mechanism,” Int. J. Mech. Mater. Des. 8, 121128 (2012).
14. Lopes A. Mendes and Almeida F., “The generalized momentum approach to the dynamic modeling of a 6-dof parallel manipulator,” Multibody Syst. Dyn. 21, 123146 (2009).
15. Lopes A. M., “Dynamic modeling of a Stewart platform using the generalized momentum approach,” Commun. Nonlinear Sci. Numer. Simul. 14, 33893401 (2009).
16. Miller K., “Optimal design and modeling of spatial parallel manipulators,” Int. J. Robot. Res. 23, 127140 (2004).
17. Gallardo J., Rico J., Frisoli A., Checcacci D. and Bergamasco M., “Dynamics of parallel manipulators by means of screw theory,” Mech. Mach. Theory 38, 11131131 (2003).
18. Staicu S. and Zhang D., “A novel dynamic modelling approach for parallel mechanisms analysis,” Robot. Comput.-Integr. Manuf. 24, 167172 (2008).
19. Pedrammehr S., Qazani M. R. C., Abdi H. and Nahavandi S., “Mathematical modelling of linear motion error for Hexarot parallel manipulators,” Appl. Math. Modelling 40, 942954 (2016).
20. Lebret G., Liu K. and Lewis F. L., “Dynamic analysis and control of a Stewart platform manipulator,” J. Robot. Syst. 10, 629655 (1993).
21. Ting Y., Chen Y. S. and Jar H. C., “Modeling and control for a Gough-Stewart platform CNC machine,” J. Robot. Syst. 21, 609623 (2004).
22. Rahmani A., Ghanbari A. and Pedrammehr S., “Kinematic analysis for hybrid 2-(6-UPU) manipulator by wavelet neural network,” Adv. Mater. Res. 1016, 726730 (2014).
23. Guo H. and Li H., “Dynamic analysis and simulation of a six degree of freedom Stewart platform manipulator,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 220, 6172 (2006).
24. Do W. and Yang D., “Inverse dynamic analysis and simulation of a platform type of robot,” J. Robot. Syst. 5, 209227 (1988).
25. Pedrammehr S., Mahboubkhah M. and Khani N., “Improved dynamic equations for the generally configured Stewart platform manipulator,” J. Mech. Sci. Technol. 26, 711721 (2012).
26. Dasgupta B. and Mruthyunjaya T., “A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory 33, 11351152 (1998).
27. Dasgupta B. and Mruthyunjaya T., “Closed-form dynamic equations of the general Stewart platform through the Newton–Euler approach,” Mech. Mach. Theory 33, 9931012 (1998).
28. Harib K. and Srinivasan K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21, 541554 (2003).
29. Mahmoodi A., Menhaj M. and Sabzehparvar M., “An efficient method for solution of inverse dynamics of Stewart platform,” Aircraft Eng. Aerospace Technol. 81, 398406 (2009).
30. Qazani M. R. C., Pedrammehr S. and Nategh M. J., “A study on motion of machine tools' hexapod table on freeform surfaces with circular interpolation,” Int. J. Adv. Manuf. Technol. 75, 17631771 (2014).
31. Pedrammehr S., Mahboubkhah M. and Pakzad S., “An Improved Solution to the Inverse Dynamics of the General Stewart Platform,” Proceedings of the Mechatronics (ICM), 2011 IEEE International Conference on, (2011) pp. 392–397.
32. Pedrammehr S., Farrokhi H., Rajab A. K. S., Pakzad S., Mahboubkhah M., Ettefagh M. M. and Sadeghi M. H., “Modal analysis of the milling machine structure through FEM and experimental test,” Adv. Mater. Res. 383, 67176721 (2012).
33. Pedrammehr S., Mahboubkhah M. and Khani N., “A study on vibration of Stewart platform-based machine tool table,” Int. J. Adv. Manuf. Technol. 65, 9911007 (2013).
34. Pedrammehr S., Mahboubkhah M., Qazani M. R. C., Rahmani A. and Pakzad S., “Forced vibration analysis of milling machine's hexapod table under machining forces,” Strojniški Vestnik-J. Mech. Eng. 60, 158171 (2014).
35. Afzali-Far B., Lidström P. and Nilsson K., “Parametric damped vibrations of Gough–Stewart platforms for symmetric configurations,” Mech. Mach. Theory 80, 5269 (2014).
36. Afzali-Far B. and Lidström P., “A Joint-Space Parametric Formulation for the Vibrations of Symmetric Gough-Stewart Platforms,” In: (Selvaraj H., Zydek D., Chmaj G. eds.), Progress in Systems Engineering. Advances in Intelligent Systems and Computing, 366. Springer, Cham.
37. Afzali-Far B., Andersson A., Nilsson K. and Lidström P., “Influence of strut inertia on the vibrations in initially symmetric Gough–Stewart Platforms—an analytical study,” J. Sound Vib. 352, 142157 (2015).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 64 *
Loading metrics...

Abstract views

Total abstract views: 261 *
Loading metrics...

* Views captured on Cambridge Core between 17th July 2017 - 24th November 2017. This data will be updated every 24 hours.