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Dynamic analysis of Hexarot: axis-symmetric parallel manipulator

Published online by Cambridge University Press:  17 July 2017

Siamak Pedrammehr
Affiliation:
Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Victoria 3217, Australia
Behzad Danaei
Affiliation:
Human and Robot Interaction Laboratory, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Hamid Abdi*
Affiliation:
Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Victoria 3217, Australia
Mehdi Tale Masouleh
Affiliation:
Human and Robot Interaction Laboratory, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Saeid Nahavandi
Affiliation:
Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Victoria 3217, Australia
*
*Corresponding author. E-mail: hamid.abdi@deakin.edu.au

Summary

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.

Type
Articles
Copyright
Copyright © Cambridge University Press 2017 

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References

1. Stewart, D., “A platform with six degrees of freedom,” Proc. Inst. Mech. Eng. 180, 371386 (1965).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
3. Isaksson, M., Brogårdh, T. and Nahavandi, S., “Parallel manipulators with a rotation-symmetric arm system,” J. Mech. Des. 134, 114503 (2012).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
8. Staicu, S., Liu, X.-J. and Wang, J., “Inverse dynamics of the HALF parallel manipulator with revolute actuators,” Nonlinear Dyn. 50, 112 (2007).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
10. Abedinnasab, M. H. and Vossoughi, G., “Analysis of a 6-DOF redundantly actuated 4-legged parallel mechanism,” Nonlinear Dyn. 58, 611622 (2009).CrossRefGoogle Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
13. Wu, P., Xiong, H. and Kong, J., “Dynamic analysis of 6-SPS parallel mechanism,” Int. J. Mech. Mater. Des. 8, 121128 (2012).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
15. Lopes, A. M., “Dynamic modeling of a Stewart platform using the generalized momentum approach,” Commun. Nonlinear Sci. Numer. Simul. 14, 33893401 (2009).CrossRefGoogle Scholar
16. Miller, K., “Optimal design and modeling of spatial parallel manipulators,” Int. J. Robot. Res. 23, 127140 (2004).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
18. Staicu, S. and Zhang, D., “A novel dynamic modelling approach for parallel mechanisms analysis,” Robot. Comput.-Integr. Manuf. 24, 167172 (2008).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
20. Lebret, G., Liu, K. and Lewis, F. L., “Dynamic analysis and control of a Stewart platform manipulator,” J. Robot. Syst. 10, 629655 (1993).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
24. Do, W. and Yang, D., “Inverse dynamic analysis and simulation of a platform type of robot,” J. Robot. Syst. 5, 209227 (1988).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
28. Harib, K. and Srinivasan, K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21, 541554 (2003).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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.Google Scholar
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).CrossRefGoogle Scholar