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Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

Published online by Cambridge University Press:  29 April 2014

Mohammad Reza Chalak Qazani
Faculty of Technology & Engineering, Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Siamak Pedrammehr*
Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul, Turkey
Arash Rahmani
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Behzad Danaei
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Mir Mohammad Ettefagh
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Aslan Khani Sheikh Rajab
Department of Mechanical Engineering, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran
Hamid Abdi
Centre for Intelligent Systems Research, Deakin University, Waurn Ponds Campus, Victoria 3217, Australia
*Corresponding author. E-mail:;


Parallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

Copyright © Cambridge University Press 2014 

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1. Hunt, K. H., “Structural kinematics of in-parallel-actuated robot-arms,” ASME J. Mech. Trans. Autom. Des. 105, 705712 (1983).Google Scholar
2. Pierrot, F., Dauchez, P. and Fournier, A., “HEXA: A Fast Six-DOF Fully-Parallel Robot,” Proceedings of the 5th International Conference on Advanced Robotics (ICRA'91), Pisa, Italy (1991) pp. 11581163.Google Scholar
3. Wiegand, A., Hebsacker, M. and Honegger, M., “Parallele Kinematik und Linearmotoren: Hexaglide-ein neues, hochdynamisches Werkzeugmaschinenkonzept,” Technische Rundschau Nr. 25 (1996).Google Scholar
4. Lallemand, J. P., Goudali, A. and Zeghloul, S., “The 6-DOF 2-Delta Parallel Robot,” Robotica 15, 407416 (1997).Google Scholar
5. Merlet, J. P., Parallel Robots (2 ed.). Solid Mechanics and Its Applications (128. Springer, Dordrecht, the Netherlands, 2006).Google Scholar
6. Stewart, D., “A platform with six degrees of freedom,” Proc. Inst. Mech. Eng. 180, 371386 (1965).Google Scholar
7. 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).Google Scholar
8. Reboulet, C., “Parallel-Structure Manipulator Device for Displacing and Orienting an Object in a Cylindrical Work Space,” U.S. Patent NO. 5, 539, 291 (1996).Google Scholar
9. Kock, S., Oesterlein, R. and Brogårdh, T., “Industrial Robot,” Patent WO 03/066289 (2003).Google Scholar
10. Merz, M. and Roy, S. N., “Parallel Robot,” U.S. Patent NO. 7, 331, 750 (2008).Google Scholar
11. Isaksson, M., Brogårdh, T. and Nahavandi, S., “Parallel manipulators with a rotation-symmetric arm system,” ASME J. Mech. Des. 134, 114503 (2012).Google Scholar
12. Isaksson, M. and Watson, M., “Workspace analysis of a novel six-degrees-of-freedom parallel manipulator with coaxial actuated arms,” ASME J. Mech. Des. 135, 19 (2013).Google Scholar
13. Qazani, M. R. Chalak, Pedrammehr, S., Rahmani, A., Shahryari, M., Rajab, A. Khani Sheykh and Ettefagh, M. M., “An experimental study on motion error of hexarot parallel manipulator,” Int. J. Adv. Manuf. Technol., (2014) doi: 10.1007/s00170-014-5685-y.Google Scholar
14. Harib, K. and Srinivasan, K., “Kinematic and dynamic analysis of Stewart platform-based machine tool structures,” Robotica 21, 541554 (2003).Google Scholar
15. Pedrammehr, S., Mahboubkhah, M. and Pakzad, S., “An improved solution to the inverse dynamics of the general Stewart platform,” Proceedings of 2011 IEEE International Conference on Mechatronics ICM 2011, 5971317 (2011) pp. 392–397.Google Scholar
16. Pedrammehr, S., Mahboubkhah, M. and Khani, N., “Improved dynamic equations for the generally configured Stewart platform manipulator,” J. Mech. Sci. Technol. 26, 711721 (2012).Google Scholar
17. 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).Google Scholar
18. Pedrammehr, S., Mahboubkhah, M., Qazani, M. R. Chalak, Rahmani, A. and Pakzad, S., “Forced vibration analysis of milling machine's hexapod table under machining forces,” Stroj. Vestn.-J. Mech. E. 60, 158171 (2014).Google Scholar
19. Yang, G., Chen, W. and Chen, I.-M., “A Geometrical Method for the Singularity Analysis of 3-RRRPlanar Parallel Robots with Different Actuation Schemes,”Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robotis and systems, Lausanne, Switzerland (2002).Google Scholar
20. Pierrota, F.1, Reynauda, C.1 and Fourniera, A.1, “DELTA: A simple and efficient parallel robot,” Robotica 8, 105109 (1990).Google Scholar
21. Li, Y. and Xu, Q., “Kinematic analysis of a 3-PRS parallel manipulator,”Robot. CIM-Int. Manuf. 23, 395408 (2007).Google Scholar
22. Xie, J., Qiang, W., Liang, B. and Li, C., “Screw Theory and Singularity Analysis of Parallel Robots,” Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, 9097248 (2006) pp. 147–152.Google Scholar
23. Oetomo, D., Liaw, H. C., Alici, G. and Shirinzadeh, B., “Direct Kinematics and Analytical Solution to 3RRR Parallel Planar Mechanisms,” IEEE International Conference on Control, Automation, Robotics and Vision, Singapore (2006) pp. 22512256.Google Scholar
24. Liu, K., Fitzgerald, J. M. and Lewis, F. L., “Kinematic analysis of a Stewart platform manipulator,” IEEE Trans. Ind. Electron. 40, 282293 (1993).Google Scholar
25. Wang, L.-C. and Oen, K.-T., “Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators,” Journal of Robotic Systems 19, 391400 (2002).Google Scholar
26. Boudreau, R., “Real time solution to the forward kinematic problem of a general spherical three-degree-of-freedom parallel manipulator,” Proceedings of ASME Design Engineering Technical Conferences 82, Boston, MA, USA (1995) pp. 965971.Google Scholar
27. Masory, O. and Wang, J., “Workspace Evaluation of Stewart Platforms,” Proceedings of the ASME 22nd Biennial Mechanisms Conference 45, Scottsdale, Arizona (1992) pp. 337346.Google Scholar
28. Fichter, E. F., “A stewart platform-based manipulator: General theory and practical construction,” Int. J. Robot. Res. 5, 157182 (1986).Google Scholar
29. Arai, T., Tanikawa, T., Merlet, J. P. and Sendai, T., “Development of a New Parallel Manipulator with Fixed Linear Actuator,” ASME Japan/USA Symposium on Flexible Automation 1, Boston, Massachusetts (1996) pp. 145149.Google Scholar
30. Conti, J. P., Clinton, C. M., Zhang, G. and Wavering, A. J., “Dynamic Variation of the Workspace of an Octahedral Hexapod Machine During Machining,” Technical Research Report, TR 97–28, ISR (University of Maryland, Maryland, 1997).Google Scholar
31. Bonev, I. A. and Ryu, J., “Workspace analysis of 6-PRRS parallel manipulators based on the vertex space concept,” Proceedings of the 1999 ASME Design Engineering Technical Conferences, Las Vegas, Nevada (Sep. 12–15, 1999).Google Scholar
32. Bonev, A. and Ryu, J., “A new approach to orientation workspace analysis of 6-DoF parallel manipulators,” Mech. Mach. Theory 36, 1528 (2001).Google Scholar
33. Pernkopf, F. and Husty, M. L., “Workspace Analysis of Stewart-Gough Manipulators Using Orientation Plots,” Proc. MUSME, 33–38 (2002).Google Scholar
34. Huang, T., Wang, J. and Whitehouse, D. J., “Closed Form Solution to Workspace of Hexapod-Based Virtual Axis Machine Tools,” ASME J. Mech. Des. 121, 2631 (1999).Google Scholar
35. Gosselin, C. M., “Determination of the workspace of 6-Dof parallel manipulators,” ASME J. Mech. Des. 112, 331336 (1990).Google Scholar
36. Majid, M. Z. A., Huang, Z. and Yao, Y. L., “Workspace analysis of a Six-Degree of freedom, three-prismatic-prismatic-spheric-revolute parallel manipulator,” Int. J. Adv. Manuf. Technol. 16, 441449 (2000).Google Scholar
37. Tahmasebi, F. and Tsai, L. W., “Workspace and singularity analysis of a novel Six-DoF parallel minimanipulator,” J. Appl. Mech. Robot. 1, 3140 (1994).Google Scholar
38. Zhu, C., Guan, L., Han, J. and Wang, L., “A New Resolution of Workspace Problem of Parallel Machine Tool,” Proceedings ofthe IEEE International Conference on Automation and Logistics Shenyang (2009) pp. 1002–1007.Google Scholar
39. Masory, O. and Wang, J., “Workspace evaluation of stewart platforms,” J. Adv. Rob. 9, 443461 (1995).Google Scholar