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A Study on the Quality of Hexapod Machine Tool's Workspace

Authors: D. Karimi, M.J. Nategh


One of the main concerns about parallel mechanisms is the presence of singular points within their workspaces. In singular positions the mechanism gains or loses one or several degrees of freedom. It is impossible to control the mechanism in singular positions. Therefore, these positions have to be avoided. This is a vital need especially in computer controlled machine tools designed and manufactured on the basis of parallel mechanisms. This need has to be taken into consideration when selecting design parameters. A prerequisite to this is a thorough knowledge about the effect of design parameters and constraints on singularity. In this paper, quality condition index was introduced as a criterion for evaluating singularities of different configurations of a hexapod mechanism obtainable by different design parameters. It was illustrated that this method can effectively be employed to obtain the optimum configuration of hexapod mechanism with the aim of avoiding singularity within the workspace. This method was then employed to design the hexapod table of a CNC milling machine.

Keywords: Singularity, Machine Tool, workspace, Hexapod

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[1] D. Ghablat, P. Wenger and Angeles J., "The iso-conditioning loci of a class of closed-chain manipulators," International Conference on Robotics And Automation, Leuven, May 1998.
[2] H. R. Mohammadi Danial and P. J. Zsombor-Murray, "The design of isotropic planar parallel manipulators," Proceedings of the 1st World Automation Congress 2, pp. 273-280, 1994.
[3] P. Nanua, K. J. Waldron and V. Murty, "Direct kinematics solution of a Stewart platform", IEEE Trans. on Robotics and Automation, vol. 6, PP. 438-444, 1990.
[4] C. Innocenti and P. Castelli, "Direct position analysis of the stewart platform mechanism", Mech. and Mach. Theory, vol. 25, PP. 611-621, 1990.
[5] J. Amit Patel and F. Kernel Ehman, "Calibration of a hexapod machine tool using a redundant leg", International Journal of Machine Tools and Manufacture, vol. 40, pp. 489-512, 2000.
[6] Xinhua Zhao and Shangxian Peng, "A successive approximation algorithm for the direct position analysis of parallel manipulators", International Journal of Mechanism and Machine Theory, vol. 35, pp. 1095-1101, 2000.
[7] X Shi. and R. G Fenton., "A complete and general solution of the forward kinematics of platforms-type robotic manipulators", IEEE Transactions on Robotics and Automation, vol. 4, pp. 3055-3062, 1994.
[8] M. W. Spong and M. Vidyasagar, "Robot dynamics and control", John Wiley and sons, New York, 1989.
[9] H. Asada, and J. J. E. Slotine, "Robot analysis and control", John Wiley and Sons, New York, 1985
[10] O. Masory and J. Wang, "Workspace evaluation of Stewart Platforms", Advanced Robotics, vol. 9, pp. 443-461, 1991.
[11] G. David Lay, "Linear algebra and its application", Addison-Wesley, 1997.