A Study on the Quality of Hexapod Machine Tool's Workspace
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56874", author = "D. Karimi and M.J. Nategh", title = "A Study on the Quality of Hexapod Machine Tool's Workspace", abstract = "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 = "Hexapod, Machine Tool, Singularity, Workspace.", volume = "3", number = "4", pages = "386-6", }