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Dynamic modeling and control design for a parallel-mechanism-based meso-milling machine tool

Published online by Cambridge University Press:  28 August 2013

Adam Y. Le ,
James K. Mills  and
Beno Benhabib
Adam Y. Le*
Affiliation:
Department of Mechanical and Industrial Engineering, 5 King's College Rd, University of Toronto, Toronto, ON M5S 3G8, Canada
James K. Mills
Affiliation:
Department of Mechanical and Industrial Engineering, 5 King's College Rd, University of Toronto, Toronto, ON M5S 3G8, Canada
Beno Benhabib
Affiliation:
Department of Mechanical and Industrial Engineering, 5 King's College Rd, University of Toronto, Toronto, ON M5S 3G8, Canada
*
*Corresponding author. E-mail: y.le@mail.utoronto.ca
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Summary

A novel rigid-body control design methodology for 6-degree-of-freedom (dof) parallel kinematic mechanisms (PKMs) is proposed. The synchronous control of PKM joints is addressed through a novel formulation of contour and lag errors. Robust performance as a control specification is addressed. A convex combination controller design approach is applied to address the problem of simultaneously satisfying multiple closed-loop specifications. The applied dynamic modeling approach allows the design methodology to be extended to 6-dof spatial PKMs. The methodology is applied to the design of a 6-dof PKM-based meso-milling machine tool and simulations are conducted.

Keywords

Parallel manipulatorsControl of robotic systemsManufacturingRobot dynamicsForce control
Type
Articles
Information
Robotica , Volume 32 , Issue 4 , July 2014 , pp. 515 - 532
Copyright
Copyright © Cambridge University Press 2013 

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References

1.Vogler, M. P., Liu, X., Kapoor, S. G., DeVor, R. E. and Ehmann, K. F., “Development of meso-scale machine tool (mMT) systems,” Technical Paper, Society of Manufacturing Engineers MS.MS02-181, 1–9, (2002).Google Scholar
2.Bang, Y.-B., Lee, K.-M. and Oh, S., “5-axis micro milling machine for machining micro parts,” Int. J. Adv. Manuf. Technol. 25 (9–10), 888–894 (2005).CrossRefGoogle Scholar
3.Kussul, E., Baidyk, T., Ruiz-Huerta, L., Caballero-Ruiz, A., Velasco, G. and Kasatkina, L., “Development of micromachine tool prototypes for microfactories,” J. Micromech. Microeng. 12 (6), 795–812 (2002).CrossRefGoogle Scholar
4.Azulay, H., Hawryluck, C., Mills, J. K. and Benhabib, B., “Configuration Design of a Meso-Milling machine,” Proceedings of the 23rd Canadian Congress of Applied Mechanics, Vancouver, Canada (2011) pp. 1024–1027.Google Scholar
5.Dasgupta, B. and Mruthyunjaya, T., “A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator,” Mech. Mach. Theory 33 (8), 1135–1152 (1998).Google Scholar
6.Tsai, L.-W., “Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work,” Trans ASME, J. Mech. Des. 122 (1), 3–9 (2000).Google Scholar
7.Abdellatif, H. and Heimann, B., “Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism,” Mech. Mach. Theory 44 (1), 192–207 (2009).CrossRefGoogle Scholar
8.Liu, G., Wu, X. and Li, Z., “Inertia Equivalence Principle and Adaptive Control of Redundant Parallel Manipulators,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington DC, USA (2002) pp. 835–840.Google Scholar
9.Weiwei, S., Shuang, C., Yaoxin, Z. and Yanyang, L., “Active joint synchronization control for a 2-DOF redundantly actuated parallel manipulator,” IEEE Trans. Control Syst. Technol. 17 (2), 416–423 (2009).Google Scholar
10.Koren, Y., “Cross-coupled biaxial computer control for manufacturing systems,” Trans. ASME, J. Dyn. Syst. Meas. Control 102 (4), 265–272, (1980).Google Scholar
11.Koren, Y. and Lo, C.-C., “Variable-gain cross-coupling controller for contouring,” CIRP Ann.–Manuf. Technol. 40 (1), 371–374 (1991).Google Scholar
12.Chiu, G.-C. and Tomizuka, M., “Contouring control of machine tool feed drive systems: A task coordinate frame approach,” IEEE Trans. Control Syst. Technol. 9 (1), 130–139 (2001).Google Scholar
13.Sencer, B., Altintas, Y. and Croft, E., “Modeling and control of contouring errors for five-axis machine tools–Part I: Modeling,” Trans ASME, J. Manuf. Sci. Eng. 131 (3), 0310061–0310068 (2009).Google Scholar
14.El Khalick M, A. and Uchiyama, N., “Contouring controller design based on iterative contour error estimation for three-dimensional machining,” Robot. Comput.-Integr. Manuf. 27 (4), 802–807 (2011).Google Scholar
15.Yang, J. and Li, Z., “A novel contour error estimation for position loop-based cross-coupled control,” IEEE/ASME Trans. Mechatronics 16 (4), 643–655 (2011).CrossRefGoogle Scholar
16.Spong, M. W. and Vidyasagar, M., “Robust linear compensator design for nonlinear robotic control,” IEEE J. Robot. Autom. 3 (4), 345–351 (1987).Google Scholar
17.Boyd, S. P. and Barratt, C. H., Linear Controller Design: Limits of Performance (Prentice Hall, Englewood Cliffs, NJ, 1991).Google Scholar
18.Liu, H. H. and Mills, J. K., “Robot trajectory control system design for multiple simultaneous specifications: Theory and experimentation,” Trans. ASME, J. Dyn. Syst., Meas. Control 120 (4), 520–523 (1998).Google Scholar
19.Honegger, A. E., Langstaff, G. Q., Phillip, A. G. and Vanravenswaay, T. D., “Development of an automated microfactory: Part 1–microfactory architecture and sub-systems development,” Trans. North Am. Manuf. Res. Inst. SME 34, 341–348 (2006).Google Scholar
20.Jahanmir, S., Ren, Z., Heshmat, H. and Tomaszewski, M., “Design and evaluation of an ultrahigh speed micro-machining spindle,” Mach. Sci. Technol. 14 (2), 224–243 (2010).Google Scholar
21.Mahmoodi, M., Le, Y., Mills, J. K. and Benhabib, B., “An Active Dynamic Model for a Parallel-Mechanism-Based Meso-Milling Machine Tool,” Proceedings of the 23rd Canadian Congress of Applied Mechanics, Vancouver, Canada (2011) pp. 1032–1035.Google Scholar
22.Mahmoodi, M., Mills, J. and Benhabib, B., “Structural Vibration Modeling of a Novel Parallel Mechanism-Based Reconfigurable Meso-Milling Machine Tool (RmMT),” Proceedings of the 1st International Conference on Virtual Machining Process Technology, Montreal, Canada (2012).Google Scholar
23.Le, Y., Mills, J. and Benhabib, B., “Convex Combination Control Design for 6 DOF Spatial Reconfigurable Meso-Milling Machine Tool,” Proceedings of the 1st International Conference on Virtual Machining Process Technology, Montreal, Canada (2012).Google Scholar
24.Kim, J., Cho, K., Hwang, J., Iurascu, C. and Park, F., “Eclipse-RP: A new RP machine based on repeated deposition and machining,” Proc. Inst. Mech. Eng. 216 (K1), 13–20 (2002).Google Scholar
25.Li, Y. and Xu, Q., “Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism,” Robotica 23 (2), 219–229 (2005).Google Scholar
26.Chen, C.-T., “A Lagrangian formulation in terms of quasi-coordinates for the inverse dynamics of the general 6–6 Stewart platform manipulator,” JSME Int. J. C 46 (3), 1084–1090 (2003).Google Scholar
27.Kim, J. and Park, F. C., “Direct kinematic analysis of 3-RS parallel mechanisms,” Mech. Mach. Theory 36 (10), 1121–1134 (2001).CrossRefGoogle Scholar
28.Sciavicco, L. and Siciliano, B., Modeling and Control of Robot Manipulators (The McGraw-Hill Companies, Inc., New York, N. Y., 1996).Google Scholar
29.Kreyszig, E., Differential Geometry (University of Toronto Press, Toronto, 1959).Google Scholar
30.Abdallah, C., Dawson, D., Dorato, P. and Jamshidi, M., “Survey of robust control for rigid robots,” IEEE Control Syst. 11 (2), 24–30 (1991).Google Scholar
31.Miao, J., Chen, G., Lai, X., Li, H. and Li, C., “Review of dynamic issues in micro-end-milling,” Int. J. Adv. Manuf. Technol. 31 (9–10), 897–904 (2007).Google Scholar
32.Fu, K. and Mills, J. K., “A convex approach solving simultaneous mechanical structure and control system design problems with multiple closed-loop performance specifications,” Trans. ASME G 127 (1), 57–68 (2005).Google Scholar