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Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed

Published online by Cambridge University Press:  11 August 2009

Xuping Zhang ,
James K. Mills  and
William L. Cleghorn
Xuping Zhang*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, CanadaM5S 3G8
James K. Mills
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, CanadaM5S 3G8
William L. Cleghorn
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, CanadaM5S 3G8
*
*Corresponding author. E-mail: zhxp@mie.utoronto.ca
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Summary

The effect of axial forces on the dynamic properties is formulated and investigated for a 3-PRR planar parallel manipulator with three flexible intermediate links. A dynamic model of the manipulator system is developed based on the assumed mode method with the consideration of the effect of longitudinal forces on lateral stiffness is included. The flexible intermediate links are modeled as Euler–Bernoulli beams with pinned-pinned boundary conditions, which are verified by experimental modal tests. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic behavior including the effect of axial forces on lateral deformation is investigated, and configuration-dependant frequencies are analyzed. Numerical simulations of configuration-dependent frequency properties and axial forces are performed to illustrate the effect of axial forces on the dynamic behaviors of the flexible parallel manipulator. Simulation results of mode amplitudes, deformations, axial forces, inertial, and coupling forces are presented, and further validate the theoretical derivations. These analyses and results provide a new and valuable insight to the design and control of the parallel manipulators with flexible intermediate links.

Keywords

Flexible manipulatorsParallel manipulatorsAssumed mode methodDynamic stiffeningAxial force
Type
Article
Information
Robotica , Volume 28 , Issue 4 , July 2010 , pp. 607 - 619
Copyright
Copyright © Cambridge University Press 2009

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References

1.Dasgupta, B. and Mruthyunjaya, T. S., “The Stewart platform manipulator: A review,” Mech. Mach. Theory, 35, 25–40 (2000).CrossRefGoogle Scholar
2.Wang, X. and Mills, J. K., “Experimental Modal Analysis of Flexible Linkages in a Smart Parallel Platform,” Proceeding of the 7th CANSMART Meeting – International Workshop on Smart Materials and Structures, Montreal, Canada (2004) pp. 37–46.Google Scholar
3.Lowen, G. G. and Chassapis, C., “The elastic behavior of linkage: An update,” Mech. Mach. Theory, 21 (1), 33–42 (1986).CrossRefGoogle Scholar
4.Shabana, A. A., “Flexible multibody dynamics: review of past and recent developments,” Multibody Syst. Dyn., 1, 189–222 (1997).CrossRefGoogle Scholar
5.Dwivedy, S. K. and Eberhard, P., “Dynamic analysis of flexible manipulators, a literature review,” Mech. Mach. Theory, 41, 749–777 (2006).CrossRefGoogle Scholar
6.Giovagnoni, M., “Dynamics of flexible closed-chain manipulator,” ASME Des. Tech. Conf., 69 (2), 483–490 (1992).Google Scholar
7.Lee, J. D. and Geng, Z., “Dynamic model of a flexible Stewart platform,” Comput. Struct., 48 (3), 367–374 (1993).Google Scholar
8.Fattah, A., Angeles, J. and Misra, A. K., “Dynamics of a 3-DOF Spatial Parallel Manipulator with Flexible Links,” Proceedings of IEEE International Conference of Robotics and Automation, Nagoya, Japan (1995) pp. 274–632.Google Scholar
9.Zhou, Z., Xi, J. and Mechefske, C. K., “Modeling of a fully flexible 3PRS manipulator for vibration analsysis,” J. Mech. Des., 128, 403–412 (2006).CrossRefGoogle Scholar
10.Kang, B. S. and Mills, J. K., “Dynamic modeling of structurally-flexible planar parallel manipulator,” Robotica, 20 (3), 329–339 (2002).CrossRefGoogle Scholar
11.Zhang, X., Mills, J. K. and Cleghorn, W. L., “Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate links,” J. Intell. Robot. Syst., 50, 323–340 (2007).CrossRefGoogle Scholar
12.Sunada, W. and Dubowsky, S., “The application of the finite element methods to the dynamic analysis of flexible spatial and co-planar linkage systems,” ASME J. Mech. Des., 103 (3), 643–651 (1981).Google Scholar
13.Cleghorn, W. L., Fenton, R. G. and Tabarrok, B., “Finite element analysis of high-speed flexible mechanisms,” Mech. Mach. Theory, 16, 407–424 (1981).CrossRefGoogle Scholar
14.Thompson, B. S. and Sung, C. K., “A variational formulation for the nonlinear finite element analysis of flexible linkages: Theory, implementation and experimental results,” ASME J. Mech. Trans. Autom. Des., 106, 482–488 (1984).CrossRefGoogle Scholar
15.Bayo, E., “A fininte element approach to control the end-point motion of single-link flexible robot,” J. Robot. Syst., 4 (1), 63–75 (1987).CrossRefGoogle Scholar
16.Naganathan, G. and Soni, A. H., “Coupling effects of kinematics and flexibility in manipulators,” Int. J. Robot. Res., 6 (1), 75–85 (1987).CrossRefGoogle Scholar
17.Yang, Z. and Sadler, J. P., “Large-displacement finite element analysis of flexible linkages,” ASME J. Mech. Des. 112, 175–182, (1990).CrossRefGoogle Scholar
18.Book, W. J., “Recursive Lagrangian dynamics of fexible manipulator arms,” Int. J. Robot. Res., 3 (3), 87–101 (1984).CrossRefGoogle Scholar
19.Asada, H., Ma, Z.-D. and Tokumaru, H., “Inverse dynamics of flexible robot arms: Modeling and computation for trajectory control,” ASME. J. Dyn. Sys. Meas. Control, 112, 177–185 (1990).CrossRefGoogle Scholar
20.Theodore, R. J. and Ghosal, A., “Comparison of the assumed modes and finite element models for flexible multi-link manipulators,” Int. J. Robot. Res. 14, 91–111, (1995).CrossRefGoogle Scholar
21.Korayem, M. H., Nikoobin, A. and Azimirad, V., “Trajectory optimization of flexible link manipulators in point-to-point motion,” Robotica (2008). doi: 10.1017/S0263574708005183.CrossRefGoogle Scholar
22.Meek, J. K. and Liu, H., “Nonlinear dynamics analysis of flexible beams under large overall motions and the flexible manipulator simulation,” Comput. Struct. 56 (1), 1–14, (1995).CrossRefGoogle Scholar
23.Kane, T. R., Ryan, R. R. and Banerjee, A. K., “Dynamics of cantilever beam attached to a moving base,” J. Guid. Control Dyn., 10, 139–150 (1987).Google Scholar
24.Yoo, H. H., Ryan, R. R. and Scott, R. A., “Dynamics of flexible beams undergoing overall motions,” J. Sound Vib., 181 (2), 261–278 (1995).CrossRefGoogle Scholar
25.Pieboeuf, J. and Moore, B., “On the foreshortening effects of a rotating flexible beam suing different methods,” Mech. Based Des. Struct. Mach., 30 (1), 83–102 (2002).CrossRefGoogle Scholar
26.Behzad, M. and Bastam, A. R., “Effect of centrifugal force on natural frequency of lateral vibration of rotation shafts,” J. Sound Vib., 274 (3–5), 985–995 (2004).Google Scholar
27.Liu, J. Y. and Hong, J. Z., “Dynamics of three-dimensional beams undergoing large overall motion,” Eur. J. Mech. – A Solids, 23 (6), 1051–1068 (2004).CrossRefGoogle Scholar
28.Bokaian, A., “Natural frequencies of beams under compressive axial loads,” J. Sound Vib., 126 (1), 49–65 (1988).Google Scholar
29.Gong, S. W., “Perfectly flexible mechanism and integrated mechanism system design,” Mech. Mach. Theory, 39, 1155–1174 (2004).Google Scholar
30.Bellezza, F., Lanari, L. and Ulivi, G., “Exact Modeling of the Flexible Slewing Link,” Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, Ohio (1990) pp. 734–739.Google Scholar
31.Low, K. H. and Lau, M. W. S., “Experimental investigation of the boundary condition of slewing beams using a high-speed camera system,” Mech. Mach. Theory, 30, 629–643 (1995).CrossRefGoogle Scholar
32.Shabana, A. A., “Resonance conditions and deformable body co-ordinate systems,” J. Sound Vib., 192, 389–398 (1996).CrossRefGoogle Scholar
33.Zhang, X., Mills, J. K. and Cleghorn, W. L., “Effect of Axial Forces on Lateral Stiffness of a Flexible 3-PRR Parallel Manipulator Moving with Hight-Speed,” IEEE International Conference on Information and Automation, Hunan, China (2008) pp. 1458–1463.Google Scholar
34.Rao, S. S., Mechanical Vibrations, 4th ed. (Addison-Wesley, Reading, Massachusetts, 2006).Google Scholar
35.Ewins, D. J., Modal Testing: Theory, Practice and Application, 2nd ed. (Research Studies Press, New York, 2000).Google Scholar
36.Solve initial value problems for ordinary differential equations (ODEs), MATLAB Function Reference, The Math Works, Inc. 1994–2005.Google Scholar
37.Radisavljevic, V. and Baruh, H., “A comparison of shortening of the projection to axial elasticity,” J. Sound Vib., 276, 81–103 (2004).CrossRefGoogle Scholar
38.Naguleswaran, S., “Vibration of an Euler–Bernoulli stepped beam carrying a non-symmetrical rigid body at the step,” J. Sound Vib., 271, 1121–1132 (2004).Google Scholar
39.Chen, S. R., Cai, C. S., Chang, C. C. and Gu, M., “Modal coupling assessment and approximated prediction of coupled multimode wind vibration of long-span bridges,” J. Wind Eng. Ind. Aerodyn., 92, 393–412 (2004).CrossRefGoogle Scholar
40.Mohamed, Z., Chee, A. K., Mohd Hashim, A. W. I., Tokhi, M. O., Amin, S. H. M. and Mamat, R., “Techniques for vibration control of a flexible robot manipulator,” Robotica, 24, 499–511 (2006).CrossRefGoogle Scholar