Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-29T07:13:05.825Z Has data issue: false hasContentIssue false

Approximate analytical solution for vibration of a 3-PRP planar parallel robot with flexible moving platform

Published online by Cambridge University Press:  13 June 2014

Mahdi Sharifnia*
Affiliation:
Mechanical Engineering Department, Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran
Alireza Akbarzadeh
Affiliation:
Mechanical Engineering Department, Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran
*
*Corresponding author. E-mail: sharifnia.mehdi@gmail.com

Summary

In this research, using an approximate analytical method, vibration analysis of a 3-PRP (active prismatic—P, passive revolute—R, passive prismatic—P) planar parallel robot having a flexible moving platform is presented. A specific architecture of the 3-PRP parallel robot, also known as the ST (Star-Triangle) parallel robot, is considered. The moving platform of the robot, called the star, is assumed to be made of three flexible beams shaped like a star. For analytical modeling, each of the three beams of the star is assumed to be a discrete Euler–Bernoulli beam with a passive prismatic joint. Continuity equations at the center of the star are used to relate vibrations of the three beams. The vibration behavior of each beam is modeled using previously developed constrained motion equations for a planar Euler–Bernoulli beam having a prismatic joint. In this paper, previously presented “constrained assumed modes method” is further developed to solve the constrained motion equation for the ST parallel robot. The solution method is used to obtain the vibration of the robot for the inverse dynamics problem and simultaneously provides generalized constraint forces. Furthermore, the solution method can be used for the direct dynamics problem of the ST robot. Several input trajectories are considered to investigate the different behavior for the center of the star. For each of the trajectories, three different groups of mode shapes are considered and their vibrational responses are compared. In this research, for the first time, effects of the passive prismatic joint parameters such as mass, rotational moment of inertia, and its actual length are considered in an analytical model. Finally, the analytical solution and a FEM (Finite Element Method) software solution are compared.

Type
Articles
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Fattah, A., Angeles, J. and Misra, A. K., “Direct Kinematics of a 3-DOF Spatial Parallel Manipulator with Flexible Legs,” Proceedings of the 23rd ASME Mechanisms Conference, Minneapolis, USA (Sep. 11–14, 1994), vol. 72, pp. 285291.Google Scholar
2.Fattah, A., Angeles, J. and Misra, A. K., “Dynamics of a 3-DOF Spatial Parallel Manipulator with Flexible Links,” Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan (May 21–27, 1995) Vol. 1, pp. 627632.CrossRefGoogle Scholar
3.Fattah, A., Misra, A. K. and Angeles, J., “Dynamics of a Flexible-Link Planar Parallel Manipulator in Cartesian Space,” Proceedings of the 20th ASME Design Automation Conference, Minneapolis, USA (Sep. 11–14, 1994), vol. 69(2), pp. 483490.Google Scholar
4.Piras, G., Cleghorn, W. L. and Mills, J. K., “Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links,” Mech. Mach. Theory 40, 849862 (2005).CrossRefGoogle Scholar
5.Wang, X. and Mills, J. K., “Dynamic modeling of a flexible-link planar parallel platform using a substructuring approach,” Mech. Mach. Theory 41, 671687 (2006).CrossRefGoogle Scholar
6.Zhaocai, D. and Yueqing, Y., “Dynamic modeling and inverse dynamic analysis of flexible parallel robots,” Int. J. Adv. Robot. Syst. 5 (1), 115122 (2008).CrossRefGoogle Scholar
7.Zhou, Z., Xi, J. and Mechefske, C. K., “Modeling of a fully flexible 3-PRS manipulator for vibration analsysis,” J Mech. Des. 128, 403412 (2006).CrossRefGoogle Scholar
8.Shan-zeng, L., Yue-qing, Y., Zhen-cai, Z., Li-ying, S. and Qing-bo, L., “Dynamic modeling and analysis of 3-RRS parallel manipulator with flexible links,” J. Cent. South Univ. Technol. 17, 323331 (2010).Google Scholar
9.Kang, B. and Mills, J. K., “Dynamic modeling of structurally-flexible planar parallel manipulator,” Robotica 20, 329339 (2002).CrossRefGoogle Scholar
10.Zhang, X., Mills, J. K. and Cleghorn, W. L., “Vibration control of elastodynamic response of a 3-PRR flexible parallel manipulator using PZT transducers,” Robotica 26, 655665 (2008).CrossRefGoogle Scholar
11.Giovagnoni, M., “Dynamics of Flexible Closed-chain Manipulator,” Proceedings of the ASME Design Technical Conference, Scottsdale, USA (1992), vol. 69(2), pp. 483490.Google Scholar
12.Lee, J. D. and Geng, Z., “Dynamic model of a flexible Stewart platform,” Comput. Struct. 48 (3)367374 (1993).CrossRefGoogle Scholar
13.Dwivedy, S. K. and Eberhard, P., “Dynamic analysis of flexible manipulators, a literature review,” Mech. Mach. Theory 41, 749777 (2006).CrossRefGoogle Scholar
14.Sharifnia, M. and Akbarzadeh, A., “An Analytical Model for Vibration and Control of a PR-PRP Parallel Robot with Flexible Platform and Prismatic Joint,” Journal of Vibration and Controlw, Published online before print, 2 April 2014, doi: 10.1177/1077546314528966.Google Scholar
15.Sharifnia, M. and Akbarzadeh, A., “Dynamics and Vibration of a 3-PSP Parallel Robot with Flexible Moving Platform,” Accepted for publication, Journal of Vibration and Control.Google Scholar
16.Ibrahimbegovic, A. and Mamouri, S., “On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3D geometrically exact beam model,” Comput. Methods Appl. Mech.Eng. 188, 805831 (2000).CrossRefGoogle Scholar
17.Bauchau, O. A., “On the modeling of prismatic joints in flexible multi-body systems,” Comput. Methods Appl. Mech. Eng. 181, 87105 (2000).CrossRefGoogle Scholar
18.Stoenescu, E. D. and Marghitu, D. B., “Effect of prismatic joint inertia on dynamics of kinematic chains,” Mech. Mach. Theory 39, 431443 (2004).CrossRefGoogle Scholar
19.Daniali, H. R. Mohammadi, Zsombor-Murray, P. J. and Angeles, J., “The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators,” In: Computational Kinematics edited by Angeles, J., Hommel, G., and Kovacs, P., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 153164 (1993).CrossRefGoogle Scholar
20.Ronchi, S., Company, O., Pierrot, F. and Fournier, A., “PRP Planar Parallel Mechanism in Configurations Improving Displacement Resolution,” Proceedings of the 1st International Conference on Positioning Technology, Hamamatsu, Japan (Jun. 9–11, 2004), pp. 279284.Google Scholar
21.Taghvaeipour, A., Angeles, J. and Lessard, L., “On the elastostatic analysis of mechanical systems,” Mech. Mach. Theory 58, 202216 (2012).CrossRefGoogle Scholar
22.Vidoni, R., Gasparetto, A. and Giovagnoni, M., “Design and implementation of an ERLS-based 3-D dynamic formulation for flexible-link robots,” Robot. Comput.-Integr. Manuf. 29 (2), 273282 (2013).CrossRefGoogle Scholar
23.Mosayebi, M., Ghayour, M. and Sadigh, M. J., “A nonlinear high gain observer based input-output control of flexible link manipulator,” Mech. Res. Commun. 45, 3441 (2012).CrossRefGoogle Scholar
24.Staufer, P. and Gattringer, H., “State estimation on flexible robots using accelerometers and angular rate sensors,” Mechatronics 22 (8), 10431049 (2012).CrossRefGoogle Scholar
25.Dokainish, M. A. and Kumar, R., “Experimental and theoretical analysis of the transverse vibrations of a beam having bilinear support,” Exp. Mech. 11 (6), 263270 (1971).CrossRefGoogle Scholar