Vibration Analysis of 2-PR(Pa)U- 2-PR(Pa)R New Parallel Mechanism

Document Type: Original Article


Department of Mechanical Engineering, University of Tabriz, Iran


Parallel kinematic machines, are closed loop structures which have more accuracy, stiffness and ability to withstand high loads. In this paper the vibration equations of the new parallel mechanism, that has higher stiffness because of parallelogram system and fixed length pods, have been derived by analytical approach. Whereas the proposed mechanism is applied as a machine tools, its vibrational behavior investigation has key impact factor. All the kinematic chains of the mechanism have been taken into consideration to achieve the coupled system of equations. To extract mechanism natural frequencies, modal analysis is carried out using three methods including analytical, finite element (FEM) and experimental method on parallel mechanism which has four degrees of freedom including three linear motion along the x, y and z axes and a rotary motion about x axis. Finally the natural frequencies and mode shapes obtained from analytical, experimental and FEM were compared. It is worth noting that all the frequencies obtained from three methods had little differences.


[1]     Tsai, L., “Robot Analysis: The Mechanics of Serial and Parallel Manipulators”, WILEY, 1999.

[2]     Merlet, J. P., “Parallel Robots”, Kluwer academic publishers, 2001.

[3]     Wu, J., Yin, Z., “A Novel 4-DOF Parallel Manipulator H4”, Parallel Manipulators, Towards New Applications, no. April, 2008, pp. 405–448.

[4]     Altintas, Y., “Manufacturing Automation”, London, UK: Cambridge University Press, 2000.

[5]     Schmitz, T. L., Smith, K. S., “Machining Dynamics: Frequency Response to Improved Productivity”, Springer US, 2009.

[6]     Budak, E., “Analytical Models for High Performance Milling. Part I: Cutting Forces, Structural Deformations and Tolerance Integrity”, Int. J. Mach. Tools Manuf., Vol. 46, No. 12–13, 2006, pp. 1478–1488.

[7]     Budak, E., “Analytical Models for High Performance Milling. Part II: Process Dynamics and Stability”, Int. J. Mach. Tools Manuf., Vol. 46, No. 12–13, 2006, pp. 1489–1499.

[8]     Pedrammehr, S., Farrokhi, H., Rajab, A. K. S., Pakzad, S., Mahboubkhah, M., Ettefagh, M. M. and Sadeghi, M. H., “Modal Analysis of the Milling Machine Structure Through FEM and Experimental Test”, Adv. Mat. Res., Vol. 383, 2012, pp. 6717-6721.

[9]     Patwari, A. U., Faris, W. F., Nurul Amin, A. K. M., and Loh, S. K., “Dynamic Modal Analysis of Vertical Machining Centre Components”, Adv. Acoust. Vib., Vol. 2009, pp. 1–10.

[10]  Wu, Z., Xu, C., Zhang, J., Yu, D., and Feng, P., “Modal and Harmonic Response Analysis and Evaluation of Machine Tools”, Proc. - 2010 Int. Conf. Digit. Manuf. Autom. ICDMA 2010, Vol. 1, 2010, pp. 929–933.

[11]  Le Lan, J. V., Marty, A., and Debongnie, J. F., “A Stability Diagram Computation Method for Milling Adapted to Automotive Industry”, CIRP - High Perform. Cut. 2006.

[12]  Budak, E., Tunç, L. T., Alan, S., and Özgüven, H. N., “Prediction of Workpiece Dynamics and Its Effects on Chatter Stability in Milling”, CIRP Ann. - Manuf. Technol., Vol. 61, No. 1, 2012, pp. 339–342.

[13]  Mahdavinejad, R., “Finite Element Analysis of Machine and Workpiece Instability in Turning”, Int. J. Mach. Tools Manuf., Vol. 45, No. 7–8, 2005, pp. 753–760.

[14]  Doman, D. A., Warkentin, A., and Bauer, R., “Finite Element Modeling Approaches in Grinding”, Int. J. Mach. Tools Manuf., Vol. 49, No. 2, 2009, pp. 109–116.

[15]  Yuan, S. X., Wen, X. L., Zhang, Y. M., “Modal Analysis on the Truss Structures of Machine Tool”, Adv. Mater. Res., Vol. 118–120, 2010, pp. 972–976.

[16]  Sahu, S., Choudhury, B. B., and Biswal, B. B., “A Vibration Analysis of a 6 Axis Industrial Robot Using FEA”, Mater. Today Proc., Vol. 4, No. 2, 2017, pp. 2403–2410.

[17]  Zhang, X., Huang, R., Yao, S. and Dong, X., “Finite Element Analysis and Vibration Control of the Substation Charged Maintenance Robot”, 4th International Conference on Applied Robotics for the Power Industry (CARPI), China, 2016, pp. 1–4.

[18]  Flint, E., Anderson, E., “Multi-Degree of Freedom Parallel Actuation System Architectures for Motion Control”, AIAA, No.4750, 2001, pp. 1–16.

[19]  Mahboubkhah, M., Nategh, M., and Khadem, S., “A Comprehensive Study on the Free Vibration of Machine Tools’ Hexapod Table”, Int. J. Adv. Manuf. Technol., Vol. 40, No. 11–12, 2009, pp. 1239–1251.

[20]  Mahboubkhah, M., Nategh, M., and Khadem, S., “Vibration Analysis of Machine Tool’s Hexapod Table”, Int. J. Adv. Manuf. Technol., Vol. 38, No. 11–12, 2008, pp. 1236–1243.

[21]  Pedrammehr, S., Mahboubkhah, M., and Khani, N., “Natural Frequencies and Mode Shapes for Vibrations of Machine Tools’ Hexapod Table”, 1st Int. Conf. Acoust. Vib. (ISAV2011), Tehran, Iran, pp. 1–8.

[22]  Pedrammehr, S., Mahboubkhah, M., Qazani, M. R. C., Rahmani, A., and Pakzad, S., “Forced Vibration Analysis of Milling Machine’s Hexapod Table Under Machining Forces”, Stroj. Vestnik/Journal Mech. Eng., Vol. 60, No. 3, 2014, pp. 158–171.

[23]  Law, M., Ihlenfeldt, S., Wabner, M., Altintas, Y., and Neugebauer, R., “Position-Dependent Dynamics and Stability of Serial-Parallel Kinematic Machines”, CIRP Ann. - Manuf. Technol., Vol. 62, No. 1, 2013, pp. 375–378.

[24]  Sharifnia, M., Akbarzadeh, A., “Approximate Analytical Solution for Vibration of a 3-PRP Planar Parallel Robot with Flexible Moving Platform”, Robotica, Vol. 34, No. 1, 2016, pp. 71–97.

[25]  Pedrammehr, S., Danaei, B., Abdi, H., Masule, M. T. and Nahavandi, S., “Dynamic Analysis of Hexarot: Axis Symmetric Parallel Manipulator, Robotica”, 2017, pp. 1-16. doi:10.1017/S0263574717000315.

[26]  Zheng, K., Zhang, Q., “Comprehensive Analysis of the Position Error and Vibration Characteristics of Delta Robot”, Adv. Robot., Vol. 30, No. 20, 2016, pp. 1322–1340.

[27]  Chen, Z. S., Liu, M., Kong, M. X., and Ji, C., “Modal Analysis of High-Speed Parallel Manipulator with Flexible Links”, Appl. Mech. Mater., Vol. 826, 2016, pp. 8–14.

[28]  Guo, S., He, Y., Shi, L., Pan, S., and Tang, K., “Modal and Fatigue Analysis of Critical Components of an Amphibious Spherical Robot”, Microsyst. Technol., Vol. 23, 2016, pp. 2233–2247.