Longitudinal and Lateral Vibration Analysis of Cables in a Cable Robot Using Finite Element Method

Document Type: Original Article


1 H. Tourajizadeh, Assistant Professor, Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran *Corresponding author

2 Department of Mechanical Engineering, Iran University of Science and Technology, Iran


In this paper, vibrational response of a variable-length cable in longitudinal, lateral and torsional directions is analysed in a cable robot using FE method. The flexibility of cables has remarkable effect on positioning of the end-effector in cable robots. Also considering the fact that the length of the cables are time dependent in a dynamic cable structure like robocrane, the numerical approaches are preferable compared to analytic solutions. To do so, the cable is divided into finite elements in which the virtual work equation and Galerkin method can be implemented for the equations. Considering the stiffness matrix, the characteristic equations and Eigen values of each element can be defined. A simulation study is done in the ANSIS on a planar robocrane with 2-DOF and also for a spatial case with 6-DOF that is controlled by the aid of six variable-length flexible cables in the space for two different types of solid and flexible end-effectors. Whole the cable robot flexibility is analyzed simultaneously instead of separation calculation of each cable. Not only all of the 3-D vibrating behaviour of the whole structure is studied in this paper but also the lengths of the cables are considered as variable. The vibrating response of mode shapes, amplitude and frequencies are extracted and analysed, and the results are compared for two case of solid and flexible end-effector which shows the effect of the flexibility in the position of the end-effector and the tension of the cables in different situations.


[1] Zhang, X., Mills, J. K., and Cleghorn, W. L., “Coupling Characteristics of Rigid Body Motion and Elastic Deformation of a 3-PRR Parallel Manipulator with Flexible Links”, Multibody System Dynamics, Vol. 21, No. 2, 2009, pp. 167-192.

[2] Caracciolo, R., Richiedei, D. and Trevisani, A., “Experimental Validation of a Model-Based Robust Controller for Multi-Body Mechanisms with Flexible Links”, Multibody System Dynamics, Vol. 20, 2008, pp. 129–145.

 [3] Diao, X. and Ma, O., “Vibration Analysis of Cable-Driven Parallel Manipulators”, Multibody System Dynamics, Vol. 21, No. 4, 2009, pp. 347-360.

[4] Oh, S.R., Mankala, K.K., Agrawal, S.K. and Albus, J.S., “Dynamic Modeling and Robust Controller Design of a Two-Stage Parallel Cable Robot”, Multibody System Dynamics, Vol. 13, No. 4, 2005, pp. 385–399.

[5] Heyden, T. and Woernle, Ch., “Dynamics and Flatness-Based Control of a Kinematically Undetermined Cable Suspension Manipulator”, Multibody System Dynamics, Vol. 16, No. 2, 2006, pp. 155-177.

[6] Kamman, J. W. and Huston, R. L., “Multibody Dynamics Modeling of Variable Length Cable Systems”, Multibody System Dynamics, Vol. 5, No. 3, 2001, pp. 211-21.

[7] Yanai, N., Yamamoto, M. and Mohri, A., “Feedback Control for Wire-Suspended Mechanism with Exact Linearization”, Intelligent Robots and System, IEEE/RSJ International Conference, 3, 2002, pp. 2213-2218.

[8] Fang, Sh., Franitza, D., Torlo, M., Bekes, F., and Hiller, M., “Motion Control of a Tendon-Based Parallel Manipulator Using Optimal Tension Distribution”, IEEE/ASME, Transaction on Mechatronics, Vol. 9, No. 3, 2004, pp. 561 – 568.

[9] Pappas, G. J., Lygeros, J. and Godbole, D. N.,  “Stabilization and Tracking of Feedback Linearization Systems under Input Constarints”, Intelligent Machines and Robotic Laboratory Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley CA-94720.

[10] Oh, S. R. and Agrawal, S. K., “Cable-Suspended Planar Parallel Robots with Redundant Cables, Controllers with Positive Cable Tensions”, Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE-19716, U.S.A, 2005.

[11] Hashemi, S. M. and Roach, A., “A Dynamic Finite Element for Vibration Analysis of a Cable and Wire Rope”, Asian Journal of Civil Engineering, Vol. 7, No. 5, 2006, pp. 487-500.

[12] Wang, P. H., Fung, R. F. and Lee, M. J., “Finite Element Analysis of a Three Dimensional Underwater Cable with Time Dependent Length”, Journal of Sound and Vibration, Vol. 209, No. 2, pp. 223-249, 1998.

[13] Georgakis, C. T. and Taylor, C.A., “Nonlinear Dynamics of Cable Stays”, Department of Civil Engineering, Earthquake Engineering Research Center, University of Bristol, UK, Journal of Sound and Vibration, No. 281, 2005, pp. 537–564.

[14] Fung, R. F., Lul, Y. and Huang, S. C., “Dynamic Modeling and Vibration Analysis of a Flexible Cable-Stayed Beam Structure”, Journal of Sound and Vibration,Vol. 254, No. 4, 2002, pp. 717–726.

[15] Williams, R. L. and Gallina, P., Rossi A., “Planar Cable Direct Driven Robots; Part 1, Kinematics and Statics”, ASME Design Technical Conferences, 2001.

[16] Williams, R. L., Gallina, P. and Rossi A., “Planar Cable Direct Driven Robots; Part 2, Dynamics and control”, ASME Design Technical Conferences, 2001.

[17] Alp, A. B. and Agrawal, S. K., “Cable Suspended Robots, Design, Planning and Control”, Department of Mechanical Engineering, University of Delaware, Newark, DE- 19716,USA, 2001.

[18] Samaras, R.K., Skop, R.A. and Milburn, D.A., “An Analysis of Coupled Extensional-Torsional Oscillations in Wire-Rope”, Transaction of the ASME, Journal of Engineering for Industry; Vol. 96, No. 4, 1974, pp. 1130-1135.

[19] Zhang Y., Agrawal S.K. and Piovoso M.J., “Coupled Dynamics of Flexible Cables and Rigid End-Effector For a Cable Suspended Robot”, American Control Conference, Vol. 14, No. 16, 2006.