Research Papers

Dynamic Analysis of Cable-Driven Parallel Manipulators Using a Variable Length Finite Element

[+] Author and Article Information
Jingli Du

Key Laboratory of Electronic Equipment
Structure Design of Ministry of Education,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: jldu@mail.xidian.edu.cn

Chuanzhen Cui

Key Laboratory of Electronic Equipment
Structure Design of Ministry of Education,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: czcui@mail.xidian.edu.cn

Hong Bao

Key Laboratory of Electronic Equipment
Structure Design of Ministry of Education,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: bh-029@163.com

Yuanying Qiu

Key Laboratory of Electronic Equipment
Structure Design of Ministry of Education,
Xidian University,
Xi'an, Shaanxi 710071, China
e-mail: yyqiu@mail.xidian.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 3, 2013; final manuscript received January 17, 2014; published online September 12, 2014. Assoc. Editor: José L. Escalona.

J. Comput. Nonlinear Dynam 10(1), 011013 (Sep 12, 2014) (7 pages) Paper No: CND-13-1187; doi: 10.1115/1.4026570 History: Received July 03, 2013; Revised January 17, 2014

Cable-driven parallel manipulator (CDPM) is a good solution to achieving large workspace. However, unavoidable vibrations of long cables can dramatically degrade the positioning performance in large workspace applications. Most work so far on cable-driven parallel manipulators (CDPMs) simply neglected the dynamics of the cables themselves. In this paper dynamic modeling of large CDPMs is addressed using a variable domain finite element method (FEM). A cable element with variable length is derived using the absolute nodal coordinate formulation to facilitate motion analysis of CDPMs. The effects of cable length variation and the resulting mass variation are also considered. Based on this element dynamics model of CDPMs can be readily obtained using the standard assembling operation in the FEM. Numerical results showed that the effect of the derivatives of cable length variation and that of the mass variation are trivial.

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Bostelman, R., Shackleford, W., Proctor, F., Albus, J., and Lytle, A., 2002, “The Flying Carpet: A Tool to Improve Ship Repair Efficiency,” Proceedings of the American Society of Naval Engineers Symposium on Manufacturing Technology for Ship Construction and Repair, pp. 1–9.
Du, J. L., Bao, H., Cui, C. Z., and Yang, D. W., 2012, “Dynamic Analysis of Cable-Driven Parallel Manipulators With Time-Varying Cable Lengths,” Finite Elem. Anal. Design, 48(1), pp. 1392–1399. [CrossRef]
Meunier, G., Boulet, B., and Nahon, M., 2009, “Control of an Overactuated Cable-Driven Parallel Mechanism for a Radio Telescope Application,” IEEE T. Contr. Syst. T., 17(5), pp. 1043–1054. [CrossRef]
Oh, S. R., and Agrawal, S. K., 2005, “A Reference Governor Based Controller for a Cable Robot Under Input Constraints,” IEEE T. Contr. Syst. T., 13(4), pp. 639–645. [CrossRef]
Hassan, M., and Khajepour, A., 2011, “Analysis of Bounded Cable Tensions in Cable-Actuated Parallel Manipulators,” IEEE T. Robot., 27(5), pp. 891–900. [CrossRef]
Tabarrok, B., Leech, C. M., and Kim, Y. I., 1974, “On the Dynamics of an Axially Moving Beam,” J. Franklin Inst., 297(3), pp. 201–220. [CrossRef]
Wickert, J. A., and Mote, C. D., Jr., 1989, “On the Energetics of Axially Moving Continua,” J. Acoust. Soc. Am., 85(3), pp. 1365–1368. [CrossRef]
Lee, S. Y. and Mote, C. D., Jr., 1997, “A Generalized Treatment of the Energetics of Translating Continua, Part I: Strings and Second Order Tensioned Pipes,” J. Sound Vib., 204(5), pp. 717–734. [CrossRef]
Mankala, K. K., and AgrawalS. K., 2005, “Dynamic Modeling and Simulation of Satellite Tethered Systems,” ASME J. Vib. Acoust., 127(2), pp. 144–156. [CrossRef]
Zhu, W. D., and Chen, Y., 2006, “Theoretical and Experimental Investigation of Elevator Cable Dynamics and Control,” ASME J. Vib. Acoust., 128(1), pp. 66–78. [CrossRef]
Wang, P. H., Fung, R. F., and Lee, M. J., 1998, “Finite Element Analysis of a Three-Dimensional Underwater Cable With Time-Dependent Length,” J. Sound Vib., 209(2), pp. 223–249. [CrossRef]
Stylianou, M., and Tabarrok, B., 1994, “Finite Element Analysis of an Axially Moving Beam, Part I: Time Integration,” J. Sound Vib., 178(4), pp. 433–453. [CrossRef]
Chang, J. R., Lin, W. J., Huang, C. J., and Choi, S. T., 2010, “Vibration and Stability of an Axially Moving Rayleigh Beam,” Appl. Math. Model., 34(6), pp. 1482–1497. [CrossRef]
Moustafa, K. A. F., Gad, E. H., El-Moneer, A. M. A., and Ismail, M. I. S., 2005, “Modelling and Control of Overhead Cranes With Flexible Variable-Length Cable by Finite Element Method,” T. I. Meas. Control, 27(1), pp. 1–20. [CrossRef]
Fung, R. F., Lu, L. Y., and Huang, S. C., 2002, “Dynamic Modelling and Vibration Analysis of a Flexible Cable-Stayed Beam Structure,” J. Sound Vib., 254(4), pp. 717–726. [CrossRef]
Hong, D., and Ren, G., 2011, “A Modeling of Sliding Joint on One-Dimensional Flexible Medium,” Multibody Syst. Dyn., 26(1), pp. 91–106. [CrossRef]
Escalona, J. L., 2012, “Modeling Hoisting Machines With the Arbitrary Lagrangian-Eulerian Absolute Nodal Coordinate Formulation,” The 2nd Joint International Conference on Multibody System Dynamics, pp. 281–282.
Dmitrochenko, O., 2008, “Finite Elements Using Absolute Nodal Coordinates for Large-Deformation Flexible Multibody Dynamics,” J. Comput. Appl. Math., 215(2), pp. 368–377. [CrossRef]
McIver, D. B., 1973, “Hamilton's Principle for Systems of Changing Mass,” J. Eng. Math., 7(3), pp. 249–261. [CrossRef]
Humer, A., 2013, “Dynamic Modeling of Beams With Non-Material, Deformation-Dependent Boundary Conditions,” J. Sound Vib., 332(3,4), pp. 622–641. [CrossRef]


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Fig. 1

Cable element using absolute nodal coordinates

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Fig. 3

A typical CDPM for large workspace application

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Fig. 4

Cable length variation for the trajectory

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Fig. 5

Cable tension variation for the trajectory

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Fig. 2

Spatial discretization of a cable in CDPMs

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Fig. 8

Midpoint vibration of cable 1 in local cable frame

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Fig. 6

Vibration of the end-effector with different element numbers

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Fig. 7

Spectrum of the divergence

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Fig. 9

Vibration of the end-effector with different elastic modulus of cables

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Fig. 10

Elastic force of cable 1 at end-effector end

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Fig. 11

The negligible force components of cable 1

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Fig. 12

End tensions of cable 1



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