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Research Papers

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

[+] Author and Article Information
Jingli Du

Professor
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

Lecturer
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

Professor
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

Professor
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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Figures

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Fig. 1

Cable element using absolute nodal coordinates

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Fig. 2

Spatial discretization of a cable in CDPMs

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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. 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. 8

Midpoint vibration of cable 1 in local cable frame

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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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