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Research Papers

Dynamics Analysis of Parallel Mechanism With Flexible Moving Platform Based on Floating Frame of Reference Formulation

[+] Author and Article Information
Gengxiang Wang

Faculty of Mechanical and Precision Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373, No. 5 South Jinhua Road,
Xi'an, Shaanxi 710048, China
e-mail: wanggengxiang@xaut.edu.cn

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 18, 2018; final manuscript received February 20, 2019; published online May 17, 2019. Assoc. Editor: Clement Gosselin.

J. Mechanisms Robotics 11(4), 041002 (May 17, 2019) (11 pages) Paper No: JMR-18-1228; doi: 10.1115/1.4043045 History: Received July 18, 2018; Accepted February 28, 2019

The dynamics model of 4-SPS/PS parallel mechanism with a flexible moving platform is formulated based on the equation of motion. Firstly, the dynamics model of flexible moving platform is formulated based on the floating frame of reference formulation. In order to avoid the wrong solutions caused by an inappropriate set of reference conditions, the fixed-fixed reference conditions are carefully selected according to the structure of parallel mechanism. Secondly, considering that the original Craig–Bampton (CB) method only represents the free-free modes. In order to use CB method to obtain fixed-fixed modes, the original CB method is improved by imposing the reference conditions prior to obtaining the static correction modes and fixed interface modes. In addition, the dynamics analysis of 4-SPS/PS parallel mechanism with flexible moving platform based on both free-free modes and fixed-fixed modes are implemented, respectively. Finally, the simulations show that the dynamic responses obtained using fixed-fixed modes are close to the ideal dynamic response, which proves the correctness of improved CB method. Moreover, the maximum percentage error of simulation results between using free-free modes and using fixed-fixed modes exceeds 100%, it is clear that the solutions based on free-free modes are not reasonable. Eventually, the conclusions prove that the deformation caused by high-speed and heavy-load should not be neglected in the parallel mechanism.

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Figures

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Fig. 1

Structure of 4-SPS/PS parallel mechanism

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Fig. 2

Geometry of the thin plate element

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Fig. 3

12 DOF quadrilateral thin plate element

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Fig. 4

Mode shape and associated frequencies corresponding to free-free modes

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Fig. 5

Mode shape and associated frequencies corresponding to fixed-fixed modes

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Fig. 6

Trajectory of moving platform around y0-axis

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Fig. 7

Computational strategy for the dynamics model of 4-SPS/PS parallel mechanism with flexible moving platform

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Fig. 8

Dynamic performance of parallel mechanism with flexible moving platform using free-free modes (■ 16 modes; ● 17 modes; ▲ 18 modes; ► 20 modes; ◄ ideal).

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Fig. 9

Stress components of nodal 13 on the flexible moving platform based on free-free modes: (a) (■ 16 modes; ● 17 modes; ▲ 18 modes; ► 20 modes); (b) (■ 15 modes; ● 16 modes; ▲ 18 modes; ► 20 modes)

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Fig. 10

Dynamic performance of parallel mechanism with flexible moving platform using fixed-fixed modes: (a)–(c) (▲ 6 modes; ▼ 9 modes; ● 10 modes; ► 20 modes; ◄ ideal); (d) (■ 11 modes; ● 12 modes; ▲ 13 modes; ► 20 modes; ◄ ideal)

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Fig. 11

Stress components of nodal 13 on the flexible moving platform based on fixed-fixed modes: (a) (▲ 6 modes; ▼ 9 modes; ◆ 10 modes; ► 20 modes); (b) (■ 11 modes; ● 12 modes; ▲ 13 modes; ► 20 modes)

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