Research Papers

A Pseudo-Static Model for Dynamic Analysis on Frequency Domain of Distributed Compliant Mechanisms

[+] Author and Article Information
Mingxiang Ling

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China;
Institute of Systems Engineering,
China Academy of Engineering Physics,
No.28, Mianshan road,
Mianyang 621999, China
e-mail: ling_mx@163.com

Larry L. Howell

Department of Mechanical Engineering,
Brigham Young University,
435S CTB,
Provo, UT 84602
e-mail: lhowell@byu.edu

Junyi Cao

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
No.64, Xianning road,
Xi'an 710049, China
e-mail: caojy@mail.xjtu.edu.cn

Zhou Jiang

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
No.64, Xianning road,
Xi'an 710049, China
e-mail: jiangzhou_xy@163.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received January 12, 2018; final manuscript received June 22, 2018; published online July 18, 2018. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 10(5), 051011 (Jul 18, 2018) (10 pages) Paper No: JMR-18-1010; doi: 10.1115/1.4040700 History: Received January 12, 2018; Revised June 22, 2018

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

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Fig. 1

Comparison of three kinds of compliance/stiffness matrices of the flexure hinge or the flexible beam

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Fig. 2

Nodal displacement and nodal force of the flexible beam

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Fig. 3

Procedure of the pseudo-static modeling method

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Fig. 4

Pseudo-static modeling of an XY monolithic precision positioning stage: (a) schematic of the example And (b) numbering of subelements

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Fig. 5

Results of the displacement amplification ratio with different methods

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Fig. 6

Results of the input stiffness with different methods

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Fig. 7

Influence of the thickness of the input ports on the static performance

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Fig. 8

The first six vibration modes calculated by FEM

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Fig. 9

Comparison of the forced dynamic response



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