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Research Papers: Design Automation

Modeling and Analysis of a Precise Multibeam Flexural Pivot

[+] Author and Article Information
Zhao Hongzhe

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: hongzhezhao@gmail.com

Han Dong

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: sy1607604@buaa.edu.cn

Bi Shusheng

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: bishusheng@gmail.com

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 28, 2016; final manuscript received April 27, 2017; published online June 15, 2017. Assoc. Editor: Nam H. Kim.

J. Mech. Des 139(8), 081402 (Jun 15, 2017) (9 pages) Paper No: MD-16-1726; doi: 10.1115/1.4036836 History: Received October 28, 2016; Revised April 27, 2017

The center shift, a common problem existing in rotating flexural pivots, is diminished in a multibeam flexural pivot by the internal interaction among these beams. The objectives of this paper are to develop a model for this flexural pivot and to analyze the interaction. First, the calculus of variations with a Lagrange multiplier is exploited to develop the model based on energy approach. Then, the properties of a conservative system are utilized to analyze the constraint characteristics of these beams, and two different load sequences are taken into account to formulate the rotating stiffness of the flexural pivot. The three methods that are used to develop the same model are compared to show their respective advantages, and the analysis of the internal constraints offers several significant qualitative and quantitative design insights. Furthermore, the circular arc motion is expanded to the elliptic arc motion, and an approximate replacement is therefore presented. Furthermore, the circular arc motion is expanded to the elliptic arc motion, and an approximate replacement is therefore presented.

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Figures

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Fig. 1

The loads and displacements of a deformed beam

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Fig. 2

Parameter definitions of a multibeam flexural pivot: (a) geometric parameters, (b) loads and displacements, and (c) the configuration with a negative λ

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Fig. 3

Deformed configuration in step 1

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Fig. 4

Deformed configuration in steps 2 and 3 (load sequence 1): (a) step 2 (beam end is NOT at the circle) and (b) step 3

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Fig. 5

Deformed configuration in steps 2 and 3 (load sequence 2): (a) step 2 (beam end is NOT at the circle) and (b) step 3

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Fig. 6

Differences between load sequences 1 and 2: (a) differences between steps 1 and 3, (b) load sequence 1, and (c) load sequence 2

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Fig. 7

Boundary constraints for step 3: (a) pinned end and (b) fixed end

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Fig. 8

Different boundary constraints in the overall flexural pivot: (a) boundary constraints and axial forces and (b) axial forces are replaced by symmetric constraints

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Fig. 9

Boundary constraint of elliptic arc motion

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Fig. 10

Two elliptic arcs are approximately replaced by two circular arcs: (a) elliptic arc 1 and (b) elliptic arc 2

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Fig. 11

FEA versus the developed model: (a) pivots 1–3 and (b) pivots 4–7

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