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Research Papers

Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam Constraint Model

[+] Author and Article Information
Guimin Chen

State Key Laboratory for
Manufacturing Systems Engineering,
Shaanxi Key Lab of Intelligent Robots,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi, China
e-mail: guimin.chen@gmail.com

Fulei Ma

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an 710071, Shaanxi, China
e-mail: fuleima@gmail.com

Guangbo Hao

School of Engineering,
University College Cork,
Cork, Ireland
e-mail: g.hao@ucc.ie

Weidong Zhu

Department of Mechanical Engineering,
University of Maryland,
Baltimore County, Baltimore, MD 21250
e-mail: wzhu@umbc.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 24, 2018; final manuscript received September 22, 2018; published online November 12, 2018. Assoc. Editor: James J. Joo.

J. Mechanisms Robotics 11(1), 011002 (Nov 12, 2018) (10 pages) Paper No: JMR-18-1078; doi: 10.1115/1.4041585 History: Received March 24, 2018; Revised September 22, 2018

Understanding and analyzing large and nonlinear deflections are the major challenges of designing compliant mechanisms. Initially, curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross section, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM), which is termed as the chained BCM (CBCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

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Figures

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Fig. 1

An initially curved beam subject to combined force and moment loads at its free end

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Fig. 2

Discretization of a circular-arc beam at its undeflected position

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Fig. 3

The ith element at its deflection position

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Fig. 4

Deflections of a quarter circle

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Fig. 5

Convergence analysis results

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Fig. 6

Deflection of a half circle

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Fig. 7

Buckling-arc follower in long dwell mechanism

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Fig. 8

The force-deflection curve of the buckling-arc follower

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Fig. 9

Bistable mechanism employing initially curved beams

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Fig. 10

The force-deflection curve of the bistable mechanism

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Fig. 11

Circular-path guided compliant mechanism employing an parabolic-shape beam

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Fig. 12

Deflected configurations of the parabolic-shape beam

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Fig. 13

The input moment Mr versus the crank angle ϕ

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Fig. 14

Diagram of flexural pivot with two parabola beams

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Fig. 15

Kinetostatic behaviors of the flexural pivot

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Fig. 16

Deflected configurations of the flexural pivot for different moments

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