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Research Papers

Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model

[+] Author and Article Information
Guimin Chen

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

Ruiyu Bai

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an, Shaanxi 710071, China

1Corresponding author.

Manuscript received June 18, 2015; final manuscript received January 20, 2016; published online March 10, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(4), 041011 (Mar 10, 2016) (9 pages) Paper No: JMR-15-1148; doi: 10.1115/1.4032632 History: Received June 18, 2015; Revised January 20, 2016

Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research community of compliant mechanisms. This work presents a method called chained spatial-beam constraint model (CSBCM) for modeling large spatial deflections of flexible bisymmetric beams in compliant mechanisms. CSBCM is based on the spatial-beam constraint model (SBCM), which was developed for the purpose of accurately predicting the nonlinear constraint characteristics of bisymmetric spatial beams in their intermediate deflection range. CSBCM deals with large spatial deflections by dividing a spatial beam into several elements, modeling each element with SBCM, and then assembling the deflected elements using the transformation defined by Tait–Bryan angles to form the whole deflection. It is demonstrated that CSBCM is capable of solving various large spatial deflection problems either the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict large spatial deflections of flexible beams, as compared to the available nonlinear finite element analysis (FEA) results obtained by ansys. The results also demonstrated the unique capabilities of CSBCM to solve large spatial deflection problems that are outside the range of ansys.

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Figures

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Fig. 1

Three-dimensional deflection of a spatial cantilever beam subject to combined force and moment loads at its free end (the sign convention for forces and moments follows the right-hand rule)

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Fig. 2

Discretization of the spatial beam and the coordinates of the nodes with respect to the fixed coordinate frame

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Fig. 3

Tait–Bryan angles for ith SBCM element (the sign convention for the angles follows the right-hand rule)

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Fig. 7

Deflected configurations for the beam subject to combined loads

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Fig. 6

Deflected configurations for the beam subject to combined loads

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Fig. 5

The deflected configurations of the beam subject to pure end moments

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Fig. 4

The deflected configurations of the beam subject to pure end forces

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Fig. 8

Circular-guided spatial compliant mechanism

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Fig. 10

Deflected configurations of the beam at different crank angles

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Fig. 11

Driving torque Tin versus crank angle ϕ

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