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Research Papers

Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model Concept

[+] Author and Article Information
Ashok Midha

Professor of Mechanical Engineering,
Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409-0050
e-mail: midha@mst.edu

Sushrut G. Bapat

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409-0050
e-mail: sgb8cc@mst.edu

Adarsh Mavanthoor

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409-0050
e-mail: ad.mavanthoor@yahoo.com

Vivekananda Chinta

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409-0050
e-mail: vc6gc@mst.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 30, 2013; final manuscript received July 21, 2014; published online December 4, 2014. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 7(3), 031007 (Aug 01, 2015) (10 pages) Paper No: JMR-13-1173; doi: 10.1115/1.4028131 History: Received August 30, 2013; Revised July 21, 2014; Online December 04, 2014

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of parametric, static equilibrium and compatibility equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end displacement boundary conditions, depending on the locations and types of the effecting loads on the beam to meet these boundary conditions. A unique solution may exist when a third beam end displacement boundary condition is specified; however, this selection is not unconditional. A concept of characteristic deflection domain is proposed to assist with the selection of the third boundary condition to yield a realistic solution. The analysis method is also used to synthesize a simple, fully compliant mechanism utilizing the fixed-guided compliant segments.

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References

Figures

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Fig. 3

Deformed state of fixed-guided compliant beam (a) with positive beam end angle, and (b) considered as two compliant segments: (c) segment 1, (d) segment 2; (e) PRBM of segment 1, and (f) PRBM of segment 2

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Fig. 2

(a) Fixed-free compliant beam in its deformed position and (b) PRBM of the fixed-free beam superimposed on the deformed state

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Fig. 1

Fixed-guided compliant beam with end forces and opposing moment in its (a) deformed position with positive slope at beam end point, and (b) deformed position with negative slope at beam end point

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Fig. 4

Displacement plots for effecting load combinations for a fixed-guided compliant beam

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Fig. 6

Vector-loop diagram for PRBM in Fig. 5

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Fig. 8

Flowchart for determining deflection domain

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Fig. 9

Deflection domain plots for various beam end angles

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Fig. 10

(a) Configuration used for a compliant microrestraining mechanism, (b) mechanism configuration and coordinates for synthesis, and (c) a computer aided design (CAD) rendering of the design

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Fig. 7

Flowchart for estimating feasible values of L1

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Fig. 5

A fixed-guided compliant beam with positive end slope in its deformed state

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Fig. 11

Graphical beam displacement comparisons among the methods for Ex. 1 of Table 3

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