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Research Papers

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

[+] Author and Article Information
Quentin T. Aten, Shannon A. Zirbel, Brian D. Jensen

Department of Mechanical Engineering,  Brigham Young University, Provo, UT 84602

Larry L. Howell1

Department of Mechanical Engineering,  Brigham Young University, Provo, UT 84602lhowell@byu.edu

1

Corresponding author.

J. Mech. Des 133(6), 061009 (Jun 21, 2011) (9 pages) doi:10.1115/1.4004016 History: Received January 26, 2011; Revised March 28, 2011; Published June 21, 2011; Online June 21, 2011

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) An example underactuated single degree of freedom mechanism, and (b) its pseudorigid-body model

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Figure 2

An example underactuated 2-DOF compliant mechanism. The length of r2 is specified, leaving 1 DOF unspecified.

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Figure 3

Comparison of virtual work analysis and MinPE analysis of a 2-DOF triple-slider mechanism shown in Fig. 2. Both models were given a single input of r2 and solved for θ3, r3, r1, and Fin.

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Figure 4

Schematic representation of a LET joint showing critical dimensions, the intended torsional and bending deflections about the X axis and the parasitic extension or compression in the Y direction

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Figure 5

A 1-DOF pseudorigid-body model of the LET joint modeling only rotation about a single axis

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Figure 6

A 5-DOF pseudorigid-body model of the LET joint, which models three rotations and two translations

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Figure 7

Dimensioned schematic of the fully compliant, lamina-emergent constant-force mechanism

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Figure 8

A polypropylene constant-force lamina-emergent mechanism in its as-fabricated and deflected positions

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Figure 9

A 1-DOF pseudorigid-body crank-slider model of the lamina-emergent constant-force mechanism shown in Fig. 7 based on the 1-DOF model of the LET joint shown in Fig. 5

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Figure 10

(a) Comparison of the force-displacement results from the 1-DOF PRBM, 13-DOF PRBM, FEA, and experimental data from the constant-force mechanism. (b) Absolute error of the 1-DOF PRBM and 13-DOF PRBM as compared to the FEA results.

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Figure 11

(a) Comparison of the angle of the constant-force mechanism’s rigid link Ra predicted by the 1-DOF PRBM, 13-DOF PRBM, and FEA. (b) Absolute error of the 1-DOF PRBM and 13-DOF PRBM as compared to the FEA results.

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Figure 12

A 13-DOF pseudorigid-body model based on the 5-DOF model of the LET joint shown in Fig. 6

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Figure 13

Labeled photograph of the constant-force lamina-emergent mechanism undergoing testing in a custom-built force-displacement measurement system

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