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Research Papers

Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms

[+] Author and Article Information
Dana E. Vogtmann

Graduate Research Assistant

Satyandra K. Gupta

Professor
Fellow ASME

Sarah Bergbreiter

Assistant Professor
Mem. ASME
e-mail: sarahb@umd.edu
Department of Mechanical Engineering,
Institute for Systems Research,
University of Maryland,
College Park, MD 20742

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 7, 2012; final manuscript received August 6, 2013; published online October 10, 2013. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 5(4), 041017 (Oct 10, 2013) (12 pages) Paper No: JMR-12-1203; doi: 10.1115/1.4025298 History: Received December 07, 2012; Revised August 06, 2013

Accurate analysis models are critical for effectively utilizing elastomeric joints in miniature compliant mechanisms. This paper presents work toward the characterization and modeling of miniature elastomeric hinges. Characterization was carried out in the form of several experimental bending tests and tension tests on representative hinges in five different configurations. The modeling portion is achieved using a planar pseudo rigid body (PRB) analytical model for these hinges. A simplified planar 3-spring PRB analytical model was developed, consisting of a torsional spring, an axial spring, and another torsional spring in series. These analytical models enable the efficient exploration of large design spaces. The analytical model has been verified to within an accuracy of 3% error in pure bending, and 7% in pure tension, when compared to finite element analysis (FEA) models. Using this analytical model, a complete mechanism—a robotic leg consisting of four rigid links and four compliant hinges—has been analyzed and compared to a corresponding FEA model and a fabricated mechanism.

Copyright © 2013 by ASME
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References

Figures

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Fig. 1

A hexapedal robot fabricated using the LaCER process

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Fig. 2

Detail of the leg mechanism used in the hexapedal robot

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Fig. 3

Example LaCER process sequence for a simple two-link mechanism with a single compliant joint. The rigid material is represented in gray, while the compliant material is represented in yellow with black hatching.

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Fig. 4

Schematic and photograph of five different hinge geometries. Geometry type 1 is 180 deg, type 2 is 90 deg with a rounded hinge shape, type 3 is 90 deg with a trapezoidal hinge shape, type 4 is 135 deg with a rounded hinge shape, and type 5 is 135 deg with a trapezoidal hinge shape.

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Fig. 5

Bending test setup

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Fig. 6

Test setup mechanism schematic

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Fig. 7

Free body diagram of test setup lever arm

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Fig. 8

A comparison of experimental and FEA results under pure bending load for geometries 1, 2, and 4 (left), and geometries 3 and 5 (right)

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Fig. 9

A comparison of experimental and FEA results under pure tension load

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Fig. 10

One type of observed hinge behavior that cannot be modeled using the single spring pseudo-rigid body model. This behavior can be captured by the 3-spring PRB model with a bend in each torsion spring and (optionally) a stretch in the axial spring.

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Fig. 11

Configuration of a three spring pseudo-rigid body model

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Fig. 12

A schematic of the front face of a trapezoidal hinge, with the centerline and effective lengths shown, as well as θtrap

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Fig. 13

Comparison of the effective length of a rectangular compliant hinge to a trapezoidal hinge with angle θtrap

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Fig. 14

A schematic of a hinge with adhesion geometry extending into the rigid links a distance lg. This adhesion geometry affects the stiffness of the hinge in tension.

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Fig. 15

Correction factors for kl3spr for a 1 mm long hinge over a range of 0–0.6 mm adhesion geometry. These values were taken over a strain range of 20–30%.

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Fig. 16

A comparison of FEA and 3-spring PRB results under pure bending load for geometries 1, 2, and 4 (left), and geometries 3 and 5 (right). The 1-spring PRB results are similar to the 3-spring model.

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Fig. 17

A comparison of FEA and 3-spring PRB results under a pure tension load

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Fig. 18

Forces as applied to the ten different PRB models with different spring counts

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Fig. 19

The inner angle results for FEA simulations and ten different PRB models with different numbers of springs. Angles were taken for a load of 20 mN applied in (a) pure bending, (b) pure tension, and (c) bending/tension, and at a load of 14 mN for (d) bending/compressive.

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Fig. 20

Leg geometry and parameters

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Fig. 21

The leg modeled in MSC Adams, and the two different loading conditions

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Fig. 22

The x and y positions of the robot foot, relative to the initial position, under three different ground reaction force loadings

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Fig. 23

The x and y positions of the robot foot, relative to the initial position, over a full crank rotation

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Fig. 24

The x and y positions of the robot foot, relative to the initial position, under three different ground reaction force loadings

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Fig. 25

The x and y positions of the robot foot, relative to the initial position, over a full crank rotation

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