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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.

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References

Wood, R. J., Avadhanula, S., Sahai, R., Steltz, E., and Fearing, R. S., 2008, “Microrobot Design Using Fiber Reinforced Composites,” J. Mech. Des., 130(5), p. 052304. [CrossRef]
Weiss, L., Merz, R., Prinz, F., Neplotnik, G., Padmanabhan, P., Schultz, L., and Ramaswami, K., 1997, “Shape Deposition Manufacturing of Heterogeneous Structures,” J. Manuf. Syst., 16(4), pp. 239–248. [CrossRef]
Bejgerowski, W., Gerdes, J. W., Gupta, S. K., and Bruck, H. A., 2011, “Design and Fabrication of Miniature Compliant Hinges for Multi-Material Compliant Mechanisms,” Int. J. Adv. Manuf. Technol., 57(5–8), pp. 437–452. [CrossRef]
Vogtmann, D. E., Gupta, S. K., and Bergbreiter, S., 2011, “Multi-Material Compliant Mechanisms for Mobile Millirobots,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp. 3169–3174.
Hoover, A., Steltz, E., and Fearing, R., 2008, “RoACH: An Autonomous 2.4 g Crawling Hexapod Robot,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 26–33.
Birkmeyer, P., Peterson, K., and Fearing, R. S., 2009, “DASH: A Dynamic 16 g Hexapedal Robot,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2683–2689.
Kim, S., Clark, J. E., and Cutkosky, M. R., 2006, “iSprawl: Design and Tuning for High-Speed Autonomous Open-Loop Running,” Int. J. Robot. Res., 25(9), pp. 903–912. [CrossRef]
Noh, M., Kim, S.-W., An, S., Koh, J.-S., and Cho, K.-J., 2012, “Flea-Inspired Catapult Mechanism for Miniature Jumping Robots,” IEEE Trans. Rob. Autom., 28(5), pp. 1007–1018. [CrossRef]
Hines, L., Arabagi, V., and Sitti, M., 2012, “Shape Memory Polymer-Based Flexure Stiffness Control in a Miniature Flapping-Wing Robot,” IEEE Trans. Rob. Autom., 28(4), pp. 987–990. [CrossRef]
Vogtmann, D. E., Gupta, S. K., and Bergbreiter, S., 2011, “A Systematic Approach to Designing Multi-Material Miniature Compliant Mechanisms,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE), pp. 211–221.
Frecker, M. I., Powell, K. M., and Haluck, R., 2005, “Design of a Multifunctional Compliant Instrument for Minimally Invasive Surgery,” ASME J. Biomech. Eng., 127(6), pp. 990–993. [CrossRef]
Puangmali, P., Liu, H., Seneviratne, L. D., Dasgupta, P., and Althoefer, K., 2012, “Miniature 3-Axis Distal Force Sensor for Minimally Invasive Surgical Palpation,” IEEE/ASME Trans. Mechatron., 17(4), pp. 646–656. [CrossRef]
Bachta, W., Renaud, P., Laroche, E., and Gangloff, J., 2011, “The Cardiolock Project: Design of an Active Stabilizer for Cardiac Surgery,” ASME J. Mech. Des., 133(7), p. 071002. [CrossRef]
Awtar, S., Trutna, T. T., Nielsen, J. M., Abani, R., and Geiger, J., 2010, “FlexDex: A Minimally Invasive Surgical Tool With Enhanced Dexterity and Intuitive Control,” ASME J. Med. Devices, 4(3), p. 035003. [CrossRef]
Solano, B., Gallant, A., Greggains, G. D., Wood, D., and Herbert, M., 2008, “Low Voltage Microgripper for Single Cell Manipulation,” Adv. Sci. Technol., 57, pp. 67–72. [CrossRef]
Yu, J., Bi, S., Zong, G., Dai, J., and Liu, X.-J., 2006, “Mobility Characteristics of a Flexure-Based Compliant Manipulator With Three Legs,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1076–1081.
Yong, Y. K., Aphale, S., and Reza Moheimani, S., 2009, “Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning,” IEEE Trans. Nanotechnol., 8(1), pp. 46–54. [CrossRef]
Li, Y., and Xu, Q., 2009, “Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator,” IEEE Trans. Rob. Autom., 25(3), pp. 645–657. [CrossRef]
Mohd Zubir, M. N., and Shirinzadeh, B., 2009, “Development of a High Precision Flexure-Based Microgripper,” Precis. Eng., 33(4), pp. 362–370. [CrossRef]
Jensen, K. A., Lusk, C. P., and Howell, L. L., 2006, “An XYZ Micromanipulator With Three Translational Degrees of Freedom,” Robotica, 24(3), pp. 305–314. [CrossRef]
Todd, B., Jensen, B. D., Schultz, S. M., and Hawkins, A. R., 2010, “Design and Testing of a Thin-Flexure Bistable Mechanism Suitable for Stamping From Metal Sheets,” ASME J. Mech. Des, 132(7), p. 071011. [CrossRef]
Su, H.-J., and McCarthy, J. M., 2007, “Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy,” ASME J. Mech. Des., 129(10), pp. 1094–1098. [CrossRef]
Chen, G., Gou, Y., and Zhang, A., 2011, “Synthesis of Compliant Multistable Mechanisms Through Use of a Single Bistable Mechanism,” ASME J. Mech. Des., 133(8), p. 081007. [CrossRef]
Mavanthoor, A., and Midha, A., 2006, “Bistable Compliant Four-Bar Mechanisms With a Single Torsional Spring,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE), Vol. 2006, pp. 151–157.
Park, H. S., and Sitti, M., 2009, “Compliant Footpad Design Analysis for a Bio-Inspired Quadruped Amphibious Robot,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 645–651.
Asbeck, A. T., and Cutkosky, M. R., 2012, “Designing Compliant Spine Mechanisms for Climbing,” ASME J. Mech. Rob., 4(3), p. 031007. [CrossRef]
Berselli, G., Vertechy, R., Vassura, G., and Parenti-Castelli, V., 2011, “Optimal Synthesis of Conically Shaped Dielectric Elastomer Linear Actuators: Design Methodology and Experimental Validation,” IEEE/ASME Trans. Mechatron., 16(1), pp. 67–79. [CrossRef]
Plante, J.-S., and Dubowsky, S., 2007, “On the Performance Mechanisms of Dielectric Elastomer Actuators,” Sens. Actuators, A, 137(1), pp. 96–109. [CrossRef]
Cappelleri, D. J., Krishnan, G., Kim, C., Kumar, V., and Kota, S., 2010, “Toward the Design of a Decoupled, Two-Dimensional, Vision-Based μN Force Sensor,” ASME J. Mech. Rob., 2(2), p. 021010. [CrossRef]
Zhao, K., Schmiedeler, J. P., and Murray, A. P., 2012, “Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE ).
Hoetmer, K., Woo, G., Kim, C., and Herder, J., 2010, “Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing,” ASME J. Mech. Rob., 2(4), p. 041007. [CrossRef]
Howell, L., 2001, Compliant Mechanisms, Wiley, New York.
Su, H.-J., 2009, “A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads,” ASME J. Mech. Rob., 1(2), p. 021008. [CrossRef]
Howell, L. L., DiBiasio, C. M., Cullinan, M. A., Panas, R. M., and Culpepper, M. L., 2010, “A Pseudo-Rigid-Body Model for Large Deflections of Fixed-Clamped Carbon Nanotubes,” ASME J. Mech. Rob., 2(3), p. 034501. [CrossRef]
Chen, G., Wilcox, D. L., and Howell, L. L., 2009, “Fully Compliant Double Tensural Tristable Micromechanisms (DTTM),” J. Micromech. Microeng., 19(2), p. 025011. [CrossRef]
Hetrick, J. A., and Kota, S., 1999, “An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms,” ASME J. Mech. Des., 121(2), pp. 229–234. [CrossRef]
Baek, S. S., Ma, K. Y., and Fearing, R. S., 2009, “Efficient Resonant Drive of Flapping-Wing Robots,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2854–2860.
Sahai, R., Galloway, K. C., and Wood, R. J., 2013, “Elastic Element Integration for Improved Flapping-Wing Micro Air Vehicle Performance,” IEEE Trans. Rob. Autom., 29(1), pp. 32–41. [CrossRef]
Kim, S.-W., Koh, J.-S., Cho, M., and Cho, K.-J., 2010, “Towards a Bio-Mimetic Flytrap Robot Based on a Snap-Through Mechanism,” Proceedings of the IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, pp. 534–539.
Arruda, E. M., and Boyce, M. C., 1993, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41(2), pp. 389–412. [CrossRef]
Gerratt, A. P., Penskiy, I., and Bergbreiter, S., 2013, “In Situ Characterization of PDMS in SOI-MEMS,” J. Micromech. Microeng., 23(4), p. 045003. [CrossRef]

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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