Research Papers

A Model for Multi-Input Mechanical Advantage in Origami-Based Mechanisms

[+] Author and Article Information
Jared Butler

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: jaredbutler@byu.net

Landen Bowen

Department of Mechanical Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: landen.bowen@gmail.com

Eric Wilcox

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: ewwilcox@gmail.com

Adam Shrager

Department of Mechanical Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: adam.shrager@gmail.com

Mary I. Frecker

Department of Mechanical Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: mxf36@engr.psu.edu

Paris von Lockette

Department of Mechanical Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mial: prv2@engr.psu.edu

Timothy W. Simpson

Department of Mechanical Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: tws8@engr.psu.edu

Robert J. Lang

Lang Origami,
Alamo, CA 94507
e-mail: robert@langorigami.com

Larry L. Howell

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

Spencer P. Magleby

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: magleby@byu.edu

1Corresponding author.

Portions of this work were presented at IDETC 2015 as paper number 47708.Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 8, 2018; final manuscript received August 1, 2018; published online September 17, 2018. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 10(6), 061007 (Sep 17, 2018) (9 pages) Paper No: JMR-18-1064; doi: 10.1115/1.4041199 History: Received March 08, 2018; Revised August 01, 2018

Mechanical advantage is traditionally defined for single-input and single-output rigid-body mechanisms. A generalized approach for identifying single-output mechanical advantage for a multiple-input compliant mechanism, such as many origami-based mechanisms, would prove useful in predicting complex mechanism behavior. While origami-based mechanisms are capable of offering unique solutions to engineering problems, the design process of such mechanisms is complicated by the interaction of motion and forces. This paper presents a model of the mechanical advantage for multi-input compliant mechanisms and explores how modifying the parameters of a model affects their behavior. The model is used to predict the force-deflection behavior of an origami-based mechanism (Oriceps) and is verified with experimental data from magnetic actuation of the mechanism.

Copyright © 2018 by ASME
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Salamon, B. , and Midha, A. , 1998, “ An Introduction to Mechanical Advantage in Compliant Mechanisms,” ASME J. Mech. Des., 120(2), pp. 311–315. [CrossRef]
Zhou, L. , Marras, A. E. , Castro, C. E. , and Su, H.-J. , 2016, “ Pseudorigid-Body Models of Compliant Dna Origami Mechanisms,” ASME J. Mech. Rob., 8(5), p. 051013. [CrossRef]
Miyashita, S. , Guitron, S. , Ludersdorfer, M. , Sung, C. R. , and Rus, D. , 2015, “ An Untethered Miniature Origami Robot That Self-Folds, Walks, Swims, and Degrades,” IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, May 26–30, pp. 1490–1496.
Miyashita, S. , Guitron, S. , Yoshida, K. , Li, S. , Damian, D. D. , and Rus, D. , 2016, “ Ingestible, Controllable, and Degradable Origami Robot for Patching Stomach Wounds,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 909–916.
Taylor, A. , Miller, M. , Fok, M. , Nilsson, K. , and Tse, Z. T. H. , 2016, “ Intracardiac Magnetic Resonance Imaging Catheter With Origami Deployable Mechanisms,” ASME J. Med. Devices, 10(2), p. 020957. [CrossRef]
Johnson, M. , Chen, Y. , Hovet, S. , Xu, S. , Wood, B. , Ren, H. , Tokuda, J. , and Tse, Z. T. H. , 2017, “ Fabricating Biomedical Origami: A State-of-the-Art Review,” Int. J. Comput. Assisted Radiol. Surg., 12(11), pp. 1–10. [CrossRef]
Zirbel, S. , Magleby, S. , Howell, L. , Lang, R. , Thomson, M. , and Trease, B. , 2013, “ Accommodating Thickness in Origami-Based Deployable arrays1,” ASME J. Mech. Des., 135(11), p. 111005. [CrossRef]
Butler, J. , Morgan, J. , Pehrson, N. , Tolman, K. , Bateman, T. , Magleby, S. P. , and Howell, L. L. , 2016, “ Highly Compressible Origami Bellows for Harsh Environments,” ASME Paper No. DETC2016-59060.
Qiao, Q. , Yuan, J. , Shi, Y. , Ning, X. , and Wang, F. , 2017, “ Structure, Design, and Modeling of an Origami-Inspired Pneumatic Solar Tracking System for the Npu-Phonesat,” ASME J. Mech. Rob., 9(1), p. 011004. [CrossRef]
Miyashita, S. , DiDio, I. , Ananthabhotla, I. , An, B. , Sung, C. , Arabagi, S. , and Rus, D. , 2015, “ Folding Angle Regulation by Curved Crease Design for Self-Assembling Origami Propellers,” ASME J. Mech. Rob., 7(2), p. 021013. [CrossRef]
Baranger, E. , Guidault, P.-A. , and Cluzel, C. , 2011, “ Numerical Modeling of the Geometrical Defects of an Origami-like Sandwich Core,” Compos. Struct., 93(10), pp. 2504–2510. [CrossRef]
Nojima, T. , and Saito, K. , 2006, “ Development of Newly Designed Ultra-Light Core Structures,” JSME Int. J. Ser. A Solid Mech. Mater. Eng., 49(1), pp. 38–42. [CrossRef]
Cheng, Q. , Song, Z. , Ma, T. , Smith, B. , Tang, R. , Yu, H. , Jiang, H. , and Chan, C. , 2013, “ Folding Paper-Based Lithium-Ion Batteries for Higher Areal Energy Densities,” Nano Lett., 13(10), pp. 4969–4974. [CrossRef] [PubMed]
Firouzeh, A. , and Paik, J. , 2017, “ An Under-Actuated Origami Gripper With Adjustable Stiffness Joints for Multiple Grasp Modes,” Smart Mater. Struct., 26(5), p. 055035. [CrossRef]
Chen, Y. , Lv, W. , Li, J. , and You, Z. , 2017, “ An Extended Family of Rigidly Foldable Origami Tubes,” ASME J. Mech. Rob., 9(2), p. 021002. [CrossRef]
Firouzeh, A. , and Paik, J. , 2015, “ Robogami: A Fully Integrated Low-Profile Robotic Origami,” ASME J. Mech. Rob., 7(2), p. 021009. [CrossRef]
Zhang, K. , Qiu, C. , and Dai, J. S. , 2016, “ An Extensible Continuum Robot With Integrated Origami Parallel Modules,” ASME J. Mech. Rob., 8(3), p. 031010. [CrossRef]
Pagano, A. , Yan, T. , Chien, B. , Wissa, A. , and Tawfick, S. , 2017, “ A Crawling Robot Driven by Multi-Stable Origami,” Smart Mater. Struct., 26(9), p. 094007. [CrossRef]
Onal, C. L. , Wood, R. J. , and Rus, D. , 2013, “ An Origami-Inspired Approach to Worm Robots,” IEEE Trans. Mechatronics, 18(2), pp. 430–438. [CrossRef]
Felton, S. , Tolley, M. , Demaine, E. , Rus, D. , and Wood, R. , 2014, “ A Method for Building Self-Folding Machines,” Science, 345(6197), pp. 644–646. [CrossRef] [PubMed]
Guang, C. , and Yang, Y. , 2018, “ Single-Vertex Multicrease Rigid Origami With Nonzero Thickness and Its Transformation Into Deployable Mechanisms,” ASME J. Mech. Rob., 10(1), p. 011010. [CrossRef]
Yang, Y. , and You, Z. , 2018, “ Geometry of Transformable Metamaterials Inspired by Modular Origami,” ASME J. Mech. Rob., 10(2), p. 021001.
Edmondson, B. , Bowen, L. , Grames, G. , Magleby, S. , Howell, L. , and Bateman, T. , 2013, “ Oriceps: Origami-Inspired Forceps,” ASME Paper No. SMASIS2013-3299.
Bowen, L. , Grames, C. , Magleby, S. , Lang, R. , and Howell, L. , 2013, “ A Classification of Action Origami as Systems of Spherical Mechanisms,” ASME J. Mech. Des., 135(11), p. 111008. [CrossRef]
Midha, A. , Hall, A. S. , Her, I. , and Bubel, G. , 1984, “ Mechanical Advantage of Single-Input and Multiple-Output Ports Mechanical Device,” ASME J. Mech. Trans., Autom. Des., 106(4), pp. 462–469. [CrossRef]
Wang, M. Y. , 2009, “ Mechanical and Geometric Advantages in Compliant Mechanism Optimization,” Front. Mech. Eng. China, 4(3), pp. 229–241. [CrossRef]
Shafer, J. , 2010, Origami Ooh La La!, CreateSpace Independent Publishing Platform, Lexington, KY.
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Liu, Y. , Boyles, J. , Genzer, J. , and Dickey, M. , 2012, “ Self-Folding of Polymer Sheets Using Local Light Absorption,” Soft Matter, 8(6), pp. 1764–1769.
Ryu, J. , D'Amato, M. , Cui, X. , Long, K. , Qi, H. , and Dunn, M. , 2012, “ Photo-Origami - Bending and Folding Polymers With Light,” Appl. Phys. Lett., 100(16), p. 161908.
Sun, W. , Liu, F. , Ma, Z. , Li, C. , and Zhou, J. , 2016, “ Soft Mobile Robots Driven by Foldable Dielectric Elastomer Actuators,” J. Appl. Phys., 120(8), p. 084901. [CrossRef]
Ahmed, S. , Lauff, C. , Crivaro, A. , McGough, K. , Sheridan, R. , Frecker, M. , Lockette, P. , Ounaies, Z. , Simpson, T. , Lien, J. , and Strzelec, R. , 2013, “ Multi-Field Responsive Origami Structures: Preliminary Modelling and Experiments,” ASME Paper No. V06BT07A028.
Ahmed, S. , Ounaies, Z. , and Frecker, M. , 2014, “ Investigating the Performance and Properties of Dielectric Elastomer Actuators as a Potential Means to Actuate Origami Structures,” Smart Mater. Struct., 23(9), p. 094003.
McGough, K. , Ahmed, S. , Frecker, M. , and Ounaies, Z. , 2014, “ Finite Element Analysis and Validation of Dielectric Elastomer Actuators Used for Active Origami,” Smart Mater. Struct., 23(9), p. 094002.
Shigemune, H. , Maeda, S. , Hara, Y. , Hosoya, N. , and Hashimoto, S. , 2016, “ Origami Robot: A Self-Folding Paper Robot With an Electrothermal Actuator Created by Printing,” IEEE/ASME Trans. Mechatronics, 21(6), pp. 2746–2754. [CrossRef]
Bowen, L. , Springsteen, K. , Ahmed, S. , Arrojado, E. , Frecker, M. , Simpson, T. W. , Ounaies, Z. , and von Lockette, P. , 2017, “ Design, Fabrication, and Modeling of an Electric–Magnetic Self-Folding Sheet,” ASME J. Mech. Rob., 9(2), p. 021012. [CrossRef]
Cowan, B. , and von Lockette, P. R. , 2017, “ Fabrication, Characterization, and Heuristic Trade Space Exploration of Magnetically Actuated Miura-Ori Origami Structures,” Smart Mater. Struct., 26(4), p. 045015. [CrossRef]
Crivaro, A. , Sheridan, R. , Frecker, M. , Simpson, T. W. , and Von Lockette, P. , 2016, “ Bistable Compliant Mechanism Using Magneto Active Elastomer Actuation,” J. Intell. Mater. Syst. Struct., 27(15), pp. 2049–2061. [CrossRef]
Guitron, S. , Guha, A. , Li, S. , and Rus, D. , 2017, “ Autonomous Locomotion of a Miniature, Untethered Origami Robot Using Hall Effect Sensor-Based Magnetic Localization,” IEEE International Conference on Robotics and Automation (ICRA), Singapore, May 29–June 3, pp. 4807–4813.
Salerno, M. , Zuliani, F. , Firouzeh, A. , and Paik, J. , 2017, “ Design and Control of a Low Profile Electromagnetic Actuator for Foldable Pop-Up Mechanisms,” Sens. Actuators A: Phys., 265, pp. 70–78.
Hernandez, E. A. P. , Hartl, D. J. , Malak, R. J. , Akleman, E. , Gonen, O. , and Kung, H.-W. , 2016, “ Design Tools for Patterned Self-Folding Reconfigurable Structures Based on Programmable Active Laminates,” ASME J. Mech. Rob., 8(3), p. 031015. [CrossRef]
Hawkes, E. , An, B. , Benbernou, N. M. , Tanaka, H. , Kim, S. , Demaine, E. D. , Rus, D. , and Wood, R. J. , 2010, “ Programmable Matter by Folding,” Proc. Natl. Acad. Sci., 107(28), pp. 12441–12445.
Bowen, L. , Springsteen, K. , Feldstein, H. , Frecker, M. , Simpson, T. , and von Lockette, P. , 2015, “ Development and Validation of a Dynamic Model of Magneto-Active Elastomer Actuation of the Origami Waterbomb Base,” ASME J. Mech. Des., 7(1), p. 011010.
Sheridan, R. , Roche, J. , Lofland, S. , and von Lockette, P. , 2014, “ Numerical Simulation and Experimental Validation of the Large Deformation Bending and Folding Behavior of Magneto-Active Elastomer Composites,” Smart Mater. Struct., 23(9), p. 094004.
Lang, R. J. , Magleby, S. , and Howell, L. , 2015, “ Single-Degree-of-Freedom Rigidly Foldable Origami Flashers,” ASME Paper No. DETC2015-46961.
Griffiths, D. J. , 1999, Introduction to Electrodynamics, 3rd ed., Prentice Hall, Upper Saddle River, NJ.
Lang, R. J. , Tolman, K. A. , Crampton, E. B. , Magleby, S. P. , and Howell, L. L. , 2018, “ A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering,” ASME Appl. Mech. Rev., 70(1), p. 010805. [CrossRef]


Grahic Jump Location
Fig. 1

Oriceps being actuated

Grahic Jump Location
Fig. 2

Oriceps fold pattern. Solid lines represent valley folds, while dotted lines represent mountain folds.

Grahic Jump Location
Fig. 3

Open and closed positions of the Oriceps

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Fig. 4

Mechanical advantage model of the Oriceps (reduced by symmetry). Input (light) and output (dark) moments are indicated.

Grahic Jump Location
Fig. 5

Partially folded vertex within the Oriceps with sector angles (α) and exterior dihedral angles (γ) shown. The ground link (α3) is indicated with hatched lines.

Grahic Jump Location
Fig. 6

Oriceps fold pattern with placement of the magnets and their respective poling directions: (a) Short arrows represent individual magnet poling directions. (b) Long arrow represents applied magnetic field direction. Torque directions shown in black.

Grahic Jump Location
Fig. 7

Comparison of degree-4 vertex theoretical mechanical advantage profiles throughout actuation for the rigid-body Oriceps and the compliant Oriceps. The stiffness in (b) is varied by changing the modulus of elasticity, where E represents the modulus for the design in (a): (a) comparison of Oriceps under varying magnetic field strength and (b) comparison of Oriceps with varying stiffness.

Grahic Jump Location
Fig. 8

Oriceps fold pattern with vertices numbered 1–4, actuation inputs, and force outputs

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Fig. 9

Predicted blocked force output at varying values of γ3

Grahic Jump Location
Fig. 10

Experimental setup to test force output during magnetic actuation

Grahic Jump Location
Fig. 11

Oriceps being actuated in an applied magnetic field. Poling directions of each magnet are indicated in the center of the image and the magnetic field with arrows across the top and bottom of the image.

Grahic Jump Location
Fig. 12

Calculated blocked force output at γ3 = 35 deg as compared to experimental data. The standard deviation of sampled points is represented with error bars.



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