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Research Papers

Repelling-Screw Based Force Analysis of Origami Mechanisms

[+] Author and Article Information
Chen Qiu

Centre for Robotic Research,
King’s College London,
London WC2R 2LS, UK
e-mail: chen.qiu@kcl.ac.uk

Ketao Zhang

Mem. ASME
Centre for Robotic Research,
Kings’s College London,
London WC2R 2LS, UK
e-mail: ketao.zhang@kcl.ac.uk

Jian S. Dai

ASME Fellow
Chair of Mechanisms and Robotics
MoE Key Laboratory for Mechanism Theory and
Equipment Design,
Tianjin University,
Tianjin, 300072, China;
Centre for Robotic Research,
King’s College London,
London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

1Corresponding author.

Manuscript received May 31, 2015; final manuscript received August 24, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031001 (Mar 07, 2016) (10 pages) Paper No: JMR-15-1122; doi: 10.1115/1.4031458 History: Received May 31, 2015; Revised August 24, 2015

This paper provides an approach to model the reaction force of origami mechanisms when they are deformed. In this approach, an origami structure is taken as an equivalent redundantly actuated mechanism, making it possible to apply the forward-force analysis to calculating the reaction force of the origami structure. Theoretical background is provided in the framework of screw theory, where the repelling screw is introduced to integrate the resistive torques of folded creases into the reaction-force of the whole origami mechanism. Two representative origami structures are then selected to implement the developed modeling approach, as the widely used waterbomb base and the waterbomb-based integrated parallel mechanism. With the proposed kinematic equivalent, their reaction forces are obtained and validated, presenting a ground for force analysis of origami-inspired mechanisms.

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References

Kanade, T. , 1980, “ A Theory of Origami World,” Artif. Intell., 13(3), pp. 279–311. [CrossRef]
Lang, R. J. , and Hull, T. C. , 2005, “ Origami Design Secrets: Mathematical Methods for an Ancient Art,” Math. Intell., 27(2), pp. 92–95.
Dai, J. , and Jones, J. R. , 2002, “ Kinematics and Mobility Analysis of Carton Folds in Packing Manipulation Based on the Mechanism Equivalent,” Proc. Inst. Mech. Eng., Part C, 216(10), pp. 959–970. [CrossRef]
Dai, J. , and Caldwell, D. , 2010, “ Origami-Based Robotic Paper-and-Board Packaging for Food Industry,” Trends Food Sci. Technol., 21(3), pp. 153–157. [CrossRef]
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Carroll, D. W. , Magleby, S. P. , Howell, L. L. , Todd, R. H. , and Lusk, C. P. , 2005, “ Simplified Manufacturing Through a Metamorphic Process for Compliant Ortho-Planar Mechanisms,” ASME Paper No. IMECE2005-82093.
Winder, B. G. , Magleby, S. P. , and Howell, L. L. , 2009, “ Kinematic Representations of Pop-Up Paper Mechanisms,” J. Mech. Rob., 1(2), p. 021009. [CrossRef]
Song, J. , Chen, Y. , and Lu, G. , 2012, “ Axial Crushing of Thin-Walled Structures With Origami Patterns,” Thin-Walled Struct., 54, pp. 65–71. [CrossRef]
Ma, J. , and You, Z. , 2014, “ Energy Absorption Of Thin-Walled Square Tubes With A Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation,” ASME J. Appl. Mech., 81(1), p. 011003. [CrossRef]
Zirbel, S. A. , Lang, R. J. , Thomson, M. W. , Sigel, D. A. , Walkemeyer, P. E. , Trease, B. P. , Magleby, S. P. , and Howell, L. L. , 2013, “ Accommodating Thickness in Origami-Based Deployable Arrays,” ASME J. Mech. Des., 135(11), p. 111005. [CrossRef]
Chen, Y. , Peng, R. , and You, Z. , 2015, “ Origami of Thick Panels,” Science, 349(6246), pp. 396–400. [CrossRef] [PubMed]
Bassik, N. , Stern, G. M. , and Gracias, D. H. , 2009, “ Microassembly Based on Hands Free Origami With Bidirectional Curvature,” Appl. Phys. Lett., 95(9), p. 091901. [CrossRef]
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. [CrossRef]
Lee, D.-Y. , Kim, J.-S. , Kim, S.-R. , Koh, J.-S. , and Cho, K.-J. , 2013, “ The Deformable Wheel Robot Using Magic-Ball Origami Structure,” ASME Paper No. DETC2013-13016.
Onal, C. D. , Wood, R. J. , and Rus, D. , 2013, “ An Origami-Inspired Approach to Worm Robots,” IEEE/ASME Trans. Mechatron., 18(2), pp. 430–438. [CrossRef]
Vander Hoff, E. , Jeong, D. , and Lee, K. , 2014, “ Origamibot-i: A Thread-Actuated Origami Robot for Manipulation and Locomotion,” 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), Chicago, Sept. 14–18, pp. 1421–1426.
Zhang, K. , Qiu, C. , and Dai, J. S. , 2015, “ Helical Kirigami-Enabled Centimeter-Scale Worm Robot With Shape-Memory-Alloy Linear Actuators,” J. Mech. Rob., 7(2), p. 021014. [CrossRef]
Dai, J. S. , and Jones, J. R. , 1999, “ Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds,” ASME J. Mech. Des., 121(3), pp. 375–382. [CrossRef]
Bowen, L. A. , Grames, C. L. , Magleby, S. P. , Howell, L. L. , and Lang, R. J. , 2013, “ A Classification of Action Origami as Systems of Spherical Mechanisms,” ASME J. Mech. Des. 135(11), p. 111008. [CrossRef]
Hull, T. , 1994. “ On the Mathematics of Flat Origamis,” Congressus Numerantium, pp. 215–224.
Liu, H. , and Dai, J. , 2002, “ Carton Manipulation Analysis Using Configuration Transformation,” Proc. Inst. Mech. Eng., Part C, 216(5), pp. 543–555. [CrossRef]
Mitani, J. , 2009, “ A Design Method for 3D Origami Based on Rotational Sweep,” Comput. Aided Des. Appl., 6(1), pp. 69–79.
Dai, J. S. , Wang, D. , and Cui, L. , 2009, “ Orientation and Workspace Analysis of the Multifingered Metamorphic Handmetahand,” IEEE Trans. Rob., 25(4), pp. 942–947. [CrossRef]
Wilding, S. E. , Howell, L. L. , and Magleby, S. P. , 2012, “ Spherical Lamina Emergent Mechanisms,” Mech. Mach. Theory, 49, pp. 187–197. [CrossRef]
Bowen, L. , Frecker, M. , Simpson, T. W. , and von Lockette, P. , 2014, “ A Dynamic Model of Magneto-Active Elastomer Actuation of the Waterbomb Base,” ASME Paper No. DETC2014-35407.
Yao, W. , and Dai, J. S. , 2008, “ Dexterous Manipulation of Origami Cartons With Robotic Fingers Based on the Interactive Configuration Space,” ASME J. Mech. Des., 130(2), p. 022303. [CrossRef]
Zhang, K. , Fang, Y. , Fang, H. , and Dai, J. S. , 2010, “ Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism,” J. Mech. Rob., 2(3), p. 031014. [CrossRef]
Wei, G. , and Dai, J. S. , 2014, “ Origami-Inspired Integrated Planar-Spherical Overconstrained Mechanisms,” ASME J. Mech. Des., 136(5), p. 051003. [CrossRef]
Beex, L. A. , and Peerlings, R. H. , 2009, “ An Experimental and Computational Study of Laminated Paperboard Creasing and Folding,” Int. J. Solids Struct., 46(24), pp. 4192–4207. [CrossRef]
Felton, S. M. , Tolley, M. T. , Shin, B. , Onal, C. D. , Demaine, E. D. , Rus, D. , and Wood, R. J. , 2013, “ Self-Folding With Shape Memory Composites,” Soft Matter, 9(32), pp. 7688–7694. [CrossRef]
Ahmed, S. , Lauff, C. , Crivaro, A. , McGough, K. , Sheridan, R. , Frecker, M. , von Lockette, P. , Ounaies, Z. , Simpson, T. , Lien, J. , and Strzelec, R. , 2013, “ Multi-Field Responsive Origami Structures: Preliminary Modeling and Experiments,” ASME Paper No. DETC2013-12405.
Delimont, I. L. , Magleby, S. P. , and Howell, L. L. , 2015, “ Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms,” J. Mech. Rob., 7(1), p. 011009. [CrossRef]
Dai, J. S. , and Cannella, F. , 2008, “ Stiffness Characteristics of Carton Folds for Packaging,” ASME J. Mech. Des., 130(2), p. 022305. [CrossRef]
Qiu, C. , Aminzadeh, V. , and Dai, J. S. , 2013, “ Kinematic Analysis and Stiffness Validation of Origami Cartons,” ASME J. Mech. Des., 135(11), p. 111004. [CrossRef]
Mentrasti, L. , Cannella, F. , Pupilli, M. , and Dai, J. S. , 2013, “ Large Bending Behavior of Creased Paperboard. I. Experimental Investigations,” Int. J. Solids Struct., 50(20), pp. 3089–3096. [CrossRef]
Mentrasti, L. , Cannella, F. , Pupilli, M. , and Dai, J. S. , 2013, “ Large Bending Behavior Of Creased Paperboard. II. Structural Analysis,” Int. J. Solids Struct., 50(20), pp. 3097–3105. [CrossRef]
Hanna, B. H. , Lund, J. M. , Lang, R. J. , Magleby, S. P. , and Howell, L. L. , 2014, “ Waterbomb Base: A Symmetric Single-Vertex Bistable Origami Mechanism,” Smart Mater. Struct., 23(9), p. 094009. [CrossRef]
Hanna, B. H. , Magleby, S. , Lang, R. J. , and Howell, L. L. , “ Force-Deflection Modeling for Generalized Origami Waterbomb-Base Mechanisms,” ASME J. Appl. Mech., 82(8), p. 081001. [CrossRef]
Dai, J. S. , and Jones, J. R. , 2001, “ Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications,” Mech. Mach. Theory, 36(5), pp. 633–651. [CrossRef]
Zhang, K. , Qiu, C. , and Dai, J. S. , 2015, “ An Origami-Parallel Structure Integrated Deployable Continuum Robot,” ASME Paper No. DETC2015-46504.
Zhang, K. , and Fang, Y. , 2008, “ Kinematics and Workspace Analysis of a Novel Spatial 3-DOF Parallel Manipulator,” Prog. Nat. Sci., 18(4), pp. 432–440.
Murray, R. M. , Li, Z. , Sastry, S. S. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Lipkin, H. , and Duffy, J. , 1985, “ The Elliptic Polarity of Screws,” ASME J. Mech, Trans., Autom. Des., 107(3), pp. 377–387. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The equivalent mechanism of an origami waterbomb base

Grahic Jump Location
Fig. 2

Geometrical relationships of the equivalent spherical joint A

Grahic Jump Location
Fig. 3

Schematic diagram of the waterbomb-base integrated parallel mechanism

Grahic Jump Location
Fig. 4

Geometrical relationships of the Limb B1A1P1

Grahic Jump Location
Fig. 5

Linear motion of the origami mechanism

Grahic Jump Location
Fig. 6

Variations of crease rotation angles and reaction force in the linear-motion mode of origami mechanism. (a) Crease rotation angles θs with respect to θ1. (b) Reaction force with respect to θ1.

Grahic Jump Location
Fig. 7

Rotational motion of the origami mechanism

Grahic Jump Location
Fig. 8

Variations of crease rotation angles and reaction force in the rotational-motion mode of origami mechanism. (a) Crease rotation angles θs with respect to θ1 and (b) reaction force with respect toθ1.

Grahic Jump Location
Fig. 9

A general configuration of the origami-enabled parallel mechanism

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