Abstract
Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved lamina emergent torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.
References
1.
Nelson
, T. G.
, Zimmerman
, T. K.
, Magleby
, S. P.
, Lang
, R. J.
, and Howell
, L. L.
, 2019
, “Developable Mechanisms on Developable Surfaces
,” Sci. Rob.
, 4
(27
), p. eaau5171
. 2.
Nelson
, T. G.
, and Herder
, J. L.
, 2018
, “Developable Compliant-Aided Rolling-Contact Mechanisms
,” Mech. Mach. Theory
, 126
, pp. 225
–242
. 3.
Jacobsen
, J. O.
, Winder
, B. G.
, Howell
, L. L.
, and Magleby
, S. P.
, 2010
, “Lamina Emergent Mechanisms and Their Basic Elements
,” ASME J. Mech. Rob.
, 2
(1
), p. 011003
. 4.
Greenwood
, J. R.
, Magleby
, S. P.
, and Howell
, L. L.
, 2019
, “Developable Mechanisms on Regular Cylindrical Surfaces
,” Mech. Mach. Theory.
, 142
, p. 103584
. 5.
Peyron
, Q.
, Rabenorosoa
, K.
, Andreff
, N.
, and Renaud
, P.
, 2019
, “A Numerical Framework for the Stability and Cardinality Analysis of Concentric Tube Robots: Introduction and Application to the Follow-the-Leader Deployment
,” Mech. Mach. Theory.
, 132
, pp. 176
–192
. 6.
Venkiteswaran
, V. K.
, Sikorski
, J.
, and Misra
, S.
, 2019
, “Shape and Contact Force Estimation of Continuum Manipulators Using Pseudo Rigid Body Models
,” Mech. Mach. Theory.
, 139
, pp. 34
–45
. 7.
Lim
, J. J.
, and Erdman
, A. G.
, 2003
, “A Review of Mechanism Used in Laparoscopic Surgical Instruments
,” Mech. Mach. Theory.
, 38
(11
), pp. 1133
–1147
. 8.
Xue
, R.
, Du
, Z.
, Yan
, Z.
, and Ren
, B.
, 2019
, “An Estimation Method of Grasping Force for Laparoscope Surgical Robot Based on the Model of a Cable-Pulley System
,” Mech. Mach. Theory.
, 134
, pp. 440
–454
. 9.
Chang
, J.
, Boules
, M.
, Rodriguez
, J.
, and Kroh
, M.
, 2016
, “Minilaparoscopy With Interchangeable, Full 5-mm End Effectors: First Human Use of a New Minimally Invasive Operating Platform
,” J. Laparoendosc. Adv. Surg. Tech. Videoscopy
, 26
(1
), pp. 1
–5
. 10.
Zoppi
, M.
, Sieklicki
, W.
, and Molfino
, R.
, 2008
, “Design of a Microrobotic Wrist for Needle Laparoscopic Surgery
,” ASME J. Mech. Des.
, 130
(10
), p. 102306
. 11.
Gafford
, J.
, Ding
, Y.
, Harris
, A.
, McKenna
, T.
, Polygerinos
, P.
, Holland
, D.
, Walsh
, C.
, and Moser
, A.
, 2015
, “Shape Deposition Manufacturing of a Soft, Atraumatic, and Deployable Surgical Grasper
,” ASME J. Mech. Rob.
, 7
(2
), p. 021006
. 12.
Howell
, L. L.
, 2001
, Compliant Mechanisms
, John Wiley & Sons
, New York
.13.
Seymour
, K.
, Sheffield
, J.
, Magleby
, S. P.
, and Howell
, L. L.
, 2019
, “Cylindrical Developable Mechanisms for Minimally Invasive Surgical Instruments
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Anaheim, CA
.14.
Megaro
, V.
, Zehnder
, J.
, Bächer
, M.
, Coros
, S.
, Gross
, M. H.
, and Thomaszewski
, B.
, 2017
, “A Computational Design Tool for Compliant Mechanisms
,” ACM Tran. Graphics
, 36
, pp. 82:1
–82:12
. 15.
Su
, H.
, 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
. 16.
Pedersen
, C.
, Buhl
, T.
, and Sigmund
, O.
, 2001
, “Topology Synthesis of Large-Displacement Compliant Mechanisms
,” Int. J. Num. Methods Eng.
, 50
(12
), pp. 2683
–2705
. 17.
Sigmund
, O.
, 1997
, “On the Design of Compliant Mechanisms Using Topology Optimization
,” Mech. Struct. Mach.
, 25
(4
), pp. 493
–524
. 18.
Aten
, Q. T.
, Jensen
, B. D.
, Tamowski
, S.
, Wilson
, A. M.
, Howell
, L. L.
, and Burnett
, S. H.
, 2012
, “Nanoinjection: Pronuclear DNA Delivery Using a Charged Lance
,” Transgenic. Res.
, 21
(6
), pp. 1279
–1290
. 19.
Last
, M.
, Subramaniam
, V.
, and Pister
, K.
, 2012
, “Out-of-plane Motion of Assembled Microstructures Using a Singlemask SOI Process
,” IEEE 13th International Conference on Solid-State Sensors, and Microsystems
, Seoul, South Korea
, Vol. 2
.20.
Jacobsen
, J.
, Chen
, G.
, Howell
, L.
, and Magleby
, S.
, 2012
, “Lamina Emergent Torsional (LET) Joint
,” Mech. Mach. Theory.
, 56
, pp. 1
–15
. 21.
Nelson
, T. G.
, Lang
, R. J.
, Pehrson
, N. A.
, Magleby
, S. P.
, and Howell
, L. L.
, 2016
, “Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays
,” ASME J. Mech. Rob.
, 8
(3
), p. 031006
. 22.
Pehrson
, N. A.
, Bilancia
, P.
, Magleby
, S.
, and Howell
, L.
, 2020
, “Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays
,” ASME J. Mech. Des.
, 142
(9
), p. 093301
. 23.
Zimmerman
, T.
, Butler
, J.
, Frandsen
, D.
, Burrow
, D.
, Fullwood
, D.
, Magleby
, S.
, and Howell
, L.
, 2018
, “Modified Material Properties in Curved Panels Through Lamina Emergent Torsional Joints
,” ReMAR International Conference on Reconfigurable Mechanisms and Robots
, Delft, The Netherlands
, pp. 1
–9
.24.
Hwang
, I.-H.
, Shim
, Y.-S.
, and Lee
, J.-H.
, 2003
, “Modeling and Experimental Characterization of the Chevron-Type Bi-Stable Microactuator
,” J. Micromech. Microeng.
, 13
(6
), pp. 948
–954
. 25.
Ferreira
, H.
, 2015
, “Equipment in Laparoscopic Surgery,” A Manual of Minimally Invasive Gynecological Surgery
, M.
Agarwal
, ed., The Health Sciences
, New Delhi
, pp. 3
–12
.26.
Li
, L.
, Zhang
, D.
, Guo
, S.
, and Qu
, H.
, 2019
, “Design, Modeling, and Analysis of Hybrid Flexure Hinges
,” Mech. Mach. Theory.
, 131
, pp. 300
–316
. 27.
Linß
, S.
, Gräser
, P.
, Räder
, T.
, Henning
, S.
, Theska
, R.
, and Zentner
, L.
, 2018
, “Influence of Geometric Scaling on the Elasto-Kinematic Properties of Flexure Hinges and Compliant Mechanisms
,” Mech. Mach. Theory.
, 125
, pp. 220
–239
. 28.
Midha
, A.
, and Kuber
, R.
, 2014
, “Closed-Form Elliptic Integral Solution of Initially-Straight and Initially-Curved Small-Length Flexural Pivots
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Buffalo, NY
.29.
Howell
, L. L.
, Midha
, A.
, and Norton
, T.
, 1996
, “Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms
,” ASME J. Mech. Des.
, 118
(1
), pp. 126
–131
. 30.
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
. 31.
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
. 32.
Chen
, G.
, Magleby
, S. P.
, and Howell
, L. L.
, 2018
, “Membrane-Enhanced Lamina Emergent Torsional Joints for Surrogate Folds
,” ASME J. Mech. Des.
, 140
(6
), p. 062303
. 33.
Seymour
, K.
, Burrow
, D.
, Avila
, A.
, Bateman
, T.
, Morgan
, D. C.
, Magleby
, S. P.
, and Howell
, L. L.
, 2018
, “Origami-Based Deployable Ballistic Barrier
,” 7OSME 7th International Meeting on Origami in Science, Mathematics and Education
, Oxford, UK
, pp. 763
–777
.34.
Villiers
, M. D.
, 1994
, “The Role and Function of a Hierarchical Classification of Quadrilaterals
,” Learn. Math.
, 14
(1
), pp. 11
–18
.35.
DeFigueiredo
, B. P.
, Zimmerman
, T. K.
, Russell
, B. D.
, and Howell
, L. L.
, 2018
, “Regional Stiffness Reduction Using Lamina Emergent Torsional Joints for Flexible Printed Circuit Board Design
,” ASME J. Electron. Packag.
, 140
(4
), p. 041001
. 36.
Xie
, Z.
, Qiu
, L.
, and Yang
, D.
, 2018
, “Using the Parts Used to Be Removed to Improve Compliant Joint’s Performance
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Quebec City, Canada
.37.
Klett
, Y.
, 2018
, “PALEO: Plastically Annealed Lamina Emergent Origami
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Quebec City, Canada
.38.
Alfattani
, R.
, and Lusk
, C.
, 2016
, “A Lamina-Emergent Frustum Using a Bistable Collapsible Compliant Mechanism (BCCM)
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 5A: 40th Mechanisms and Robotics Conference
, Paper No. DETC2016-59590
, p. V05AT07A014
.39.
Xie
, Z.
, Qiu
, L.
, and Yang
, D.
, 2017
, “Design and Analysis of Outside-Deployed Lamina Emergent Joint (OD-LEJ)
,” Mech. Mach. Theory.
, 114
, pp. 111
–124
. 40.
Xie
, Z.
, Qiu
, L.
, and Yang
, D.
, 2018
, “Design and Analysis of a Variable Stiffness Inside-Deployed Lamina Emergent Joint
,” Mech. Mach. Theory.
, 120
, pp. 166
–177
. 41.
Hyatt
, L. P.
, Lytle
, A.
, Magleby
, S. P.
, and Howell
, L. L.
, 2020
, “Designing Developable Mechanisms From Flat Patterns
,” ASME IDETC/CIE International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, St. Louis, MO (Virtual Event)
.42.
Jog
, C.
, 2015
, Continuum Mechanics: Foundations and Applications of Mechanics
, 3rd ed., Vol. 1
, Cambridge University Press
, Cambridge
.43.
Roark
, R. J.
, and Young
, W. C.
, 1975
, Formulas for Stress and Strain
, McGraw-Hill
, New York
.44.
McNaney
, J.
, Imbeni
, V.
, Jung
, Y.
, Papadopoulos
, P.
, and Ritchie
, R.
, 2003
, “An Experimental Study of the Superelastic Effect in a Shape-Memory Nitinol Alloy Under Biaxial Loading
,” Mech. Mater.
, 35
(10
), pp. 969
–986
. 45.
Qian
, H.
, Li
, H.
, Song
, G.
, and Guo
, W.
, 2013
, “Recentering Shape Memory Alloy Passive Damper for Structural Vibration Control
,” Math. Prob. Eng.
, 2013
, pp. 1
–13
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