Abstract
Developable mechanisms provide unparalleled compactness and deployability. This paper explores the kinematic behavior of developable mechanisms that conform to regular cylindrical surfaces. Design considerations that aid in the dimensional synthesis of these mechanisms are developed and demonstrated through case studies. The design implications, limitations, and opportunities associated with regular cylindrical developable mechanisms are discussed through the lens of both an analytical and graphical methods.
Issue Section:
Design of Mechanisms and Robotic Systems
References
1.
Song
, X.
, Guo
, H.
, Liu
, S.
, Meng
, F.
, Chen
, Q.
, Liu
, R.
, and Deng
, Z.
, 2019
, “Cable-Truss Hybrid Double-Layer Deployable Mechanical Network Constructed of Bennett Linkages and Planar Symmetric Four-Bar Linkages
,” Mech. Mach. Theory
, 133
, pp. 459
–480
. 2.
Qi
, X.
, Huang
, H.
, Li
, B.
, and Deng
, Z.
, 2016
, “A Large Ring Deployable Mechanism for Space Satellite Antenna
,” Aerosp. Sci. Technol.
, 58
, pp. 498
–510
. 3.
Cheng
, P.
, Ding
, H.
, Cao
, W.-A.
, Gosselin
, C.
, and Geng
, M.
, 2021
, “A Novel Family of Umbrella-Shaped Deployable Mechanisms Constructed by Multi-Layer and Multi-Loop Spatial Linkage Units
,” Mech. Mach. Theory
, 161
, p. 104169
. 4.
Nelson
, T. G.
, Zimmerman
, T. K.
, Lang
, R. J.
, Magleby
, S. P.
, and Howell
, L. L.
, 2019
, “Developable Mechanisms on Developable Surfaces
,” Sci. Robot.
, 4
(27
), p. 5171
. 5.
Seymour
, K.
, Sheffield
, J.
, Magleby
, S. P.
, and Howell
, L. L.
, 2019
, “Cylindrical Developable Mechanisms for Minimally Invasive Surgical Instruments
,” ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Anaheim, CA
, Aug. 18–21
.6.
Greenwood
, J. R.
, Magleby
, S. P.
, and Howell
, L. L.
, 2019
, “Developable Mechanisms on Regular Cylindrical Surfaces
,” Mech. Mach. Theory
, 142
, p. 103584
. 7.
Struik
, D. J.
, 1961
, Lectures on Classical Differential Geometry
, Courier Corporation
, New York
.8.
Zimmerman
, T.
, 2018
, “A Definition and Demonstration of Developable Mechanisms
,” Master’s thesis, Brigham Young University, Provo, UT.9.
Hyatt
, L. P.
, Magleby
, S. P.
, and Howell
, L. L.
, 2020
, “Developable Mechanisms on Right Conical Surfaces
,” Mech. Mach. Theory
, 149
, p. 103813
. 10.
Butler
, J.
, Greenwood
, J.
, Howell
, L. L.
, and Magleby
, S.
, 2021
, “Limits of Extramobile and Intramobile Motion of Cylindrical Developable Mechanisms
,” ASME J. Mech. Rob.
, 13
(1
), p. 011024
. 11.
Woodland
, M.
, Hsiung
, M.
, Matheson
, E. L.
, Safsten
, C. A.
, Greenwood
, J.
, Halverson
, D. M.
, and Howell
, L. L.
, 2021
, “Analysis of the Rigid Motion of a Conical Developable Mechanism
,” ASME J. Mech. Rob.
, 13
(3
), p. 031008
. 12.
Butler
, J.
, Greenwood
, J.
, Howell
, L. L.
, and Magleby
, S.
, 2021
, “Bistability in Cylindrical Developable Mechanisms Through the Principle of Reflection
,” ASME J. Mech. Des.
, 143
(8
), p. 083302
. 13.
Sheffield
, J. L.
, Sargent
, B.
, and Howell
, L.
, 2022
, “Embedded Linear-Motion Developable Mechanisms on Cylindrical Developable Surfaces
,” ASME IDETC Design Conference
, St. Louis, MO
, Aug. 14–17
.14.
Ferguson
, E. S.
, 2021
, Kinematics of Mechanisms From the Time of Watt
, Good Press
, Boca Raton, FL
.15.
McCarthy
, J. M.
, and Soh
, G. S.
, 2010
, Geometric Design of Linkages
, Springer Science & Business Media
, New York
.16.
Hartenberg
, R.
, and Danavit
, J.
, 1964
, Kinematic Synthesis of Linkages
, McGraw-Hill
, New York
.17.
Uicker
, J. J.
, Pennock
, G. R.
, Shigley
, J. E.
, and Mccarthy
, J. M.
, 2003
, Theory of Machines and Mechanisms
, Vol. 768, Oxford University Press
, New York
.18.
Norton
, R. L.
, 2004
, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines
, McGraw-Hill Professional
, New York
.19.
Cleghorn
, W.
, and Dechev
, N.
, 2015
, Mechanics of Machines
, Oxford University Press
, Oxford
.20.
Angeles
, J.
, and Bai
, S.
, 2022
, Kinematics of Mechanical Systems: Fundamentals, Analysis and Synthesis
, Springer Nature
, New York
.21.
Hunt
, K. H.
, 1978
, Kinematic Geometry of Mechanisms
, Oxford University Press
, Oxford
.22.
Erdman
, A. G.
, and Gustafson
, J.
, 1977
, “Lincages: Linkage Interactive Computer Analysis and Graphically Enhanced Synthesis Package
,” American Society of Mechanical Engineers (Paper) (77-DET-5).
23.
Burmester
, L. E. H.
, 1888
, Lehrbuch der Kinematik: Für studirende der Maschinen-Technik, Mathematik und Physik geometrisch dargestellt. Die ebene Bewegung. Mit einem Atlas von 57 lithographirten Tafeln
, Vol. 1
, Felix
, Leipzig, Germany
.24.
Jiménez
, J.
, Alvarez
, G.
, Cardenal
, J.
, and Cuadrado
, J.
, 1997
, “A Simple and General Method for Kinematic Synthesis of Spatial Mechanisms
,” Mech. Mach. Theory
, 32
(3
), pp. 323
–341
.25.
Kinzel
, E. C.
, Schmiedeler
, J. P.
, and Pennock
, G. R.
, 2006
, “Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming
,” ASME J. Mech. Des.
, 128
(5
), pp. 1070
–1079
. 26.
Mirth
, J. A.
, 2012
, “The Application of Geometric Constraint Programming to the Design of Motion Generating Six-Bar Linkages
,” International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Chicago, IL
, Aug. 12–15
, Vol. 45035, American Society of Mechanical Engineers, pp. 1503
–1511
.27.
Mirth
, J. A.
, 2012
, “Parametric Modeling: A New Paradigm for Mechanisms Education?
” International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Chicago, IL
, Aug. 12–15
, Vol. 45035, American Society of Mechanical Engineers, pp. 1497
–1502
.28.
Zimmerman
, R. A.
, 2018
, “Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles
,” ASME J. Mech. Rob.
, 10
(2
), p. 025004
. 29.
Zimmerman
, R. A.
, 2013
, “Planar Linkage Synthesis for Rigid Body Guidance Using Poles and Rotation Angles
,” Volume 6A: 37th Mechanisms and Robotics Conference
, Portland, OR
, Aug. 4–7
, ASME, p. V06AT07A038.30.
Zimmerman
, R. A.
, 2014
, “Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles
,” Volume 5B: 38th Mechanisms and Robotics Conference
, Buffalo, NY
, Aug. 17–20
, ASME, p. V05BT08A086.31.
Zimmerman
, R. A.
, 2015
, “Planar Linkage Synthesis for Function Generation Using Poles and Rotation Angles
,” Volume 5B: 39th Mechanisms and Robotics Conference
, Boston, MA
, Aug. 2–5
, ASME, p. V05BT08A066.32.
Purwar
, A.
, Deshpande
, S.
, and Ge
, Q.
, 2017
, “Motiongen: Interactive Design and Editing of Planar Four-Bar Motions for Generating Pose and Geometric Constraints
,” ASME J. Mech. Rob.
, 9
(2
), p. 024504
. 33.
Freudenstein
, F.
, 1954
, Design of Four-Link Mechanisms
, Columbia University
, New York
.34.
Sandor
, G. N.
, 1959
, A General Complex-Number Method for Plane Kinematic Synthesis with Applications
, Columbia University
, New York
.35.
Kaufman
, R.
, 1978
, “Mechanism Design by Computer
,” Mach. Des.
, 50
(HS-025 808U
), pp. 94
–100
.36.
Erdman
, A. G.
, 1981
, “Three and Four Precision Point Kinematic Synthesis of Planar Linkages
,” Mech. Mach. Theory
, 16
(3
), pp. 227
–245
. 37.
Erdman
, A. G.
, Sandor
, G. N.
, and Kota
, S.
, 1997
, Mechanism Design: Analysis and Synthesis
, Prentice-Hall
, Upper Saddle River, NJ
.38.
Erdman
, A.
, Sandor
, G.
, and Kota
, S.
, 1984
, Advanced Mechanism Design: Analysis and Synthesis
, Prentice-Hall
, Upper Saddle River, NJ
.39.
Loerch
, R.
, Erdman
, A.
, Sandor
, G.
, and Midha
, A.
, 1976
, “Synthesis of Four Bar Linkages With Specified Ground Pivots
,” Proceedings of 4th Applied Mechanisms Conference
, Chicago, IL
, Nov. 3–5
, pp. 101
–106
.40.
Raghavan
, M.
, and Roth
, B.
, 1995
, “Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators
,” J. Vib. Acoust.
, 117
(B
), pp. 71
–79
.41.
Kimbrell
, J. T.
, 1991
, Kinematics Analysis and Synthesis
, McGraw-Hill Science, Engineering & Mathematics
, New York
.42.
Natesan
, A. K.
, 1994
, Kinematic Analysis and Syn thesis of Four-bar Mechanisms for Straight Line Coupler Curves
, Rochester Institute of Technology
, New York
.43.
Wu
, R.
, Li
, R.
, and Bai
, S.
, 2021
, “A Fully Analytical Method for Coupler-Curve Synthesis of Planar Four-Bar Linkages
,” Mech. Mach. Theory
, 155
, p. 104070
. 44.
Li
, X.
, Wei
, S.
, Liao
, Q.
, and Zhang
, Y.
, 2020
, “A Novel Analytical Method for Four-Bar Path Generation Synthesis Based on Fourier Series
,” Mech. Mach. Theory
, 144
, p. 103671
. 45.
Pickard
, J. K.
, Carretero
, J. A.
, and Merlet
, J.-P.
, 2020
, “Appropriate Synthesis of the Four-Bar Linkage
,” Mech. Mach. Theory
, 153
, p. 103965
. 46.
Hernández
, A.
, Munoyerro
, A.
, Urizar
, M.
, and Amezua
, E.
, 2021
, “Comprehensive Approach for the Dimensional Synthesis of a Four-Bar Linkage Based on Path Assessment and Reformulating the Error Function
,” Mech. Mach. Theory
, 156
, p. 104126
.47.
Hassanzadeh
, N.
, and Perez-Gracia
, A.
, 2022
, “Mixed Position and Twist Space Synthesis of 3R Chains
,” Robotics
, 11
(1
), p. 13
. 48.
Baigunchekov
, Z.
, Laribi
, M. A.
, Mustafa
, A.
, and Kassinov
, A.
, 2021
, “Kinematic Synthesis and Analysis of the Robomech Class Parallel Manipulator With Two Grippers
,” Robotics
, 10
(3
), p. 99
. 49.
Brake
, D. A.
, Hauenstein
, J. D.
, Murray
, A. P.
, Myszka
, D. H.
, and Wampler
, C. W.
, 2016
, “The Complete Solution of Alt-Burmester Synthesis Problems for Four-Bar Linkages
,” ASME J. Mech. Rob.
, 8
(4
), p. 041018
. 50.
Howell
, L. L.
, 2001
, Compliant Mechanisms
, John Wiley & Sons
, New York
.51.
Mironychev
, A.
, 2018
, “SAS and SSA Conditions for Congruent Triangles
,” J. Math. Syst. Sci.
, 8
(2
), pp. 59
–66
.52.
Hilbert
, D.
, 1902
, The Foundations of Geometry
, Open Court Publishing Company
, Chicago, IL
.53.
Naughton
, B. T.
, Preus
, R.
, Jimenez
, T.
, Whipple
, B.
, and Gentle
, J.
, 2020
, “Market Opportunities for Deployable Wind Systems for Defense and Disaster Response
,” Tech. rep., Sandia National Lab. (SNL-NM)
, Albuquerque, NM
.54.
Naughton
, B.
, Houchens
, B.
, Summerville
, B.
, Jimenez
, T.
, Preus
, R.
, Reen
, D.
, Gentle
, J.
, and Lang
, E.
, 2022
, “Design Guidelines for Deployable Wind Turbines for Defense and Disaster Response Missions
,” J. Phys.: Conf. Ser.
, Delft, The Netherlands
, June 1–3
.55.
Jimenez
, A.
, and Summerville
, B.
, 2022
, “Design Innovations for Deployable Wind Turbines
,” Military Engineer
, 114
(NREL/JA-7A40-79197), pp. 1
–3
.56.
Ibrahim
, A.
, Diso
, I.
, Auwal
, S.
, Ibrahim
, M. A.
, Dambatta
, M.
, and Ramesh
, S.
, 2020
, “Design of Self-Erecting Tower for a Wind Turbine
,” Int. J. Eng. Res. Technol.
, 6
(12
), pp. 63
–82
.57.
Campione
, G.
, Cannella
, F.
, Zizzo
, M.
, and Pauletta
, M.
, 2021
, “Buckling Strength of Steel Tube for Lifting Telescopic Wind Steel Tower
,” Eng. Fail. Anal.
, 121
, p. 105153
. 58.
Pantano
, A.
, Tucciarelli
, T.
, Montinaro
, N.
, and Mancino
, A.
, 2020
, “Design of a Telescopic Tower for Wind Energy Production With Reduced Environmental Impact
,” Int. J. Precis. Eng. Manuf. Green Technol.
, 7
, pp. 119
–130
. 59.
Winslow
, A. R.
, 2017
, Urban Wind Generation: Comparing Horizontal and Vertical Axis Wind Turbines
, Clark University
, Worcester, MA
. https://commons.clarku.edu/idce_masters_papers/12760.
Johari
, M. K.
, Jalil
, M.
, and Shariff
, M. F. M.
, 2018
, “Comparison of Horizontal Axis Wind Turbine (HAWT) and Vertical Axis Wind Turbine (VAWT)
,” Int. J. Eng. Technol.
, 7
(4.13
), pp. 74
–80
.61.
Gohil
, H.
, and Patel
, S.
, 2014
, “Design Procedure for Lenz Type Vertical Axis Wind Turbine for Urban Domestic Application
,” Int. J. Sci. Res. Dev.
, 2
(3
), pp. 2321
–0613
.62.
Elkhoury
, M.
, Kiwata
, T.
, and Aoun
, E.
, 2015
, “Experimental and Numerical Investigation of a Three-Dimensional Vertical-Axis Wind Turbine With Variable-Pitch
,” J. Wind Eng. Ind. Aerodyn.
, 139
, pp. 111
–123
. 63.
Bucur
, I.
, Malael
, I.
, Duran
, B.
, and Preda
, D.
, 2021
, “Drag Based Wind Turbine Lenz Type Manufacturing and Assembly
,” IOP Conf. Ser.: Mater. Sci. Eng.
, 1182
, p. 012009
.64.
Li
, S.
, Zhao
, J.
, Lu
, P.
, and Xie
, Y.
, 2010
, “Maximum Packing Densities of Basic 3D Objects
,” Chin. Sci. Bull.
, 55
(2
), pp. 114
–119
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