Research Papers

Synthesis and Design of a One Degree-of-Freedom Planar Deployable Mechanism With a Large Expansion Ratio

[+] Author and Article Information
David St-Onge

Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: david.st-onge.2@ulaval.ca

Clément Gosselin

Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: gosselin@gmc.ulaval.ca

1Corresponding author.

Manuscript received June 25, 2015; final manuscript received November 9, 2015; published online January 18, 2016. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 8(2), 021025 (Jan 18, 2016) (9 pages) Paper No: JMR-15-1156; doi: 10.1115/1.4032101 History: Received June 25, 2015; Revised November 09, 2015

This paper presents a new design of a deployable one degree-of-freedom (DOF) mechanism. Polygonal rigid-link designs are first investigated. Then, belt-driven links are considered in order to maximize the expansion ratio while avoiding flattened ill-conditioned parallelogram configurations. The planar basic shape of the proposed design is a triangle. Hence, virtually any planar or spatial surface can be created by assembling such faces. For architecture and telescopic applications, the cupola assembly is investigated. The advantages of this approach are discussed, and the scalability is demonstrated. Finally, a prototype is built for illustration purposes.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Ishii, K. , 2000, Structural Design of Retractable Roof Structures, WIT Press, Southampton, UK.
Gantes, C. , 2001, Deployable Structures: Analysis and Design, WIT Press, New York.
Imbriale, W. A. , Gao, S. , and Boccia, L. , 2012, Space Antenna Handbook, Wiley, Chichester, UK.
Pellegrino, S. , 2001, Deployable Structures, Vol. 412, Springer-Verlag, Wien, Austria.
Hoberman, C. , 1991, “ Radial Expansion/Retraction Truss Structures,” U.S. Patent No. 5,024,031.
Wei, G. , and Dai, J. S. , 2012, “ Synthesis of a Family of Regular Deployable Polyhedral Mechanisms (DPMs),” Latest Advances in Robot Kinematics, Springer, New York, pp. 123–130.
Korkmaz, K. , 2005, “ Generation of a New Type of Architectural Umbrella,” Int. J. Space Struct., 20(1), pp. 35–41. [CrossRef]
Lopatina, A. , and Morozov, E. , 2009, “ Modal Analysis of the Thin-Walled Composite Spoke of an Umbrella-Type Deployable Space Antenna,” Compos. Struct., 88(1), pp. 46–55. [CrossRef]
Wei, X.-Z. , Yao, Y.-A. , Tian, Y.-B. , and Fang, R. , 2006, “ A New Method of Creating Expandable Structure for Spatial Objects,” Proc. Inst. Mech. Eng., Part C, 220(12), pp. 1813–1818. [CrossRef]
Kiper, G. , Soylemez, E. , and Kisisel, A. O. , 2008, “ A Family of Deployable Polygons and Polyhedra,” Mech. Mach. Theory, 43(5), pp. 627–640. [CrossRef]
Agrawal, S. , and Kumar, S. , 2002, “ Polyhedral Single Degree-of-Freedom Expanding Structures: Design and Prototypes,” ASME J. Mech. Des., 124(3), pp. 473–478. [CrossRef]
Kovacs, F. , Tarnai, T. , Fowler, P. , and Guest, S. , 2004, “ A Class of Expandable Polyhedral Structures,” Int. J. Solids Struct., 41(3–4), pp. 1119–1137. [CrossRef]
Wohlhart, K. , 1995, “ New Overconstrained Spheroidal Linkages,” 9th World Congress on the Theory of Machines and Mechanism, Milan, Italy, Aug. 29–Sept. 5, Vol. 1, pp. 149–154.
Gosselin, C. , and Gagnon-Lachance, D. , 2006, “ Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces,” Proc. Inst. Mech. Eng., Part C, 220(7), p. 1011. [CrossRef]
Wohlhart, K. , 2008, “ Double-Ring Polyhedral Linkages,” First Conference on Interdisciplinary Applications in Kinematics, Lima, Perú, Jan. 9–11, pp. 1–17.
Phillips, J. , 1984/1990, Freedom Machinery, Vol. 1, Cambridge University Press, Cambridge, UK.
Guest, S. , and Fowler, P. , 2005, “ A Symmetry-Extended Mobility Rule,” Mech. Mach. Theory, 40(9), pp. 1002–1014. [CrossRef]
Loeb, A. , 1991, Space Structures, Birkhauser, Basel, Germany.
Gogu, G. , 2005, “ Chebyshev-Grübler-Kutzbachs Criterion for Mobility Calculation of Multi-Loop Mechanisms Revisited Via Theory of Linear Transformations,” Eur. J. Mech. A/Solids, 24(3), pp. 427–441. [CrossRef]
Hartenberg, R. , and Denavit, J. , 1964, Kinematic Synthesis of Linkages, McGraw-Hill, New York.
Ballia, S. S. , and Chanda, S. , 2002, “ Transmission Angle in Mechanisms (Triangle in Mech),” Mech. Mach. Theory, 37(2), pp. 175–195. [CrossRef]
Tao, D. , 1964, Applied Linkage Synthesis, Addison-Wesley, Reading, MA.
Gosselin, C. M. , Sefrioui, J. , and Richard, M. J. , 1992, “ Solutions polynomiales au problème de la cinématique directe des manipulateurs parallèles plans à trois degrés de liberté,” Mech. Mach. Theory, 27(2), pp. 107–119. [CrossRef]
Birglen, L. , Laliberté, T. , and Gosselin, C. , 2008, Underactuated Robotic Hands, Vol. 40, Springer-Verlag, Wien, Austria.
St-Onge, D. , and Gosselin, C. , 2014, “ Deployable Mechanisms for Small to Medium-Sized Space Debris Removal,” 65th International Astronautical Congress, (IAC-14), Space Debris Symposium, Toronto, Canada, Sept. 29–Oct. 3, p. 11.
Li, J. , Yan, S. , Guo, F. , and Guo, P. , 2013, “ Effects of Damping, Friction, Gravity, and Flexibility on the Dynamic Performance of a Deployable Mechanism With Clearance,” J. Mech. Eng. Sci., 227(8), pp. 1–13.
Wohlhart, K. , 2007, “ Cupola Linkages,” 12th IFToMM World Congress, Besançon, France, June 18–21, pp. 319–324.
Posamentier, A. S. , 2012, The Glorious Golden Ratio, Prometheus Books, Amherst, NY.
Wei, G. , and Dai, J. , 2014, “ Reconfigurable and Deployable Platonic Mechanisms With a Variable Revolute Joint,” Advances in Robot Kinematics, Springer, Cham, Switzerland, pp. 485–495.
Laliberté, T. , Gosselin, C. , and Côté, G. , 2001, “ A Rapid Prototyping Framework for Fast and Cost-Effective Design of Robotic Mechanism Prototypes,” IEEE Rob. Autom. Mag., 8(3), pp. 43–52. [CrossRef]
Hongwei, G. , Jing, Z. , Rongqiang, L. , and Zongquan, D. , 2013, “ Effects of Joint on Dynamics of Space Deployable Structure,” Chin. J. Mech. Eng., 26(5), pp. 861–872. [CrossRef]
Britvec, S. , 1995, Stability and Optimization of Flexible Space Structures, Birkhauser, Basel, Germany.


Grahic Jump Location
Fig. 3

Schematic representation of a deployable leg with large expansion ratio and compact design

Grahic Jump Location
Fig. 4

Retracted triangular 1DOF deployable mechanism: (a) one stage per leg from Ref. [14] and (b) three stages per leg optimized

Grahic Jump Location
Fig. 2

Schematic representation of a triangular face from Ref.[14]

Grahic Jump Location
Fig. 1

Deployment of an icosahedron with articulated faces (from Ref. [14])

Grahic Jump Location
Fig. 5

Velocity transmission ratio for all deployment positions for the schematic of Fig. 3 and the geometry of Fig. 4(b)

Grahic Jump Location
Fig. 6

Transmission angles and kinematic loops. The parallelogram included in the actuation module is not highlighted.

Grahic Jump Location
Fig. 12

Geometric representation of the retracted radial lengthHR (a) and the deployed radial length HD (b) defined in Eqs. (11) and (12)

Grahic Jump Location
Fig. 8

Transmission angles throughout a complete deployment

Grahic Jump Location
Fig. 9

Equivalence between the belt-driven and the rigid-link mechanisms

Grahic Jump Location
Fig. 10

Belt-driven mechanism (belts are represented with dotted lines)

Grahic Jump Location
Fig. 11

Virtual triangle limits: (a) correct and (b) incorrect (assuming a spatial arrangement of neighboring triangles)

Grahic Jump Location
Fig. 13

Expansion ratio as a function of the number of stages for hT=90 mm and w=17 mm

Grahic Jump Location
Fig. 14

Expansion ratio as a function of the link thickness for n=5 and ht=90 mm

Grahic Jump Location
Fig. 15

Expansion ratio as a function of the radial length of the inner triangle for w=17 mm and n=5

Grahic Jump Location
Fig. 16

Expansion ratio RP as a function of the length of the first link l1 for different values of the number of links n with a link width of 60 mm. Drop to zero occurs when the mechanism cannot fit in its retracted allowed space for further increase ofli.

Grahic Jump Location
Fig. 19

Dual-phase rotary joint: (a) initial state, (b) about to release the first axis, (c) held together with magnet, and (d) second rotation axis



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In