A Compliant 5-bar Tristable Mechanism Utilizing Metamorphic Transformation

Conference paper


Compliant multistable mechanisms, which are capable of steadily staying at multiple distinct positions without power input, have many potential applications in switches, valves, closures, relays, statically-balanced mechanisms, reconfigurable robots, and large-displacement micro actuators. In this paper, we propose a new idea of utilizing metamorphic transformations to develop compliant multistable mechanisms. By distributing the prescribed stable equilibrium positions into different metamorphic working phases, the design of a compliant multistable mechanism can be greatly simplified. The idea is demonstrated by a tristable mechanism that can metamorphically transform from a compliant 5-bar mechanism into a compliant 4-bar mechanism in a certain range of motion. The kinetostatic solution of this tristable mechanism is formulated and the kinetostatic results confirm that the mechanism has two deflected stable equilibrium positions besides its initial assembly position, with one occuring in the 4-bar working phase and the other in the 5-bar working phase. Although the discussion is limited to a planar 5-bar mechanism, the idea of utilizing metamorphic transformations to achieve multistable behivors can surely be extended to other types of linkages.


Compliant 5-bar mechanism Multistable mechanism Tristable mechanism Metamorphic mechanism 



The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 50805110 and 51175396, and the program for new century excellent talents in university under Grant No. NCET-11-0689.


  1. 1.
    Howell LL (2001) Compliant mechanisms. Wiley, New YorkGoogle Scholar
  2. 2.
    Tolou M, Estevez P, Herder JL (2011) Collinear-type statically balanced compliant micro mechanism (SB-CMM): experimental comparison between pre-curved and straight beams. Proceedings of the ASME design engineering technical conferences & computers and information in engineering conference, 28–31 August 2011, Washington, DC, USA, DETC2011-47678Google Scholar
  3. 3.
    Chen G, Zhang S (2011) Fully-compliant statically-balanced mechanisms without prestressing assembly: concepts and case studies. Mech Sci 2(2):169–174CrossRefGoogle Scholar
  4. 4.
    Hafez M, Lichter MD, Dubowsky S (2003) Optimized binary modular reconfigurable robotic devices. IEEE-ASME T Mech 8(1):304–326Google Scholar
  5. 5.
    Pucheta MA, Cardona A (2010) Design of bistable compliant mechanisms using precision-position and rigid-body replacement methods. Mech Mach Theory 45(2):304–326MATHCrossRefGoogle Scholar
  6. 6.
    Gerson Y, Krylov S, Ilic B, Schreiber D (2012) Design considerations of a large-displacement multistable micro actuator with serially connected bistable elements. Finite Element Anal Des 49(1):58–69CrossRefGoogle Scholar
  7. 7.
    Oh YS, Kota S (2009) Synthesis of multistable equilibrium compliant mechanisms using combinations of bistable mechanisms. J Mech Design, 131:021002CrossRefGoogle Scholar
  8. 8.
    Jensen BD, Howell LL, Salmon LG (1999) Design of two-link, in-plane, bistable compliant micro-mechanisms. J Mech Des 121(3):416–423CrossRefGoogle Scholar
  9. 9.
    Jensen BD, Parkinson MB, Kurabayashi K, Howell LL, Baker MS (2001) Design optimization of a fully-compliant bistable micro-mechanism. Proceedings of ASME IMECE, vol 2, pp 2931–2937, 11–16 Novemb, New York, USAGoogle Scholar
  10. 10.
    Masters ND, Howell LL (2003) A self-retracting fully compliant bistable micromechanism. J Microelectromech Syst 12:273–280CrossRefGoogle Scholar
  11. 11.
    Jensen BD, Howell LL (2003) Identification of compliant pseudo-rigid-body mechanism configurations resulting in bistable behavior. J Mech Des 125:701–708CrossRefGoogle Scholar
  12. 12.
    Jensen BD, Howell LL (2004) Bistable configurations of compliant mechanisms modeled using four links and translational joints. J Mech Des 126:657–666CrossRefGoogle Scholar
  13. 13.
    Qiu J, Lang JH, Slocum AH (2004) A curved-beam bistable mechanism. J Microelectromech Syst 13(2):137–146CrossRefGoogle Scholar
  14. 14.
    Wilcox DL, Howell LL (2005) Fully compliant tensural bistable micromechanisms (FTBM). J Microelectromech Syst 14(6):1223–1235CrossRefGoogle Scholar
  15. 15.
    Sönmez Ü, Tutum CC (2008) A compliant bistable mechanism design incorporating elastica buckling beam theory and pseudo-rigid-body model. J Mech Des 130(4):042304CrossRefGoogle Scholar
  16. 16.
    Smith CL, Lusk CP (2011) Modeling and parameter study of bistable spherical compliant mechanisms. Proceedings of ASME IDETC/CIE 2011, 28–31 August, Washington, DC, USA, DETC2011-47397Google Scholar
  17. 17.
    Pendleton TM, Jensen BD (2007) Development of a tristable compliant mechanism. Proceedings of 12TH IFToMM world congress, A835, 18–21 June, Besancon, FranceGoogle Scholar
  18. 18.
    Chen G, Aten QT, Zirbel S, Jensen BD, Howell LL (2010) A tristable mechanism configuration employing orthogonal compliant mechanisms. J Mech Robot-T ASME 2(1):014501CrossRefGoogle Scholar
  19. 19.
    Halverson PA, Howell LL, Magleby SP (2010) Tension-based multi-stable compliant rolling-contact elements. Mech Mach Theory 45(2):147–156MATHCrossRefGoogle Scholar
  20. 20.
    Chen G, Gou Y, Zhang A (2011) Synthesis of compliant multistable mechanisms through use of a single bistable compliant mechanism. J Mech Des 133(8):081007CrossRefGoogle Scholar
  21. 21.
    Han JS, Muller C, Wallrabe U, Korvink JG (2007) Design, simulation, and fabrication of a quadstable monolithic mechanism with X- and Y-directional bistable curved beams. J Mech Des 129(11):1198–1203CrossRefGoogle Scholar
  22. 22.
    Chen G, Wilcox DL, Howell LL (2009) Fully compliant double tensural tristable micromechanisms (DTTM). J Micromech Microeng 19(2):025011CrossRefGoogle Scholar
  23. 23.
    Pham H-T, Wang D-A (2011) A quadristable compliant mechanism with a bistable structure embedded in a surrounding beam structure. Sensor Actuat A-Phys 167(2):438–448CrossRefGoogle Scholar
  24. 24.
    Dai JS, Jones JR (1999) Mobility in metamorphic mechanisms of foldable/erectable kinds. J Mech Des 121(3):375–382CrossRefGoogle Scholar
  25. 25.
    Dai JS, Jones JR (2005) Matrix representation of topological changes in metamorphic mechanisms. J Mech Des 127(7):837–840CrossRefGoogle Scholar
  26. 26.
    Lan ZH, Du R (2008) Representation of topological changes in metamorphic mechanisms with matrices of the same fimension. J Mech Des 130(7):074501CrossRefGoogle Scholar
  27. 27.
    Zhang L, Wang D, Dai JS (2008) Biological modeling and evolution based synthesis of metamorphic mechanisms. J Mech Des 130(7):072303CrossRefGoogle Scholar
  28. 28.
    Zhang K, Dai JS, Fang Y (2010) Topology and constraint analysis of phase change in the metamorphic chain and its evolved mechanism. J Mech Des 132(12):121001CrossRefGoogle Scholar
  29. 29.
    Parise JJ, Howell LL, Magleby SP (2000) Ortho-planar mechanisms. Proceedings of the 26th biennial mechanisms and robotics conference, Baltimore, MD, paper no. DETC2000/MECH-14193Google Scholar
  30. 30.
    Carroll DW, Magleby SP, Howell LL, Todd RH, Lusk CP (2005) Simplified manufacturing through a metamorphic process for compliant ortho-planar mechanisms. Proceedings of ASME IMECE, Oriando, FL, USA, 5–11, Novemb, IMECE2005-82093Google Scholar
  31. 31.
    Yang Y, Ding X, Dai J (2007) Design and analysis of an umbrella foldable complant metamorphic mechanism. Acta Aeronaut Astronaut Sinica 28(4):1014–1017 (in Chinese)Google Scholar
  32. 32.
    Li D, Zhang Z, Chen G (2011) Structure synthesis of compliant metamorphic mechanisms based on adjacency matrix operations. Chin J Mech Eng-En 24(4):522–528CrossRefGoogle Scholar
  33. 33.
    Aten QT, Zirbel S, Jensen BD, Howell LL (2011) A numerical method for position analysis of compliant mechanisms with more degrees of freedom than inputs. J Mech Des 133(6):061009CrossRefGoogle Scholar
  34. 34.
    Her I, Midha A (1987) A compliance number concept for compliant mechanisms, and type synthesis. J Mech Transm-T ASME 109(3):348–357CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.School of MechatronicsXidian UniversityXi’anChina

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