Structural and Multidisciplinary Optimization

, Volume 37, Issue 6, pp 645–651 | Cite as

Enumeration of optimal pin-jointed bistable compliant mechanisms with non-crossing members

  • M. Ohsaki
  • N. Katoh
  • T. Kinoshita
  • S. Tanigawa
  • D. Avis
  • I. Streinu
Brief Note

Abstract

An optimization approach is presented for enumerating pin-jointed bistable compliant mechanisms. In the first stage, the statically determinate trusses with non-crossing members containing a given set of nodes and some pre-defined members are regarded as minimally rigid framework or a Laman framework, and are enumerated without repetitions by the graph enumeration algorithm. In the second stage, the nodal locations and the cross-sectional areas are optimized under mechanical constraints, where the snapthrough behavior is extensively utilized to produce a pin-jointed bistable compliant mechanism. In the numerical examples, many bistable compliant mechanisms are generated to show the effectiveness of the proposed method.

Keywords

Bistable structure Compliant mechanism Minimally rigid framework Snapthrough 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arora JS, Tseng CH (1987) Idesign user’s manual, ver. 3.5. Technical report, Optimal Design Laboratory, The University of IowaGoogle Scholar
  2. Avis D, Fukuda K (1996) Reverse search for enumeration. Discrete Appl Math 65(1–3):21–46MATHCrossRefMathSciNetGoogle Scholar
  3. Avis D, Katoh N, Ohsaki M, Streinu I, Tanigawa S (2007) Enumerating non-crossing minimally rigid frameworks. Graphs Comb 23(Suppl):117–134MATHCrossRefMathSciNetGoogle Scholar
  4. Avis D, Katoh N, Ohsaki M, Streinu I, Tanigawa S (2008) Enumerating constrained non-crossing minimally rigid frameworks. Discrete Comput Geom (published online) (also available at: http://arxiv.org/abs/math/0608102v2)
  5. Bruns TE, Sigmund O (2004) Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng 193:3973–4000MATHCrossRefMathSciNetGoogle Scholar
  6. Graver J, Servatius B, Servatius H (1993) Combinatorial rigidity. Grad Stud Math 2Google Scholar
  7. Kawamoto A, Bendsøe MP, Sigmund O (2004) Planar articulated mechanism design by graph theoretical enumeration. Struct Optim 27:295–299CrossRefGoogle Scholar
  8. Klarbring A (1988) On discrete and discretized non-linear elastic structures in unilateral contact (stability, uniqueness and variational principles). Int J Solids Struct 24(5):459–479MATHCrossRefMathSciNetGoogle Scholar
  9. Larsen UD, Sigmund O, Bouswstra S (1996) Design and fabrication of compliant micromechanisms and structures with negative poisson’s ratio. In Proc. IEEE 9th annual int. workshop on micro electro mech. sys. An investigation of micro structures, sensors, actuators, machines and systems. IEEE, San Diego, CA, pp 365–371Google Scholar
  10. Mankame ND, Ananthasuresh GK (2004a) Topology optimization for synthesis of contact-aided compliant mechanisms using regularized contact modeling. Comput Struct 82:1267–1290CrossRefGoogle Scholar
  11. Mankame ND, Ananthasuresh GK (2004b) Topology synthesis of electrothermal compliant mechanisms using line elements. Struct Multidiscipl Optim 26:209–218CrossRefGoogle Scholar
  12. Masters ND, Howell LL (2003) A self-retracting fully compliant bistable micromechanism. J MEMS 12:273–280Google Scholar
  13. Nishiwaki S, Min S, Yoo J, Kikuchi N (2001) Optimal structural design considering flexibility. Comput Methods Appl Mech Eng 190:4457–4504CrossRefMathSciNetGoogle Scholar
  14. Ohsaki M (2005) Design sensitivity analysis and optimization for nonlinear buckling of finite-dimensional elastic conservative structures. Comput Methods Appl Mech Eng 194:3331–3358MATHCrossRefGoogle Scholar
  15. Ohsaki M, Ikeda K (2007) Stability and optimization of structures – generalized sensitivity analysis. Mechanical engineering series. Springer, New YorkMATHGoogle Scholar
  16. Ohsaki M, Nishiwaki S (2005) Shape design of pin-jointed multistable compliant mechanism using snapthrough behavior. Struct Optim 30:327–334CrossRefGoogle Scholar
  17. Pedersen CBW, Buhl T, Sigmund O (2002) Topology optimization of large-displacement compliant mechanisms. Int J Numer Methods Eng 44:1215–1237Google Scholar
  18. Prasad J, Diaz AR (2006) Synthesis of bistable periodic structures using topology optimization and a genetic algorithm. J Mech Des 128:1298–1306CrossRefGoogle Scholar
  19. Saxena A, Ananthasuresh GK (2003) A computational approach to the number synthesis of linkages. J Mech Des 125:110–118CrossRefGoogle Scholar
  20. Tuttle ER, Peterson SW, Titus JE (1989) Enumeration of basic kinematic chains using the theory of finite groups. J Mech Transm Autom Des 111:498–503CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • M. Ohsaki
    • 1
  • N. Katoh
    • 1
  • T. Kinoshita
    • 1
  • S. Tanigawa
    • 1
  • D. Avis
    • 2
  • I. Streinu
    • 3
  1. 1.Department of Architecture and Architectural EngineeringKyoto UniversityKyotoJapan
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada
  3. 3.Department of Computer ScienceSmith CollegeNorthamptonUSA

Personalised recommendations