Advertisement

Multibody System Dynamics

, Volume 31, Issue 3, pp 241–256 | Cite as

Unified mechanism synthesis method of a planar four-bar linkage for path generation employing a spring-connected arbitrarily sized rectangular block model

  • Bum Seok Kim
  • Hong Hee Yoo
Article

Abstract

In the present study, a unified mechanism synthesis method that carries out type and dimensional syntheses simultaneously is proposed to solve path generation synthesis of a planar four-bar linkage. A spring-connected arbitrarily sized rectangular block model is introduced and an optimization problem using the block model is formulated. Several path generation synthesis problems are successfully solved with the proposed method. It is verified that the proposed method is computationally more efficient than the previous method employing a constant size block model. Furthermore, the proposed method is shown to solve some path synthesis problems that could not be solved by the previous method. Finally, an index to define the level of difficulty of a path generation synthesis problem is proposed, and the index limit value of path generation problems that can be solved by the proposed method is obtained.

Keywords

Unified mechanism synthesis Path generation Spring-connected arbitrarily sized rectangular block model Level of difficulty index 

Notes

Acknowledgements

This work was supported by the Second Brain Korea Project 21 in 2012.

References

  1. 1.
    Hartenberg, R.S., Denavit, J.: Kinematic Synthesis of Linkages. McGraw-Hill, New York (1964) Google Scholar
  2. 2.
    Erdman, A.G.: Modern Kinematics: Developments in the Last Forty Years. Wiley, New York (1992) Google Scholar
  3. 3.
    Erdman, A.G., Sandor, G.N., Kota, S.: Mechanism Design: Analysis and Synthesis. Prentice Hall, Englewood Cliffs (2001) Google Scholar
  4. 4.
    Root, R.R., Ragsdell, K.M.: A survey of optimization methods applied to the design of mechanisms. J. Eng. Ind. 98(3), 1036–1041 (1976) CrossRefGoogle Scholar
  5. 5.
    Hansen, J.M.: Synthesis of mechanisms using time-varying dimensions. Multibody Syst. Dyn. 7(1), 127–144 (2002) CrossRefMATHGoogle Scholar
  6. 6.
    Sancibrian, R., Viadero, F., Garcia, P., Fernandez, A.: Gradient-based optimization of path synthesis problems in planar mechanisms. Mech. Mach. Theory 39(8), 839–856 (2004) CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Shiakolas, P.S., Koladiya, D., Kebrle, J.: On the optimum synthesis of six-bar linkages using differential evolution and the geometric centroid of precision positions technique. Mech. Mach. Theory 40(3), 319–335 (2005) CrossRefMATHGoogle Scholar
  8. 8.
    Saxena, A.: Synthesis of compliant mechanisms for path generation using genetic algorithm. J. Mech. Des. 127(4), 745–752 (2005) Google Scholar
  9. 9.
    Vasiliu, A., Yannou, B.: Dimensional synthesis of planar mechanisms using neural networks: application to path generator linkages. Mech. Mach. Theory 36(2), 299–310 (2001) CrossRefMATHGoogle Scholar
  10. 10.
    Saxena, A., Ananthasuresh, G.K.: A computational approach to the number of synthesis of linkages. J. Mech. Des. 125(1), 110–118 (2003) Google Scholar
  11. 11.
    Sedlaczek, K., Gaugele, T., Eberhard, P.: Topology optimized synthesis of planar kinematic rigid body mechanisms. In: Multibody Dynamics ECCOMAS Thematic Conference, Madrid, Spain, 21–24 June, 2005 Google Scholar
  12. 12.
    Pucheta, M.A., Cardona, A.: Topological and dimensional synthesis of planar linkages for multiple kinematic tasks. Multibody Syst. Dyn. 29(2), 189–211 (2013). doi: 10.1007/s11044-011-9294-3 CrossRefMathSciNetGoogle Scholar
  13. 13.
    Kim, Y.Y., Jang, G.W., Park, J.H., Hyun, J.S., Nam, S.J.: Automatic synthesis of a planar linkage mechanism with revolute joints by using spring-connected rigid block models. J. Mech. Des. 129(9), 930–940 (2007) Google Scholar
  14. 14.
    Lewis, R.M., Torczon, V.: A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J. Optim. 12(4), 1075–1089 (2002) CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mechanical EngineeringHanyang UniversitySeoulSouth Korea

Personalised recommendations