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Introducing Distance Restrictions in the Deformed Position Problem

  • I. Fernández de BustosEmail author
  • V. García Marina
  • M. Abásolo
  • R. Avilés
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 24)

Abstract

The deformed position problem is the basis for methods dealing both with synthesis and analysis of mechanisms. This paper analyzes how nonlinear restrictions can be introduced into the method so that it can be used to represent restrictions in the distance between two arbitrary points in the mechanism. The applications of this algorithm range from designing grippers to defining the required behavior of discrete elements such as springs or dampers. In order to introduce these restrictions, the original method has undergone heavy modifications to include simple Karush-Kuhn-Tucker systems along with saddle-point avoidance and under determined Hessian matrices. Two possible variants of the method were studied. Numerical results of the method have been included to demonstrate the efficiency of the alternatives offered by the method.

Keywords

Optimization Mechanism synthesis and analysis Karush-Kuhn-Tucker systems Nonlinear restrictions 

Notes

Acknowledgments

The authors wish to thank the Spanish Ministry of Science and Innovation for their support of this research (DPI grant).

References

  1. 1.
    Avilés R, Vallejo J, Aguirrebeitia J, Fernández de Bustos I, Ajuria J (2010) Optimization of linkages for generalized rigid-body guidance synthesis based on finite element models. Finite Elem Anal Des 46(9):721–731CrossRefMathSciNetGoogle Scholar
  2. 2.
    Agirrebeitia J, Avilés R, Fernández de Bustos I, Ajuria G (2008) A new APF strategy for path planning in environments with obstacles. Mech Mach Theor 40:645–658CrossRefGoogle Scholar
  3. 3.
    Nocedal J, Wright S (2006) Numerical optimization. Springer Series in Operations Research and Financial Engineering, 2nd (ed)Google Scholar
  4. 4.
    Golub GH, van Loan CF (1989) Matrix computations Johns Hopkins studies in the mathematical sciences, 3rd edn. Johns Hopkins University Press, BaltimoreGoogle Scholar
  5. 5.
    Fernández de Bustos I, Aguirrebeitia J, Ajuria G, García Marina V (2013) Rotation schemes for full pivoting factorization of indefinite symmetric matrices. Congr Numer Meth Eng 2013. Bilbao, 25–28 JuneGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • I. Fernández de Bustos
    • 1
    Email author
  • V. García Marina
    • 1
  • M. Abásolo
    • 1
  • R. Avilés
    • 1
  1. 1.University of the Basque CountryBilbaoSpain

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