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)


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.


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



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


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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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