Certified Kinematics Solution of 2-DOF Planar Parallel Continuum Mechanisms

  • Oscar Altuzarra
  • Jean Pierre MerletEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Kinematics position problems in planar parallel continuum mechanisms, whose elements are elastic rods undergoing nonlinear large deformations, are ruled by a system of nonlinear differential equations. Under some conditions, those rods can be modelled as Kirchhoff rods whose equations can be solved using elliptic integrals. The resolution has to be numerical, and two approaches for that goal are shown in this paper. On the one hand, a method based in residuals evaluation finds multiple solutions at good computational rates but with no formal guarantee on the solving of all solutions. On the other hand, a procedure based on Interval Analysis constitutes a certified solution at a higher computational cost that can be improved with a Newton scheme.


Kirchhoff rods Kinematics numerical solver interval analysis elliptic integrals 


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The authors received financial support from the Spanish Government (DPI2015-64450-R) and the Regional Government of the Basque Country (Project IT949-16).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of the Basque Country UPV/EHUBilbaoSpain
  2. 2.HEPHAISTOS project, Université Cȏte d’Azur, INRIASophia-AntipolisFrance

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