A Fast Branch-and-Prune Algorithm for the Position Analysis of Spherical Mechanisms

  • Arya ShabaniEmail author
  • Soheil SarabandiEmail author
  • Josep M. PortaEmail author
  • Federico ThomasEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Different branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.


multi-affine polynomials parallel spherical robots forward kinematics position analysis branch-and-prune algorithms 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut de Robotica i Informatica IndustrialCSIC-UPCBarcelonaSpain

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