Head movement dynamics constrained by Fick Gimbals

Indika B. Wijayasinghe, Bijoy K. Ghosh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Human head can be modeled as a perfect sphere with rotations actuated by external torques. Orientation of the head can be designated by an axis and an angle describing counterclockwise rotation required to arrive at that orientation starting from an initial primary orientation. This axis of orientation is governed by a law proposed in the 19th century by Donders and subsequently by Listing, that essentially restricts the axis to lie in a surface. We define a suitable Riemannian metric on the space of orientations and head movement trajectories are obtained by solving the associated Euler Lagrange's equation. Various choices of the Donders' surface would dictate different trajectories that connect two orientations of the head. This paper explores a choice of Donders' surface derived from Fick Gimbals, wherein the line between the two eyes remains horizontal, as the head moves. Originally, Fick had studied such head movements using a gimbal - hence the name. Various modifications of the Fick gimbal system have also been considered.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
StatePublished - 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670


  • Donders' surface
  • Fick gimbals
  • Geodesics
  • Head movement
  • Potential control


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