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A caveat concerning center of resistance

  1. Henning Dathe
  2. Hans Nägerl
  3. Dietmar Kubein-Meesenburg
  1. Biomechanics Group, Department of Orthodontics, Klinikum der Universität Göttingen, Göttingen, Germany
  1. Henning Dathe, Biomechanics Group, Department of Orthodontics, Klinikum der Universität Göttingen, Robert-Koch Str. 40, 37099 Göttingen, Germany. Email: hdathe1{at}gwdg.de

Abstract

The center of resistance is a concept in theoretical orthodontics used to describe tooth movement under loads. It is commonly used to qualitatively predict tooth movement without recourse to complex equations or simulations. We start with a survey of the historical origin of the technical term. After this, the periodontal ligament is idealized as a linear elastic suspension. The mathematical formalism of vector and tensor calculus will clarify our reasoning. We show that a point such as the center of resistance basically only exists in two dimensions or in very special symmetric spatial configurations. In three dimensions, a simple counterexample of a suspension without a center of resistance is given. A second more tooth-like example illustrates the magnitude of the effects in question in dentistry. In conclusion, the center of resistance should be replaced by a newer and wider mathematical concept, the “center of elasticity,” together with a limiting parameter, the “radius of resistance.”

Article Notes

  • Declaration of conflicting interests The authors declare that there is no conflict of interest.

  • Funding This study was supported by the German Research Foundation and the Open Access Publication Funds of the Göttingen University.

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This Article

  1. J Dent Biomech vol. 4 1758736013499770

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