title: A caveat concerning center of resistance.
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."
authors.affiliation: Biomechanics Group, Department of Orthodontics, Klinikum der Universität Göttingen, Göttingen, Germany.
authors.forename: Henning
authors.initials: H
authors.lastname: Dathe
authors.forename: Hans
authors.initials: H
authors.lastname: Nägerl
authors.forename: Dietmar
authors.initials: D
authors.lastname: Kubein-Meesenburg
keywords: Center of resistance; center of elasticity; counterexample; radius of resistance; tooth support model
references.citation: Am J Orthod Dentofacial Orthop. 1991 Apr;99(4):337-45
references.pmid: 2008893