A caveat concerning center of resistance.
A caveat concerning center of resistance.
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DOI：
10.1177/1758736013499770
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Kubein-Meesenburg D
中科院分区：
文献类型：
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作者：
Dathe H;Nägerl H;Kubein-Meesenburg D
阻力中心是理论正畸学中描述牙齿在载荷作用下运动的一个概念。它通常用于定性地预测牙齿运动，而不需要复杂的方程或模拟。我们先来调查一下这个术语的历史起源。在此之后，牙周韧带是理想的线性弹性悬架。向量和张量微积分的数学形式将阐明我们的推理。我们证明了像阻力中心这样的点基本上只存在于二维空间或非常特殊的对称空间构型中。在三维空间中，给出了无阻力中心悬架的一个简单反例。第二个更像牙齿的例子说明了在牙科中所讨论的影响的重要性。总之，阻力中心应该被一个更新、更广泛的数学概念“弹性中心”和一个极限参数“阻力半径”所取代。
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.”