Hocevar R A
Am J Orthod. 1981 Nov;80(5):457-77. doi: 10.1016/0002-9416(81)90243-8.
A simple force may cause translation and/or rotation of the tooth upon which it acts. The closer the line of force to the tooth's center of resistance, the greater is the proportion of translation relative to rotation, and vice versa. When a tooth is subjected to a tipping moment, strain is concentrated in the areas of the alveolar crest and root apex. This may explain how a light force can tip a tooth readily, while translation, involving a more even distribution of strain throughout the length of the root, requires more force with little or no moment. It is difficult to sustain a desired combination of rotational and translational movement over any significant distance. Couples induce rotation only. Couples and simple forces can be used in combinations to effect movements that are not possible with either one alone. Molars provide anchorage for incisor intrusion. This "vertical anchorage" can be reinforced by elastics producing moments opposite those produced by arch wire anchor bends. Calculation of the elastics' contribution provides an indication of the intrusive force that may be applied to incisors without reciprocal molar tipping. The common use of the term center of rotation in orthodontics may be inappropriate and/or confusing. It may be more accurate and straightforward to view most tooth movements as combinations of linear translation with rotation about the center of resistance.
一个简单的力可能会导致其所作用的牙齿发生平移和/或旋转。力线离牙齿的阻力中心越近，平移相对于旋转的比例就越大，反之亦然。当牙齿受到倾斜力矩时，应变集中在牙槽嵴和根尖区域。这或许可以解释为什么轻力能轻易使牙齿倾斜，而平移（涉及牙根全长上更均匀的应变分布）则需要更大的力且几乎没有力矩。在任何显著距离上维持期望的旋转和平移运动组合都很困难。力偶仅产生旋转。力偶和简单力可以组合使用，以实现单独使用任何一种都无法实现的运动。磨牙为切牙的压低提供支抗。这种“垂直支抗”可以通过产生与弓丝锚固弯曲所产生的力矩相反的力矩的弹力来加强。弹力贡献的计算提供了一个指标，表明在不引起磨牙反向倾斜的情况下可施加于切牙的压低力。正畸学中旋转中心这一术语的常用可能并不恰当和/或令人困惑。将大多数牙齿运动视为围绕阻力中心的线性平移与旋转的组合可能更准确和直接。
