Abstract The location of the terminal hinge axis of the temporomandibular joint is still a very wide-spread procedure in dentistry in order to replicate the movement in various articulator devices. Especially pantographic methods are claimed to provide accurate measurements and, additionally, are seen to be able to separate a pure rotation of the joint from a movement with an arbitrary combined shift and rotation. In the latter application, these methods were used in a lot of studies as a reference standard. The aim of this study was to analyze, whether common pantographic methods in general are able to distinguish between a pure rotation and a movement with rotational and translational portions. The mathematical proof of this analysis was done with theoretical kinematic considerations and compared with computer simulations. The results show for the first time that there exist combinations of rotational and translational movements of the temporomandibular joint which cannot be separated from pure rotational movements using actual pantographic methods. Even more, the consequence is a shifted location of the (combined) finite center (axis) of rotation in comparison to the true center (axis) of rotation: in case of a translational portion of only 1 mm, this is a displacement of around ±6 mm and, in case of 2 mm translation, a displacement of ±12 mm. This finding necessitates a critical reinterpretation of former studies using pantographic methods as a reference standard. Further, under some circumstances it may also affect the applicability of articulator concepts and the interpretation of functional signs.

中文翻译：

---

是否可以用普通的缩放方法检测颞下颌关节的真实旋转轴？基本运动学分析

摘要 颞下颌关节末端铰链轴的定位在牙科中仍然是一个非常广泛的程序，以复制各种咬合架装置中的运动。尤其是缩放方法被要求提供准确的测量，此外，被认为能够将关节的纯旋转与具有任意组合的移位和旋转的运动分开。在后者的应用中，这些方法在许多研究中被用作参考标准。本研究的目的是分析普通的缩放方法一般是否能够区分纯旋转和具有旋转和平移部分的运动。该分析的数学证明是在理论运动学考虑下完成的，并与计算机模拟进行了比较。结果首次表明颞下颌关节存在旋转和平移运动的组合，使用实际缩放方法无法与纯旋转运动分开。更重要的是，与真正的旋转中心（轴）相比，结果是（组合的）有限旋转中心（轴）的位置发生了偏移：在平移部分仅为 1 mm 的情况下，这是大约±6 mm，在平移 2 mm 的情况下，位移为 ±12 mm。这一发现需要对以前使用缩放方法作为参考标准的研究进行批判性的重新解释。此外，在某些情况下，它还可能影响咬合架概念的适用性和功能标志的解释。