The articulators presently used in dentistry are the results of observations, experiences and researches on human mandibular motion. It would therefore be advantageous to analyze kinematically the motion and the mechanism of existing articulators, for the following reasons:
1. Articulators themselves would contain some truth of mandibular motion.
2. Articulators have the advantage, that they are mechanically clear, easily accessible, adjustable and reproducible.
3. As articulators have the accepted objective in clinical use, the kinematic analysis and the verification of motion of the articulators are important as well as that of the motion of the mandible.
A theorem in kinematics was introduced for the basis of derivation of fundamental expressions of the motion of articulators. It includes Euler's theorem which says that; an arbitrary three dimentional displacement of a rigid body can be. expressed by translation of an arbitrary fixed point on the moving rigid body and a rotation around that point.
The arbitrarily fixed point on the moving rigid body described in the above theorem can be the middle point of the inter-condylar axis in the case of protrusive movement and the opening and closing motion of the mandible, or the kinematic center of the condyle on the working side in the case of the lateral movement of the mandible.
Based upon the theorem, the fundamental expressions for the motion of articulators was derived in a.simple and clear form. In the process of arriving at the result, an approximation had been applied in view of the minute amount of mandibular rotational movement within tooth contact conditions. The approximation became valid, by investigating the secondary degree of minutae.
In addition, a comparison of the accuracies was made between Arcon and Condylar types of articulators. It is pointed out that the problem of handling articulators, for example in the idling movements during lateral movements of Condylar type articulators, is more important than the difference of type in view of accuracy.
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