Position of an arbitrary hinge axis obtained by means of an ear-bow with a sliding intercondylar axis mechanism was compared with that of true hinge axis.
Ten patients without any clinically significant symptoms of occlusion were selected as the subjects. Face-bow transfers employing arbitrary hinge axis and true hinge axis were performed, and maxillary stone casts were mounted on an articulator, respectively. Position of the maxillary stone cast oriented with arbitrary hinge axis was determined in comparison with that oriented with true hinge axis, and dimensional discrepancy between those was evaluated.
Results are as follows:
1) Arbitrary hinge axis obtained by means of an ear-bow had average dimensional discrepancy of 6.05 mm to terminal hinge axis. 60 percents of the subjects have discrepancy less than 5 mm.
2) Arbitrary hinge axis reproduced on an articulator tends to be located backward and downward. This is considered due to illf itting of the ear-piece to the auditory meatus.
3) There was no indication that the reference pin index depressed the accuracy of reproducibility of opening and closing axis.

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The fundamental expressions had been derived from the previous report in the form of being applicable to the motion of articulators in general. By applying them, the practical expressions for the motion of arbitrary fixed point on the maxillary frame, in reference to coordinates fixed on the mandibular frame, were derived from opening and closing motion, protrusive motions, left and right lateral motions respectively.
As the mathematical expressions, which were derived from this study, are based upon Euler's theorem, those expressions are justified in principle and are simple in their form, Only one variable is included in the practical expressions for opening and closing motion. This means the number of the degree of freedom is one during the motion. And two variables are included in the practical exepressions for protrusive motion, left and right lateral motions respectively. This comes from the fact that the number of the degree of freedom is two during the respctive motion.
Having applied these results to the articulator with incisal table, it is shown that frontal inclination and horizontal angle of lateral incisal path are both determined automatically, by settling sagittal inclination and horizontal angle of lateral condylar path and sagittal inclination of lateral incisal path. Thus the trough-like form of the incisal table can be calculated. This is considered to be a kinematical conclusion for the dispute between Gysi and Fisher.

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Gnathology is the science that treats of the biologics of the masticatory mechanism; that is the morphology, anatomy, history, phisiology, pathology and therapeutics of the oral organ, especially the jaw and teeth and the vital relations of this organ to the rest of the body.
It is not too much to say that the science of gnathology is based on the theory of terminal hinge axis and also centric relation.
Aside from this theory, it is really so necessary for us as the practioners to have an ability of recording them when we treat or diagnose the biologics of the masticatory mechanism by the gnathological concepts. Otherwise, the practioners who have not learned a method for precise location of the position of centric relation will have great difficulty analyzing the problems of the masticatory mechanism.
However, this is the fact that it is really a complicated matter not only recording centric relation but also understanding it for young unskilled dentists although they have learned through the seminars.
Author can find the reasons of this matter. This is the reason why there is no unifying concepts about“centric relation”, also technique how to manipulate jaw position for recording it. Since gnathology was born, a lot of methods have been advocated by many authorities, but almost of them, it is nothing and their experimental explanations are not clear.
Recently, it can be said there is growing agreement among authorities that the time honored definitions and also manipulations of“centric relation”are not valid.
The purpose of this article is to describe with above mentioned facts; (1) the concepts about centric relation concerning the jaw mechanism as lever system in mastication, (2) re-evaluation of manipulation techniques for centric relation from this standing concept, and (3) a method named“visible centric recording technique”, by which it can be grasped precise location of the position of centric relation easily as a point.

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