Kinematic Analysis of Articulator Motion

Part 2-Mathematical Expressions

Abstract

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.