[A mathematical model of 3-dimensional excursive movement of the mandible on Hanau articulator]

Aiming at filling the vacancy in the study about mandibular movement, which mainly focuses on the field of biology at present, this study builds a mathematical model of 3-dimensional excursive movement of the mandible on Hanau articulator from the viewpoint of spatial mechanisms and analytical geometry. On the basis of the theory of spatial mechanisms, the freedom of motion of Hanau articulator is analyzed, and a hypothesis of constraints is presented, the objective of which is to restrict the mandibular movement. Based on the theory of analytical geometry, a series of mathematical expressions are derived to describe the 3-dimensional movement of the mandible mounted on the articulator. With the geometrical parameters of the articulator, these mathematical equations are solved by programming in Matlab 6.5 (a language for technical computing) and VC + +6.0. Therefore, the spatial path of the arbitrary point on the mandible can be precisely described when the upper body of Hanau articulator is guided along a specific direction. This study proves that the included angle between the plane of orientation and occlusal plane is positively related to the inclination of condylar guidance and incisal guidance, therefore, provides a theoretical foundation for Hanau's laws of articulation and the Hanau Quint. The future of dentistry is basically connected with the use of computer technology. This study will be useful for the further research of the dynamic occlusion to improve dental restorative procedures by realizing future replacement of the mechanical articulator with a virtual one.