Hanau架下颌侧方运动的数学模型  

A Mathematical Model of 3-Dimensional Excursive Movement of the Mandible on Hanau Articulator

作　　者：陈晓军[1] 陆尔奕[2] 陈建军[1] 王成焘[1] 

机构地区：[1]上海交通大学生命质量与机械工程研究所,上海200030 [2]上海第二医科大学附属第九人民医院,上海200011

出　　处：《生物医学工程学杂志》2007年第3期568-573,共6页Journal of Biomedical Engineering

摘　　要：针对目前下颌运动的研究大多集中在生理学方面的不足,我们从空间机构运动理论的角度出发,对Hanau架运动链自由度进行分析并提出约束条件假设,以空间解析几何建立描述Hanau架下颌三维侧向空间运动的数学模型,通过在Matlab6.5及VC++6.0环境下编制软件程序求解,得到其任意点的运动轨迹,从而验证了髁导斜度及切导斜度与定位平面斜度成正变关系,对Hanau提出的5因素10定律提供了理论依据。该数学模型的建立将有助于深入分析下颌运动过程中上下颌的动态咬合,从而达到最终实现以虚拟架替代机械架的目的。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 Matlab6. 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.

关 键 词：Hanau[牙合]架 下颌侧方运动 数学模型 空间机构理论 

分 类 号：R311[医药卫生—基础医学] R782