中文摘要：

针对串联关节和并联关节各自的特点，提出了一种由5自由度串联机构和并联机构组成的排牙机器人．通过对排牙机器人机构的分析，建立了其运动学方程。对运动学逆问题进行了分析并且应用解析法和矩阵法推导出各个关节的位姿矩阵，在已知患者的牙弓曲线和各散牙的末端位姿时，便可通过以上算法求得各个关节的位置和姿态。最后以下左牙为算例，对各个关节的位姿矩阵进行了求解。结果表明：本文提出的算法合理有效，解决了排牙机器人部分运动学问题。

英文摘要：

Based on the characteristics of serial joints and parallel joints, we present a tooth-arrangement robot with a five degree of freedom mechanism of serial structure and parallel structure. By analyzing the tooth-arrangement robot mechanism, the equation of kinematics is built. We study its inverse kinematics and deduce the matrix of position and gesture of each joint by using analytic method. When the equation of tooth arch curve and the parameters of each tooth are known in the coordinate system, the matrix of position and gesture of each joint can be determined. Finally, we take the down-left tooth as an example ; satisfactory results are obtained, showing that the arithmetic is reasonable and efficient and can partly solve the problem of tooth arrangement robot kinematics.