Based on the characteristics of serial joints and parallel joints, we put forward a tooth-arrangement robot composed of a kind of 5 degrees of freedom mechanism of serial structure and parallel structure. Through the analysis of the tooth-arrangement robot mechanism, the equation of kinematics has been built. We analyze the question of inverse kinematics and deduce the matrix of position and gesture of each joint by using analytic method. Finally, we take down-left tooth as an example, on the condition of knowing the equation of dental arch curve and the parameters of single tooth in the coordinate system, and the matrix of position and gesture of each joint has been solved. The result shows that the arithmetic is reasonable and efficient and partly solve the problem of teeth arrangement robot kinematics.