A small polishing robot must be made to adapt the change of curvature and slope of the cutting curved surfaces when it moves on the large curved surface. This paper develops a small moving robot to move on the large curved surface and polish it which can adapt the change of curvature and slope of the cutting curved surfaces. It also establishes the kinematics model and the inverse kinematics for movement control of the robot. By analyzing the motion characteristics and the processing of automatic polishing, the paper develops the posture equation of the robot. Experiments shows the small moving robot is capable of adaptability in polishing curved surfaces.