Abstract  Arc envelope grinding method(AEGM)is an important technique for machining revolution surfaces.In order to improve the grinding precision of AEGM, the position relationship between the grinding point of the wheel and the machining curves was analyzed firstly in this article,and motion law of the grinding point was discussed.The motion speed equation of wheel grinding points was obtained during AEGM grinding of revolution surfaces having and parabola as generatrix. The research results showed that,the moving distance of the grinding point increases with the increases of radius of tip arc on the grinding wheel; the speed of the grinding point is faster with large radius of curvature.