The hyperboloidal surface was studied, which was common in complex surfaces.The mathematical model for machining hyperboloidal surface was set up.Based on the analysis of parameter characteristics of hyperboloidal surface,the variation law of the slope limit value of tangent at arbitrary point on hyperboloidal surface and the slope limit value of the axis of tool was discovered.Based on the variation law,the functional relationship between parabola parameter,tool parameter and the square of eccentricity was...