Abstract: A grinding machine is particularly adapted to produce blades and buckets of the kind used in turbines and other objects having complex curved surfaces. Data blocks representing the surface of the object to be created are stored in a computer that controls the machine to finish a rough blank into the final object. An abrasive belt passes over a nose roller to make a line contact with the workpiece. The belt and the workpiece are subject to six computer-controlled degrees of freedom: three in translation and three in rotation. The supporting arm of the nose roller can be moved angularly about the belt contact point while the nose roller can be adjusted about a perpendicular axis through the contact point of the belt. Feedback controls indicate the position of and the motion velocity about the six axes. A positional feedback indicates the precise position of the workpiece at the finishing point to permit automatic compensation for belt wear.