For fully characterizing the tooth surface errors information of the topological modification helical gear
the method on- machine topology measurement is proposed by a mathematical model of the polar coordinate
based on CNC form grinding motion function and formation mechanism of the tooth surface modification. According to the contact trace of the outline shape of grinding wheel and the workpiece
the mathematical equation of tooth flank modification theory point is derived through coordinate conversion
and the tooth surface grids are divided. The point to point topology measurement of theoretical involute is completed by using the rotary( C axis) and radial feeding motion( X axis) and axial motion( Z axis) of CNC form grinding machine. Finally
on the form grinding the topology measurement experiment is carried out
and the tooth surface errors are characterized by contour map.