The measuring method by inserting single racks has hitherto been used for helical gears in U.S A., etc., because of its several advantages over the ball inserting method ; but its fundamental theory has not been cleared up in our country. The author solved equations of involute helicoid curved surface to make it clear completely, derived calibration methods to the manufacturing errors in measuring racks, and discussed relative merits of various kinds of racks. Application of the single rack method to the analysis of helical gears will make the measurements more stable, the calculations easier, and the measurement of true eccentricity of teeth simpler, than by the ball inserting method. Moreover, the measuring instruments for this method may be available in usual gear cutting shops. Therefore, this method will be popularized as a convenient one. Thus, the analyzing method of helical gears and calibration method for measuring rack were described as applications of this theory.
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