Abstract: Based on the investigation of the design calculations used for various kinds of gears in mesh, an conception has been proposed by the author, that the cycloid can be replaced by an engaged point-(or cylindrical) tooth, I:e. by using a point-(or cylindrical) tooth located on the　surface and on the line of action of the conjugated gear to replace the original cycloidal gear, so that the engagement of the cycloidal curve is replaced by the engagement of a point (or cylindrical) tooth and then proceed the calculation. This is a new method and is much　simpler than the various kinds of calculations used nowadays.