The taper of the cone is detected by a sine gauge. When the sine gauge is placed at the exact height of the block gauge, the angle between the sine gauge working surface and the flat plate is theoretically equal to the cone angle α. If the taper value α of the cone to be measured is accurate, the upper busbar of the cone is parallel to the plate. At this time, the dial gauge should be the same at both ends of the upper busbar. But in fact it is impossible to do this completely, the cone angle is always and also allows a certain error, so the dial gauge can not read the same at both ends, but has a certain error value ΔS. If the tolerance of the taper angle α is ±δα, then the range of ΔS should meet the requirements of ±δα, which is the problem we encountered in our actual work and often solved by calculation. As shown in Figure 1, suppose the dial gauge is A at the small end and BA at the A, then the angle between the BA and the sine gauge