Taper Turning with the Compound Rest.—The amount of taper that can be turned by setting over the tailstock center and by the taper attachment is limited, as the centers can only be offset a certain distance, and the slide S ([Fig. 9]) of the attachment cannot be swiveled beyond a certain position. For steep tapers, the compound rest E is swiveled to the required angle and used as indicated in [Fig. 14], which shows a plan view of a rest set for turning the valve V. This compound rest is an upper slide mounted on the lower or main cross-slide D, and it can be turned to any angular position so that the tool, which ordinarily is moved either lengthwise or crosswise of the bed, can be fed at an angle. The base of the compound rest is graduated in degrees and the position of these graduations shows to what angle the upper slide is set. Suppose the seat of valve V is to be turned to an angle of 45 degrees with the axis or center, as shown on the drawing at A, [Fig. 15]. To set the compound rest, nuts n on either side, which hold it rigidly to the lower slide, are first loosened and the slide is then turned until the 45-degree graduation is exactly opposite the zero line; the slide is then tightened in this position. A cut is next taken across the valve by operating handle w and feeding the tool in the direction of the arrow.
Fig. 15. Example of Taper Work Turned by using Compound Rest
In this particular instance the compound rest is set to the same angle given on the drawing, but this is not always the case. If the draftsman had given the included angle of 90 degrees, as shown at B, which would be another way of expressing it, the setting of the compound rest would, of course, be the same as before, or to 45 degrees, but the number of degrees marked on the drawing does not correspond with the angle to which the rest must be set. As another illustration, suppose the valve were to be turned to an angle of 30 degrees with the axis as shown at C. In this case the compound rest would not be set to 30 degrees but to 60 degrees, because in order to turn the work to an angle of 30 degrees, the rest must be 60 degrees from its zero position, as shown. From this it will be seen that the number of degrees marked on the drawing does not necessarily correspond to the angle to which the rest must be set, as the graduations on the rest show the number of degrees that it is moved from its zero position, which corresponds to the line a—b. The angle to which the compound rest should be set can be found, when the drawing is marked as at A or C, by subtracting the angle given from 90 degrees. When the included angle is given, as at B, subtract one-half the included angle from 90 degrees to obtain the required setting. Of course, when using a compound rest, the lathe centers are set in line as for straight turning, as otherwise the angle will be incorrect.
Rules for Figuring Tapers
| Given | To Find | Rule |
| The taper per foot. | The taper per inch. | Divide the taper per foot by 12. |
| The taper per inch. | The taper per foot. | Multiply the taper per inch by 12. |
| End diameters and length of taper in inches. | The taper per foot. | Subtract small diameter from large; divide by length of taper, and multiply quotient by 12. |
| Large diameter and length of taper in inches and taper per foot. | Diameter at small end in inches. | Divide taper per foot by 12; multiply by length of taper, and subtract result from large diameter. |
| Small diameter and length of taper in inches, and taper per foot. | Diameter at large end in inches. | Divide taper per foot by 12; multiply by length of taper, and add result to small diameter. |
| The taper per foot and two diameters in inches. | Distance between two given diameters in inches. | Subtract small diameter from large; divide remainder by taper per foot, and multiply quotient by 12. |
| The taper per foot. | Amount of taper in a certain length given in inches. | Divide taper per foot by 12; multiply by given length of tapered part. |
Fig. 16. Disk Gage for Accurate Measurement of Angles and Tapers