Machinery's Handbook, 31st Edition
Sine-Bars 695 2.5939 inches when D and E are parallel, the calculator will show that the angle A of the work is 31 degrees, 15 minutes. Checking Taper per Foot with Sine-Bar.— As an example, assume that the plug gage in Fig. 2 is supposed to have a taper of 6 1 ⁄ 8 inches per foot and taper is to be checked by using a 5-inch sine-bar. The table of Tapers per Foot and Corresponding Angles on page 698 shows that the included angle for a taper of 6 1 ⁄ 8 inches per foot is 28 degrees 38 minutes 1 second, or 28.6336 degrees from the calculator. For a 5-inch sine-bar, the calculator gives a value of 2.396 inch for the height H of the gage blocks. Using this height, if the upper surface F of the plug gage is parallel to the surface plate, the angle corresponds to a taper of 6 1 ⁄ 8 inches per foot. Setting Sine-Bar having Plugs Attached to Side.— If the lower plug does not rest di- rectly on the surface plate, as in Fig. 3, the height H for the sine-bar is the difference between heights x and y , or the difference between the heights of the plugs; otherwise, the procedure in setting the sine-bar and checking angles is the same as previously described. Checking Templets Having Two Angles.— Assume that angle a of templet, Fig. 4, is 9 degrees, angle b is 12 degrees, and that edge G is parallel to the surface plate. For an angle b of 12 degrees, the calculator shows that the height H is 1.03956 inches. For an angle a of 9 degrees, the difference between measurements x and y when the sine-bar is in contact with the upper edge of the templet is 0.78217 inch. Sine-Bar Tables to Set Sine-Bars to Given Angle.— Machinery’s Handbook 31 Digi - tal Edition contains tables that give constants for sine-bars of 2.5 to 10 inches and 75 to 150 mm length. These constants represent the vertical height H for setting a sine-bar of the corresponding length to the required angle. Using Sine-Bar Tables with Sine-Bars of Other Lengths.— A sine-bar may sometimes be preferred that is longer (or shorter) than that given in available tables because of its longer working surface or because the longer center distance is conducive to greater pre- cision. To use the sine-bar tables with a sine-bar of another length to obtain the vertical distances H , multiply the value obtained from the table by the fraction (length of sine-bar used 4 length of sine-bar specified in table). Example: Use the 5-inch sine-bar table to obtain the vertical height H for setting a 10-inch sine-bar to an angle of 39 degrees. The sine of 39 degrees is 0.62932, hence the vertical height H for setting a 10-inch sine-bar is 6.2932 inches. Solution: The height H given for 39 degrees in the 5-inch sine-bar table ( Constants for 5-Inch Sine-Bar in the ADDITIONAL material in the Machinery’s Handbook 31 Digital Edition ) is 3.14660. The corresponding height for a 10-inch sine-bar is 10 ⁄ 5 3 3.14660 = 6.2932 inches. Using a Calculator to Determine Sine-Bar Constants for a Given Angle.— The con stant required to set a given angle for a sine-bar of any length can be quickly determined by using a scientific calculator. The required formulas are as follows: a) angle A given in degrees and calculator is set to measure angles in radian or a) angle A is given in radian, or b) angle A is given in degrees and calculator is set to measure angles in degrees sin H L A 180 # # π = ` j sin H L A # = ^ h where L = length of the sine-bar A = angle to which the sine-bar is to be set H = vertical height to which one end of sine-bar must be set to obtain angle A π = 3.141592654 In the previous formulas, the height H and length L must be given in the same units but may be in either metric or US units. Thus, if L is given in mm, then H is in mm; and, if L is given in inches, then H is in inches.
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