Machinery's Handbook, 31st Edition
702 ANGLES AND TAPERS To find diameter D of a large disk in contact with a small disk of diameter d given angle α . —
# = − +
D d 1 1
sin sin
a ( ⁄ 2) a ( ⁄ 2)
inches
D
d
Example: The required angle α is 15 ° . Find diameter D of a large disk that is in contact with a standard 1-inch reference disk.
. . sin sin D 1 1 75 1 7 5 1 3002 inches # ° = ° Measurement over Pins and Rolls . − + =
Measurement over Pins.— When the distance across a bolt circle is too large to measure using ordinary measuring tools, then the required distance may be found from the dis- tance across adjacent or alternate holes using one of the methods that follow:
c
c
y
d
x d
x
d
x
Fig. 1a. Fig. 1c. Even Number of Holes in Circle: To measure the unknown distance x over opposite plugs in a bolt circle of n holes ( n is even and greater than 4), as shown in Fig. 1a, where y is the distance over alternate plugs, d is the diameter of the holes, and q = 360/ n is the angle between adjacent holes, use the following general equation for obtaining x : sin x y d d i = − + Example: In a die that has six 3/4-inch diameter holes equally spaced on a circle, where the distance y over alternate holes is 4 1 ⁄ 2 inches, and the angle q between adjacent holes is 60, then . . . . sin x 60 = 4 500 0 7500 0 7500 5 0801 − + = ° Fig. 1b. In a similar problem, the distance c over adjacent plugs is given, as shown in Fig. 1b. If the number of holes is even and greater than 4, the distance x over opposite plugs is given in the following formula:
180
−
i
sin
a
k p
2 i
f
x c d 2 = − ^
+
d
h
sin
where d and q are as defined above.
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