Machinery's Handbook, 31st Edition
Measurement OVER PINS AND Rolls 703 Odd Number of Holes in Circle: In a circle as shown in Fig. 1c, where the number of holes n is odd and greater than 3, and the distance c over adjacent holes is given, then q equals 360/ n and the distance x across the most widely spaced holes is given by:
c d −
2
+
=
x
d
4 i
sin
Checking a V-Shaped Groove by Measurement Over Pins.— In checking a groove of the shape shown in Fig. 2, it is necessary to measure the dimension X over the pins of radius R . If values for the radius R , dimension Z , and the angles α and b are known, the problem is to determine the distance Y , to arrive at the required overall dimension for X . If a line AC is drawn from the bottom of the V to the center of the pin at the left in Fig. 2, and a line CB from the center of this pin to its point of tangency with the side of the V, a right-angle triangle is formed in which one side, CB , is known and one angle, CAB , can be determined. A line drawn from the center of a circle to the point of intersection of two tangents to the circle bisects the angle made by the tangent lines, and angle CAB therefore equals 1 ⁄ 2 ( α + b ). The length AC and the angle DAC can now be found, and with AC known in the right-angle triangle ADC , AD , which is equal to Y, can be found.
X Z
Y
R
R
Y
B
2
A
C D
2
Fig. 2. The value for X can be obtained from the formula csc cos X Z R 2 2 = + + a k For example, if R = 0.500, Z = 1.824, α = 45 degrees, and b = 35 degrees, . . 2 1 − + α β α β csc cos 1824 2 05 ^ a h k
. . . 1824 40 5 1 1 824 1 5557 0 99619 1 1824 1550 1 4374 # # ° ° = + + . . . . csc cos ° 2 45 35 = + = + + + = + + = °
2 45 35 1 − + ° °
X X X X
Checking Radius of Arc by Measurement Over Rolls.— The radius R of large-radius concave and convex gages of the type shown in Fig. 3a, Fig. 3b and Fig. 3c can be checked by measurement L over two rolls with the gage resting on the rolls as shown. If the diame- ter of the rolls D , the length L , and the height H of the top of the arc above the surface plate (for the concave gage, Fig. 3a) are known or can be measured, the radius R of the workpiece to be checked can be calculated trigonometrically, as follows.
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