Determining Hole Circle Coordinates Machinery's Handbook, 31st Edition
709
Hole
q = 360/5 = 72 °
D = 1
1 2 3 4 5
x H = x 1 = –
1 ⁄ 2 3 sin(0) = 0.00000
y 1 = – y 2 = – y 3 = –
1 ⁄ 2 3 cos(0) = –0.50000 1 ⁄ 2 3 cos(72) = –0.15451 1 ⁄ 2 3 cos(144) = 0.40451
x 2 = – x 3 = – x 4 = – x 5 = –
1 ⁄ 2 3 sin(72) = –0.47553 1 ⁄ 2 3 sin(144) = –0.29389 1 ⁄ 2 3 sin(216) = 0.29389
y 4 = – y 5 = –
1 ⁄ 2 3 cos(216) = 0.40451 1 ⁄ 2 3 cos(288) = –0.15451
1 ⁄ 2 3 sin(288) = 0.47553
In Fig. 1b, the origin of the coordinate system (point 0,0) is located at the top left of the figure at the intersection of the two lines labeled “Ref.” The center of the hole circle is off set from the coordinate system origin by distance X O in the +x direction, and by distance Y O in the + y direction. In practice the origin of the coordinate system can be located at any convenient distance from the center of the hole circle. In Fig. 1b, it can be determined by inspection that the distances X O = Y O = D ⁄ 2 . The equations for calculating hole positions of type “A” circles of the Fig. 1b type are almost the same as in Equation (1a), but with the addition of X O and Y O terms, as follows: (1b) Example 1(b) : Use results of Example 1 to determine hole coordinates of Fig. 1b for circle diameter = 1, and compare results with Table 1b. Hole q = 360/5 = 72 ° D = 1 X O = D ⁄ 2 = 0.50000 Y O = D ⁄ 2 = 0.50000 sin cos n n x D H X y D H Y 360 2 2 1 2 1 H O H O i π i i = = =− − + =− − + ^^ ^^ h h h h
x 1 = 0.00000 + X O = 0.50000 x 2 = –0.47553 + X O = 0.02447 x 3 = –0.29389 + X O = 0.20611 x 4 = 0.29389 + X O = 0.79389 x 5 = 0.47553 + X O = 0.97553
y 1 = –0.50000 + Y O = 0.00000 y 2 = –0.15451 + Y O = 0.34549 y 3 = 0.40451 + Y O = 0.90451 y 4 = 0.40451 + Y O = 0.90451 y 5 = –0.15451 + Y O = 0.34549
1 2 3 4 5
Type “B” Hole Circles.— Compared to type “A” hole circles, type “B” hole circles, Fig. 2a and Fig. 2b, are arranged such that the circle of holes is rotated about the center of the circle by q ⁄ 2 degrees, that is, 1 ⁄ 2 of the angle between adjacent holes. The x , y coordinates for type “B” hole circles of from 3 to 33 holes are given in Table 2a for geometry corresponding to Fig. 2a, and in Table 2b for geometry corresponding to Fig. 2b. Holes are numbered in a counterclockwise direction as shown. Coordinates given are based upon a hole circle of (1) unit diameter. For other diameters, multiply the x and y coordinates from the table by the hole circle diameter. For example, for a 3-inch or 3-centimeter hole circle diameter, multiply table values by 3. Coordinates are valid in any unit system.
X
Ref
1
5
5
1
– Y
Y
Ref
– X
+ X
4
2
2
4
+ Y
3
3
Fig. 2a. Type “B” Circle Fig. 2b. Type “B” Circle In Fig. 2a, the coordinate system origin, marked “Ref”, is at the center of the hole circle at position x = 0, y = 0. Equations for calculating hole coordinates for type “B” circles with the coordinate system origin at the center of the hole circle as in Fig. 2a are as follows: (2a) sin D H cos D H n n 360 2 π x y 1 2 i i h 1 2 i i + h H H i = = =− − + = − − a ^ a ^ k k
2
2
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