Machinery's Handbook, 31st Edition
710 Determining Hole Circle Coordinates where n = number of holes in circle; D = diameter of hole circle; q = angle between adjacent holes; x H = x coordinate at position of hole number H ; and, y H = y coordinate at position of hole number H . Example 2(a) : Calculate the hole coordinates for the 5-hole circle shown in Fig. 2a when circle diameter = 1. Compare the results to the data in Table 2a. Hole q = 360/5 = 72 ° q ⁄ 2 = 36 ° D = 1
1 2 3 4 5
x 1 = – x 2 = – x 3 = – x 4 = – x 5 = –
1 ⁄ 2 3 sin(36) = –0.29389 1 ⁄ 2 3 sin(108) = –0.47553 1 ⁄ 2 3 sin(180) = 0.00000 1 ⁄ 2 3 sin(252) = 0.47553 1 ⁄ 2 3 sin(324) = 0.29389
y 1 = – y 2 = – y 3 = – y 4 = – y 5 = –
1 ⁄ 2 3 cos(36) = –0.40451 1 ⁄ 2 3 cos(108) = 0.15451 1 ⁄ 2 3 cos(180) = 0.50000 1 ⁄ 2 3 cos(252) = 0.15451 1 ⁄ 2 3 cos(324) = –0.40451
In Fig. 2b, 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 offset 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 chosen at any convenient distance from the hole circle origin. In Fig. 2b, it can be determined by inspection that distance X O = Y O = D ⁄ 2 . The equations for calculating hole positions of type “B” circles of the Fig. 2b type are the same as in Equation (2a) but with the addition of X O and Y O terms, as follows: (2b) Example 2(b) : Use the coordinates obtained in Example 2(a) to determine the hole coor dinates of a 5-hole circle shown in Fig. 1b with circle diameter = 1. Compare the results to the data in Table 2b. Hole q = 360/5 = 72 ° q ⁄ 2 = 36 ° D = 1 X O = D ⁄ 2 = 0.50000 Y O = D ⁄ 2 = 0.50000 sin D H cos D H n n 360 2 π x X y Y 2 1 2 i i h 2 1 2 i i h H H O O i = = =− − + + = − − + + k a ^ a ^ k
1 2 3 4 5
x 1 = – x 2 = – x 3 = – x 4 = – x 5 = –
1 ⁄ 2 3 sin(36) + 0.50000 = 0.20611 1 ⁄ 2 3 sin(108) + 0.50000 = 0.02447 1 ⁄ 2 3 sin(180) + 0.50000 = 0.50000 1 ⁄ 2 3 sin(252) + 0.50000 = 0.97553 1 ⁄ 2 3 sin(324) + 0.50000 = 0.79389
y 1 = – y 2 = – y 3 = – y 4 = – y 5 = –
1 ⁄ 2 3 cos(36) + 0.50000 = 0.09549 1 ⁄ 2 3 cos(108) + 0.50000 = 0.65451 1 ⁄ 2 3 cos(180) + 0.50000 = 1.00000 1 ⁄ 2 3 cos(252) + 0.50000 = 0.65451 1 ⁄ 2 3 cos(324) + 0.50000 = 0.09549
Adapting Hole Coordinate Equations for Different Geometry.— Hole coordinate val ues in Table 1a through Table 2b are obtained using the equations given previously, along with the geometry of the corresponding figures. If the geometry does not match that given in one of the previous figures, hole coordinate values from the tables or equations will be incorrect. Fig. 3 illustrates such a case. Fig. 3 resembles a type “A” hole circle (Fig. 1b) with hole number 2 at the top, and it also resembles a type “B” hole circle (Fig. 2b) in which all holes have been rotated 90 ° clockwise. A closer look also reveals that the positive y direc- tion in Fig. 3 is opposite that used in Fig. 1b and Fig. 2b. Therefore, to determine the hole coordinates of Fig. 3 it is necessary to create new equations that match the given geometry or to modify the previous equations to match the Fig. 3 geometry.
2
3
1
+ y
30°
Ø 10.0
4
6
6.0
5
+ x
7.5
Fig. 3.
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