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Using trig in bolt patterns.

During the past few months we've been reviewing trigonometry functions and how to make trig easy to use. The examples we've used have all been turned parts. We don't want to leave out our milling friends, so lets look at how trig can be used for a milled part.

Imagine a situation where you are given this drawing, figure 1, and a calculator and asked to find the X and Y coordinates for the nine bolt holes. It might be easy to find a few holes if some were on the X and Y axes, but none are. To make matters more complex, the first hole (bolt hole A) is five degrees off of the X0.00 position. It is given that the bolt holes form a circle around the part datum. The diameter of the circle, measured from the center of the bolt holes, is 9". (figure 1)


The traditional method of solving this problem is with the use of trigonometry. Ninety-degree triangles can be drawn between the datum and the center of the holes. Using this method you would have to draw nine triangles and calculate nine trig problems.

By using a scientific calculator, a shortcut can be taken in the calculations of the bolt pattern. First, we can calculate the rotational value of each hole. The angular distance between each hole is 40[degrees] (360 / 9 = 40). Remember, the first hole (A) starts five degrees from the X0.00 position. The rest of the holes have angular positions as outlined in this chart. All angles should be calculated as an absolute value in a clockwise direction from the 12 o'clock point.

To calculate the X and Y hole position use the following elements:

1. Radius value of the pattern circle--this would be the hypotenuse of a triangle drawn between the datum and the individual hole (figure 2)


2. Angular position of the individual hole--from the chart.

3. SIN (sine) or COS (cosine) key on the scientific calculator.

The procedure is easy: Use the SIN or COS of the radial angle and multiply this by the radius value of the bolt pattern. For each hole, to find the X value, use the SIN function; and to find the Y value use the COS function.

To find the X value use the SIN function:

125 SIN x 4.5 = 3.6862

To find the Y value use the COS function:

125 COS x 4.5 = -2.5811

Notice that when using the 125[degrees] angle the calculator automatically produces a negative value for the Y-axis coordinate. Looking at the drawing confirms that the Y value is negative for this hole.

Using this method, you can calculate the coordinate positions for all bolt holes without ever drawing a triangle. A TI-30 calculator has three memory functions that will assist in these calculations. We recommend that the bolt circle radius (hypotenuse) value be stored in the memory to assist in ease of use.

Steve Rose is a professional trainer and president of RTSI, Solon, OH. Rosaleen Rose offers Internet website development. They can be reached by phone at 440.542.3066; e-mail; or on the web at
Hole Ankle X axis Y axis

A 5 0.3922 4.4829
B 45 3.1820 3.1820
C 85 4.4829 0.3922
D 125 3.6862 -2.5811
E 165 1.1647 -4.3467
F 205 -1.9018 -4.0784
G 245 -4.0784 -1.9018
H 285 -4.3467 1.1647
I 325 -2.5811 3.6862

Hole Angle

A 5
B 45
C 85
D 125
E 165
F 205
G 245
H 285
I 325
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Title Annotation:bolt holes
Author:Rose, Steve
Publication:Tooling & Production
Geographic Code:1USA
Date:Jan 1, 2006
Previous Article:Manufacturing finds itself in bullish mood.
Next Article:The year will be marked by output, adaptability.

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