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
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 axis, but none
are. To make matters
more complex, the first hole (bolt hole A) is 5 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 5 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.
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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 (fig
2)
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 degree 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 the coordinate positions for all bolt holes can be
calculated 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. |
