Trigonometry
made easy, part 3
We’ve
been discussing trigonometry. Trig
can be easy when you break it down and follow the steps outlined
here.
Step
#1:
Draw a 90º triangle; this step is often the most difficult.
Step
#2:
Label two sides of the triangle, "the known
side and the needed
side".
Step
#3:
Select the correct trig rule
Step
#4:
Calculate the unknown.
Over
the past few months we’ve reviewed drawing a 90 triangle.
We’ve labeled only two sides of the triangle and selected
the correct trig rule based on the two labeled sides.
The
only step left is to solve the problem.
This
is the part we’ve been using.
In last month’s issue the triangle was labeled as shown.
With
the sides labeled opposite and adjacent, the tangent rule was
selected.
tangent
rule
tangent of the angle = side opposite ÷ side adjacent
To
solve the problem, simply replace the words with the value of the
side of the triangle.
Tangent
rule
tangent of the angle = 0.876
÷ 1.2510
Perform
the mathematical function. Tangent of the angle =
0.7002
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Use
the calculator’s 2nd function to determine the size of
the angle. (Your
calculator may operate differently, but many operate by using the
following sequence.
0.7002
The
use of the tangent rule allows us to calculate the size of the
angle. For this part,
the angle is 34.9997º.
Follow
these four steps and you can solve most all machine shop trig
problems.
In
our business, we analyze prints and use trig to calculate part
dimensions in an effort to program the part.
Sometimes the process is reversed.
Here’s a twist on the trig process.
Here
is a program to turn the profile of the part shown.
Use the program to calculate the size of each angle.
Part
Program
G00
X0.900
Z0.050 ;
( start )
G01
Z0.
F0.008 ;
( blend face )
X1.0637
( first chamfer start )
X1.2000
Z-0.0682
( cut chamfer )
Z-0.2851
( start angle A )
X1.000
Z-0.6583
( plunge angle A )
Z-1.8341
( turn 1.0 dia. )
X1.5753
Z-2.3750
( turn angle B )
X2.800
( face up )
Remember
to work step-by-step for each angle using the 4 steps shown above.
Check our web site for the results (www.cnc-training.com).
Good luck!
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