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Shop MathRight Triangle Applications For CNC Programming 4/18/2014

By Richard Wade

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You will need a calculator similar to this

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unless you would rather work out the trigonometric functions on a circle. This is how they were constructed before calculators.

= 90

Remember two things about Right Triangles:The angles of all three corners for any triangle will add up to 180

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If one of the corners is exactly 90 degrees The other two corners must add up to exactly 90 degrees!

226890 - 22 = 68

4/18/2014Three Basic Trigonometry Functions: Sine CosineTangent

4/18/2014The two most common applications of Right Triangle Trigonometry in CNC Machining: 1. Bolt Circle calculations. 2. Turning chamfers and/or angles.

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A Bolt Circle is a method for defining hole position using a theoretical circle that passes through the center of a series of holes.

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4 HOLES EQ SPCD ON A 3.25 B.C.

20Typical Information Given

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One can almost imagine an arrow notched in the bow.

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4 HOLES EQ SPCD ON A 3.25 B.C.

20

You can easily find the hypotenuse from the data given (the bolt circle dimension is a diameter, so divide it in half to get the radius, which is also the hypotenuse of the triangle)

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but the machines control uses X and Y coordinates.

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3.25 2 = 1.6251.625207090 20 = 70What can be deduced from the information given on the part print.

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1.6252070

When going around the Corner, use Cosine!0.55581.625 x 70 COS = 0.55578

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1.6252070When going around the Corner, use Cosine!0.55581.625 x 20 COS = 1.5270

1.5270

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X= 0.5558Y= 1.5270X= 1.5270Y=-0.5558X=-0.5558Y=-1.5270X=-1.5270Y= 0.5558

4/18/2014PracticeIf the hypotenuse of a right triangle is 6.375, and one corner is shown to have a 32 angle, what is the other angle?

What are the lengths of the two other sides?

When you have your answer, press the Enter key.

4/18/2014PracticeIf the hypotenuse of a right triangle is 6.375, and one corner is shown to have a 32 angle, what is the other angle?

What are the lengths of the two other sides?

58 5.4063 and 3.3782 I just know these are the numbers you got, right?

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15.270?The Tangent function is used to solve for an unknown side when there is a known side and a known non-ninety degree angle.

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1.2500.250

3.12515Typical Information Given (side view of a round part)

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0.25015

1.250

Endpoint X = 1.250 Z = -0.250

Start-point X = ? Z = 0.00?

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0.25015

1.250

Endpoint X = 1.250 Z = -0.250

Start-point X = ? Z = 0.020

0.250 + 0.020 = 0.270

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15.2700.0724When crossing the triangle, cross a T with Tangent!

0.270 x 15 TAN = 0.07235

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0.0724 x 2 = 0.1448 Double the Result And Subtract from the X axis Endpoint.1.250 (0.0724 x 2) = 1.1052

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0.25015

1.250

Endpoint X = 1.250 Z = -0.250

Start-point X = 1.1052 Z = 0.020

1. Find and Solve the Triangle 2. Double X-axis Result 3. Subtract Dia. From X-Endpoint4. Plug Data into Program

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177.750?PracticeWhat is the length of the unknown side? When you have your answer, press the Enter key.

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177.750?PracticeWhat is the length of the unknown side? 2.3694

4/18/2014ReviewWhen using the Hypotenuse (longest side of a triangle) and the angle on the corner youre going around, use the Cosine function. When using a known side and an adjacent angle to get the opposite side (so you have to cross the triangle), use the Tangent function.

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