Identify Absolute Coordinates
6. Identify each axis (vertical milling representation) and its positive or negative value on Figure 1-6.
Figure 1-6 Identify Vertical Milling Axes, Polar Rotation, Quadrants, and Angular Values
Figure 1-7 Identify Polar Coordinate Values
Figure 1-8 Identify Polar Coordinate Values
7. Indicate the negative rotation direction for the polar coordinate system in Figure 1-6.
8. Indicate each of the polar quadrants in Figure 1-6.
9. Identify the angular value locations for 0, 90, 180, and 270 degrees in Figure 1-6.
10. Identify the polar (angular and radial) values for each of the holes in Figure 1-7.
11. Identify the polar (angular and radial) values for each of the holes in Figure 1-8.
Trigonometric Calculations
In many cases, it will be necessary to calculate the coordinate values of points for input into your CNC programs. The exercises that follow are a small sampling of the types of problems you are likely to encounter. Use your calculation skills to answer all of the problems and to prepare yourself for others when you complete the actual programming exercises in Units 3 and 4 of this workbook, the CNC Turning and Machining Center sections.
Chart 1-6 (Right Triangles) and Chart 1-7 (Oblique Triangles) are provided for your benefit. Many of the formulas shown are needed to complete the problems.
Chart 1-6 Right Triangles
| Known Sides and Angles | Unknown Sides and Angles | Area | ||
| a and b |
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| a and c |
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| b and c |
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| a and ∠ A |
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B = 90° − A |
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| a and ∠ B | b = a × tanB |
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A = 90° − B |
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| b and ∠ A | a = b × tabA |
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B = 90° − A |
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| b and ∠ B |
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A = 90° − B |
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| c and ∠ A | a = c × sinA | b = c × cosA | B = 90° − A | c2 × sinA × cos |
| c and ∠ B | a = c × cosB | b = c × sinB | A = 90° − B | c2 × sinB × cos |
Chart 1-7 Oblique Triangles
| Known Sides and Angles | Unknown Sides and Angles | Area |
