- Coordinates for 3D CAD Modeling
- Geometric Entities
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.2 Drawing Tangents to Two Circles
- 4.3 Drawing an Arc Tangent to a Line or Arc and Through a Point
- 4.4 Bisecting an Angle
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.6 Drawing a Triangle with Sides Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.8 Laying Out an Angle
- 4.9 Drawing an Equilateral Triangle
- 4.10 Polygons
- 4.11 Drawing a Regular Pentagon
- 4.12 Drawing a Hexagon
- 4.13 Ellipses
- 4.14 Spline Curves
- 4.15 Geometric Relationships
- 4.16 Solid Primitives
- 4.17 Recognizing Symmetry
- 4.18 Extruded Forms
- 4.19 Revolved Forms
- 4.20 Irregular Surfaces
- 4.21 User Coordinate Systems
- 4.22 Transformations
- Key Words
- Chapter Summary
- Skills Summary
- Review Questions
- Chapter Exercises
4.8 Laying Out an Angle
Many angles can be laid out directly with the triangle or protractor. For more accuracy, use one of the methods shown in Figure 4.31.
4.31 Laying Out Angles
Tangent Method The tangent of angle θ is y/x, and y = x tan θ. Use a convenient value for x, preferably 10 units (Figure 4.31a). (The larger the unit, the more accurate will be the construction.) Look up the tangent of angle θ and multiply by 10, and measure y = 10 tan θ.
EXAMPLE To set off 31-1/2°, find the natural tangent of 31-1/2°, which is 0.6128. Then, y = 10 units × 0.6128 = 6.128 units.
Sine Method Draw line x to any convenient length, preferably 10 units (Figure 4.31b). Find the sine of angle θ, multiply by 10, and draw arc with radius R = 10 sin θ. Draw the other side of the angle tangent to the arc, as shown.
EXAMPLE To set off 25-1/2°, find the natural sine of 25-1/2°, which is 0.4305. Then R = 10 units × 0.4305 = 4.305 units.
Chord Method Draw line x of any convenient length, and draw an arc with any convenient radius R—say 10 units (Figure 4.31c). Find the chordal length C using the formula C = 2 sin θ/2. Machinists’ handbooks have chord tables. These tables are made using a radius of 1 unit, so it is easy to scale by multiplying the table values by the actual radius used.
EXAMPLE Half of 43°20′ = 21°40′. The sine of 21°40′ = 0.3692. C = 2 × 0.3692 = 0.7384 for a 1 unit radius. For a 10 unit radius, C = 7.384 units.
EXAMPLE To set off 43°20′, the chordal length C for 1 unit radius, as given in a table of chords, equals 0.7384. If R = 10 units, then C = 7.384 units.