1. GEOMETRIC CONSTRUCTIONS
CH 7
GEOMETRIC CONSTRUCTIONS

2. LAYING OUT AN ANGLE
Tangent Method
Sine Method
Chord Method
Many angles can be laid out directly with the triangle or protractor.

3. DRAWING A SQUARE T-square Method Diameters Method
Inscribed Circle Method

4. DRAWING A HEXAGON Use a compass Centerline Variation Steps
Each side of a hexagon is equal to the radius of the circumscribed circle
Use a compass
Centerline Variation
Steps

5. DRAWING AN OCTAGON
Given a circumscribed square, (the distance “across flats”) draw the diagonals of the square. Then, use the corners of the square as centers and half the diagonal as the radius to draw arcs cutting the sides
Given an inscribed circle, or distance “across flats”, use a T-square or straightedge and a 45° triangle to draw the eight sides tangent to the circle.

7. DRAWING AN ARC TANGENT TO A LINE OR ARC AND THROUGH A POINT
Tangents

8. DRAWING AN ARC TANGENT TO TWO LINES AT RIGHT ANGLES
For small radii, such as 1/8R for fillets and rounds, it is not practicable to draw complete tangency constructions. Instead, draw a 45° bisector of the angle and locate the center of the arc by trial along this line

10. DRAWING AN ARC TANGENT TO TWO LINES AT ACUTE OR OBTUSE ANGLES

11. DRAWING AN ARC TANGENT TO AN ARC AND A STRAIGHT LINE

12. DRAWING AN ARC TANGENT TO TWO ARCS

13. DRAWING AN OGEE CURVE Connecting Two Parallel Lines
Connecting Two Nonparallel Lines

14. DRAWING A FOCI ELLIPSE

15. DRAWING A CONCENTRIC CIRCLE ELLIPSE
If a circle is viewed with the line of sight perpendicular to the plane
of the circle…
…the circle will appear as a circle, in true size and shape

16. Irregular Curves
The curves are largely successive segments of geometric curves, such as the ellipse, parabola, hyperbola, and involute.

17. DRAWING AN APPROXIMATE ELLIPSE
For many purposes, particularly where a small ellipse is required, use the approximate circular arc method.

18. DRAWING A HELIX
A helix is generated by a point moving around and along the surface of a cylinder or cone with a uniform angular velocity about the axis, and with a uniform linear velocity about the axis, and with a uniform velocity in the direction of the axis

19. DRAWING AN INVOLUTE
An involute is the path of a point on a string as the string unwinds from a line, polygon, or circle.

21. GEOMETRIC CONSTRUCTION EXERCISE 5

34. BISECTING A LINE WITH TRIANGLE AND T-SQUARE
From endpoints A and B, draw construction lines at 30°, 45°, or 60° with the given line. Then, through their intersection, C, draw a line perpendicular to the given line to locate the center D…

35. BISECTING A LINE OR CIRCULAR ARC
Compass system
Triangle and T-Square System

36. Triangles
Inclined lines can be drawn at standard angles with the 45° triangle and the 30° x 60° triangle. The triangles are transparent so that you can see the lines of the drawing through them. A useful combination of triangles is the 30° x 60° triangle with a long side of 10" and a 45° triangle with each side 8" long.

37. Any Angle in 15° Increments
With only a 30° x 60° triangle and a 45° triangle, you can draw
any angle in 15° increments
The bottom
of the triangle in
each case is resting
on the blade of the
T-square. Twenty-four 15° sectors are possible with just these two triangles used singly or in combination.

38. Protractors
For measuring or setting off angles other than those obtainable with triangles, use a protractor.
Plastic protractors are satisfactory for most angular measurements
Nickel silver protractors are available when high accuracy
is required

39. DRAWING A LINE PARALLEL TO A LINE AND AT A GIVEN DISTANCE
T-square Method
For Curves

40. DRAWING A LINE THROUGH A POINT AND PERPENDICULAR TO A LINE
When the Point Is Not on the Line
When the Point Is on the Line
T-square Method

41. ANGLES…
BISECTING AN ANGLE
TRANSFERRING AN ANGLE

42. DRAWING AN EQUILATERAL TRIANGLE
Alternative Method

43. DRAWING A REGULAR PENTAGON
Dividers Method
Geometric Method

44. FINDING THE CENTER OF A CIRCLE
This method uses the principle that any right triangle inscribed in a circle cuts off a semicircle.
Another method, slightly longer, is to reverse the procedure. Draw two nonparallel chords and draw perpendicular bisectors. The intersection of the bisectors will be the center of the circle.

45. DRAWING TANGENTS TO TWO CIRCLES

46. Drawing an Arc Tangent to Two Arcs and Enclosing One or Both

47. DRAWING A PARALLELOGRAM ELLIPSE
The intersection of like-numbered lines will be points on the ellipse. Locate points in the remaining three quadrants in a similar manner. Sketch the ellipse lightly through the points, then darken the final ellipse with the aid of an irregular curve.

48. THE CONIC SECTIONS
The conic sections are curves produced by planes intersecting a right circular cone.
Four types of curves are produced: the circle, ellipse, parabola, and hyperbola, according to the position of the planes.

49. ELLIPSE TEMPLATES
These ellipse guides are usually designated by the ellipse angle, the angle at which a circle is viewed to appear as an ellipse.

50. OBJECTIVES 1. Identify the geometry that makes up basic 2D drawings.
2. Use board drafting or 2D CAD skills to create technical figures.
3. Describe the advantages of CAD contrasted with drawing with manual instruments