DPT 1222 ENGINEERING DRAWING GEOMETRIC CONSTRUCTION 1 1

DPT 122/2 ENGINEERING DRAWING GEOMETRIC CONSTRUCTION 1

1. 6 Geometry Constructions. Table 1. 4 Geometry Construction Description. 2

1. 6 Geometry Constructions. Example 1. 22 3

1. 6 Geometry Constructions. Example 1. 23 4

1. 6 Geometry Constructions. Example 1. 24 5

1. 6 Geometry Constructions. Example 1. 25 6

1. 6 Geometry Constructions. Example 1. 26 7

1. 6 Geometry Constructions. Example 1. 27 8

1. 6 Geometry Constructions. Example 1. 28 9

1. 6 Geometry Constructions. Example 1. 29 10

1. 6 Geometry Constructions. Example 1. 30 11

1. 6 Geometry Constructions. Example 1. 31 12

1. 6 Geometry Constructions. Example 1. 32 13

1. 6 Geometry Constructions. Example 1. 33 14

1. 6 Geometry Constructions. Example 1. 34 15

1. 6 Geometry Constructions. Example 1. 35 16

1. 6 Geometry Constructions. Example 1. 36 17

1. 6 Geometry Constructions. Example 1. 37 18

1. 6 Geometry Constructions. Example 1. 38 19

1. 6 Geometry Constructions. Example 1. 39 20

1. 6 Geometry Constructions. Example 1. 40 21

1. 6 Geometry Constructions. Example 1. 41 22

1. 6 Geometry Constructions. Example 1. 42 23

1. 6 Geometry Constructions. Example 1. 43 24

1. 6 Geometry Constructions. Example 1. 44 25

1. 6 Geometry Constructions. Example 1. 44 26

1. 6 Geometry Constructions. Example 1. 45 27

1. 7 Four types of basic conic section. b) Circle. c) Ellipse. d) Parabola. e) Hyperbola. 28

29

30

31

1. 8 Helix. The helix is the curve generated by a point that revolves uniformly around and up or down the surface of a cylinder. The lead is the vertical distance that the point rises or drops in one complete revolution. To draw a helix: 1. Given the diameter of the cylinder and the lead, draw the top and front views. 2. Divide the circumference (top view) into a convenient number of parts (use 12) and label them. 3. Project lines down o the front view. 4. Divide the lead into the same number equal parts and label them. 5. The points of intersection of lines with corresponding numbers lie on the helix. Note: Since points 8 -12 lie on the back portion of the cylinder, the helix curve starting at point 7 and passing through point 8, 9, 10, 11, 12 to point 1 will appear as a hidden line. 6. If the development of the cylinder is drawn, the helix will appear as a straight line on the development. *Refer Figure 5 -25 32

33

1. 9 Parabola The parabola is a plane curve generated by a point that moves along a path equidistant from a fixed line (directrix) and a fixed point (focus). Again, these method produce an approximation of the true conic section. To construct a parabola-parallelogram method: 1. Given the sizes of the enclosing rectangle, distance AB and AC, construct a parallelogram (Fig. 5 -26 A). 2. Divide AC into a number of equal parts. Number the points as shown. Divide distance A-O into the same number of equal parts. 3. Draw a line from O to point 1 on line AC. Draw a line parallel to the axis through point 1 on line AO, intersecting the previous line O 1. The point of intersection will be one point on the parabola. 4. Proceed in the same manner to find other points on the parabola. 5. Connect the points using an irregular curve. 34

To construct a parabola-offset method: 1. Given the sizes of the enclosing rectangle, distance AB and AC, construct a parallelogram (Fig. 5 -26 B). 2. Divide OA into four equal parts. 3. The offset vary in length as the square of their distance from O. Since OA is divided into four equal part, distance AC will be divided into 42, or 16, equal divisions. Thus since )1 is one-fourth the length of OA, the length of line 1 -11 will be (1/4)2, or 1/16, the length of AC. 4. Since distance O 2 is one-half the length of OA, the length of line 2 -21 will be (1/2)2, or 1/4, the length of AC. 5. Since distance O 3 is three-fourths the length of OA, the length of line 3 -31 will be (3/4)2 , or 9/16, the length of AC. 6. Complete the parabola by joining the points with an irregular curve. 35

36