Morling K. Geometric and Engineering Drawing
Подождите немного. Документ загружается.
Geometric and Engineering Drawing194
The top drawing shows the traces of the plane after rabatment. The bottom draw-
ing shows the full projection of the plane. It should be obvious how the projection is
obtained if you are given the traces.
Figure 13.16 shows a triangular plane that is inclined to all three principal planes.
The top drawing shows the traces of the plane after rabatment. The bottom draw-
ing shows the full projection of the plane. It should be obvious how the projection is
obtained if you are given the traces.
T
V
Z
X
H
FVP
EVP
HP
Y
Third angle projection
Projection of plane
Traces of plane
Y
Y
EVP
Z
FVP
X
T
HP
H
V
Y
Y
Z
X
T
HP
H
V
Figure 13.16
To find the true angle between the HP and an oblique plane ( Fig. 13.17 ).
Y
XY
T
H
P
QS
R
V
FVP
First angle projection
HP
T
FVP
R
H
HP
S
PV
Q
X
Figure 13.17
A triangle is inserted under the oblique plane and at right angles to it. This tri-
angle, PQR, meets the HP at the same angle as the oblique plane.
The triangle is swung round until it is parallel to the FVP. Its new position is PQS
and the angle required is PS
ˆ
Q.
Further Orthographic Projection 195
To find the true angle between the VP and an oblique plane ( Fig. 13.18 ).
Y
XY
T
H
R
QS
P
V
First angle projection
T
FVP
R
H
HP
S
P
V
Q
X
Figure 13.18
A triangle is inserted under the oblique plane and at right angles to it. This triangle,
PQR, meets the FVP at the same angle as the oblique plane.
The triangle is swung round until it is parallel to the HP. Its new position is PQS
and the angle required is PS
ˆ
Q.
To find the true angle between the traces of a given oblique plane VTH
( Fig. 13.19 ).
X
Y
V
H
T
b
a
c
d
First angle projection
Figure 13.19
From any point a on the XY line draw ab (perpendicular to XY) and ac (perpen-
dicular to TH).
With centre T, radius T b , draw an arc to meet ac produced in d.
dc
ˆ
T
is the required angle.
Geometric and Engineering Drawing196
Exercise 13
(All questions originally set in imperial units.)
1. Figure 1 shows the shaped end of a square fence post. Lengths AD, BD, DC are equal.
By means of a suitable geometric construction find (a) the true length of BD, (b) the true
shape of the face ABD.
Associated Lancashire Schools Examining Board
2. Figure 2 gives the FE and plan of the roof of a house in first angle projection. Draw
the given views to a suitable scale and from them find, by construction, the true lengths of the
rafters A and B. Print these lengths under your drawing.
East Anglian Regional Examinations Board
50 mm
50 mm
A
B
88 mm
C
D
Figure 1
3500 mm
3500 mm
14000 mm
5250 mm
5250 mm
7000 mm
AB
Figure 2
Further Orthographic Projection 197
3. Figure 3 shows the projected elevation of a line AB which has a true length of 100 mm.
End B of the line is 12 mm in front of the VP; end A is also in front of the VP.
Draw the plan a, b and elevation of this line and determine and indicate its VT and HT.
Measure, state and indicate the angle of inclination of the line to the HP.
Joint Matriculation Board
4. A line AB of true length 88 mm lies in an auxiliary VP which makes an angle of 30 ° with
the VP. The line is inclined at an angle of 45 ° to the horizontal, the point B being the low-
est at a vertical distance of 12 mm above the HP and 12 mm in front of the VP.
Draw the plan and elevation of AB and clearly identify them in the drawing.
Associated Examining Board
5. The plan of a line 82 mm long is shown in Fig. 4 . The elevation of one end is at b .
Complete the elevation and measure the inclinations of the line to the HP and VP.
University of London School Examinations
Dimensions in mm
X
a
1
b
1
32
75
6
Y
Figure 3
56
10
12
44
X
a
b
Y
b′
Dimensions in mm
Figure 4
6. Figure 5 shows the plan of end A of a line AB. End A is in the plane HVT. End B is in the
HP. The line AB is perpendicular to the plane HVT .
Draw the plan and elevation of AB.
Joint Matriculation Board (HVT horizontal and vertical traces)
V
60°
45°
37 mm
43 mm H
+
a
YX
T
Figure 5
Geometric and Engineering Drawing198
7. The projections of a triangle RST are shown in Fig. 6 . Determine the true shape of the
triangle.
Associated Examining Board
8. The plan and elevation of two straight lines are given in Fig. 7 . Find the true lengths of the
lines, the true angle between them and the distance between A and C.
Southern Universities ’ Joint Board
9. Figure 8 shows the plan and elevation of a triangular lamina. Draw these two views and,
by finding the true length of each side, draw the true shape of the lamina. Measure and
state the three angles to the nearest degree.
Oxford and Cambridge Schools Examination Board
Dimensions in mm
t
1
2525
yx
S
T
12.5
37.550
56 32
12.5
s
1
r
1
R
Figure 6
b′
a′
c′
c
b
a
32
44 37
12
68 25
Dimensions in mm
2518
Figure 7
Dimensions in mm
c′
a′
b′
b
a
c
50
12.5
XY
25
75
50
62.5
2532.5
Figure 8
Further Orthographic Projection 199
10. In Fig. 9 the elevation and plan of a triangle ABC are shown. Determine the true shape
and size of the triangle.
University of London School Examinations
11. Figure 10 shows two views of an oblique triangular pyramid, standing on its base. Draw
the given view together with an auxiliary view looking in the direction of arrow A which
is perpendicular to BC. Also draw the true shapes of the sides of the pyramid. Note: Omit
dimensions but show hidden detail in all views. Scale: full size.
Oxford Local Examinations (see Chapter 10 for information not in Chapter 13).
B
BA
A
C
C
12
mm
XY
37 mm
37 mm 50 mm
75 mm
Figure 9
75
60°
A
B
C
32
82
34
6262
Dimensions in mm
Figure 10
This page intentionally left blank
Geometric and Engineering Drawing. DOI:
© 2010 Elsevier Ltd. All rights reserved.2010
10.1016/B978-0-08-096768-4.00014-0
Developments
There are three basic ways of fashioning a piece of material into a given shape. Either
you start with a solid lump and take pieces off, you can cast or mould an appropriate
material or you can bend sheet material as required.
It should be obvious that, if the last method is used, the sheet material must first
be shaped so that, after it is bent, you have the correct size and shape. If, then, a
component is to be made of sheet material, the designer must not only visualise and
draw the final three-dimensional component, but also calculate and draw the shape of
the component in the form that it will take when marked out on the two-dimensional
sheet material.
The process of unfolding the three-dimensional ‘ solid ’ is called ‘ development ’ .
The shapes of most engineering components are whole, or parts of, prisms, pyra-
mids, cylinders or cones, so this chapter deals with the development of the shapes.
Prisms
Figure 14.1 shows how a square prism is unfolded and its development obtained.
Note that where there are corners in the undeveloped solid, these are shown as
dotted lines in the development.
14
3
4
42
3
123
Figure 14.1 Developing a square prism.
Geometric and Engineering Drawing202
1
44
12
43
41
2
323
Figure 14.2 Developing a square prism.
True shape
of top
1
1
4
AA
23
65
2
6
3
54 1 2 3
A
A
4561
Figure 14.3 Developing a hexagonal prism.
To develop a square prism with an oblique top.
This development, shown in Fig. 14.2 , should be self-explanatory.
To develop a hexagonal prism with oblique ends ( Fig. 14.3 ).
The height of each corner of the development is found by projecting directly from
the orthographic view.
The shapes of the top and the bottom are found by projecting the true shapes of
the oblique faces. The top has been found by conventional means. The true shape is
projected from the elevation and transferred to the development.
The true shape of the bottom of the prism has been drawn directly on the develop-
ment without projecting the true shape from the elevation. The corner between lines
2 and 3 has been produced until it meets the projectors from corners 1 and 4. The
produced line is then turned through 90 ° and the width, 2A, marked on.
Developments 203
The development of intersecting square and hexagonal prisms meeting at
right angles ( Fig. 14.4 ).
A
Development of sides of
hexagonal prism
Development
of sides of
square prism
First angle projection
C
d
b
A
b
C
d
Figure 14.4 Developing intersecting square and hexagonal prisms meeting a right angles.
First an orthographic drawing is made and the line of interpenetration is plotted.
The development of the hexagonal prism is projected directly from the FE and the
development of the square prism is projected directly from the plan.
Projecting from the orthographic views provides much of the information required
to develop the prisms; any other information can be found on one of the orthographic
views and transferred to the developments. In this case, dimensions A, b , C and d
have not been projected but have been transferred with dividers.
The development of intersecting hexagonal and octagonal prisms meeting at
an angle ( Fig. 14.5 ).
First angle projection
2
12
36
45
1
2
3
4
5
6
1
3
4
5
6
g
e
f
h
d
Development of the sides of the octagonal prism
Development of
the sides of the
hexagonal prism
b
c
1
A
D
h
g
e
f
c
b
b
c
A
Figure 14.5 Developing intersecting hexagonal and octagonal prisms meeting at an angles.