DEVELOPMENT BY TRIANGULATION. TRIANGULAR DEVELOPMENT Triangulation is slower and more difficult than...
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DEVELOPMENT BY TRIANGULATION
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Transcript of DEVELOPMENT BY TRIANGULATION. TRIANGULAR DEVELOPMENT Triangulation is slower and more difficult than...
DEVELOPMENT BY TRIANGULATION
TRIANGULAR DEVELOPMENT Triangulation is slower and more difficult than parallel line or radial line development, but it is more practical for many types of figures. Additionally, it is the only method by which the developments of warped surfaces may be estimated.
In development by triangulation, the piece is divided into a series of triangles as in radial Line development. However, there is no one single apex for the triangles. The problem becomes one of finding the true lengths of the varying oblique lines. This is usually done by drawing a true, length diagram.
A BRIEF LOOK AT PARALLEL LINE DEVELOPMENT
THE VIEW ON THE LEFT SHOWS THE DEVELOPMENT OF A TRUNCATED CYLINDER.
PARALLEL LINES
A BRIEF LOOK AT RADIAL LINE DEVELOPMENT
RADIAL LINES OF A CONE
Triangulation Development
In this method of development the surface of the object is divided into a number of triangles. The true sizes of the triangles are found and they are drawn in order, side by side, to produce the pattern. It will be apparent that to find the true sizes of the triangles it is first necessary to find the true lengths of their sides.
TRUE LENTHS
1. REBATEMENT OR ROTATION METHOD
2. TREE METHOD
EXAMPLE 1 REBATEMENT METHOD
PLAN
ELEVATION
bcad
o
o
d c
baHP
VP
Before starting with the development you must find the true lengths of sides
‘oa’, ‘ob’, ‘oc’ and ‘od’.
The base lines, lines
‘ab’, ‘bc’, ‘cd’ and ‘da’
are all true lengths since they are all parallel or perpendicular to the reference line HP/VP.
TL
PLAN
ELEVATION
bcada1
o
o
d c
ba
The rotation method is used to find the true length of line ‘oa’.
TL
TLTL
TL
PLAN
ELEVATION
b1c1bcadd1a1
o
o
d c
baTrue lengths of the other lines are worked out.
Notice how the drawing is becoming cluttered with lines.
DEVELOPMENT
c
o
a
db
a
TL
TLTL
TL
PLAN
ELEVATION
b1c1bcadd1a1
o
o
d c
ba
To draw the development, you start by drawing one triangle first.
In the example, triangle ‘oab’ is drawn first.
Draw second triangle, triangle ‘obc’.
Draw third triangle, triangle ‘ocd’.
Draw last triangle, triangle ‘oda’.
Do not forget to use the true lengths of the lines.
EXAMPLE 1 TRUE LENGTH TREE METHOD
O
PLAN
ELEVATION
EXAMPLE 2 ROTATION METHOD
O
O
1
12
11
10
9
8
76
5
4
3
2
1
1
1110
9
34
5
6
7
8
75,94,103,112,12113,114,105,96,87
TRUE LENGTHS
O
DEVELOPMENT
PLAN
ELEVATION
Develop the given oblique cone.
Develop the given oblique cone.
Divide the oblique cone into a number of triangles.
The most convenient number is twelve since you can easily divide the base into twelve divisions and join the divisions to the apex.
Use the rotation method to find the true lengths of all lines.
Using the true lengths of the sides, draw the triangles one at a time.
Do not forge to start from the shortest side.
O
O
1
12
11
10
9
8
76
5
4
3
2
1
1110
9
34
5
6
7
8
13,114,105,96,87
PLAN
ELEVATION
O
TRUE LENGTH TREE
75,94,103,112,121
TRUE LENGTHS
O
Method 2 TRUE LENGTH TREE METHOD
TRUNCATED OBLIQUE CONE
Transition PieceOften in industry it is necessary to connect tubes and ducts of different
cross-sectional shapes and areas, especially in air conditioning, ventilation and fume extraction applications. The required change in shape and area is achieved by developing a transition piece with an inlet of a certain shape and cross-sectional area, and an outlet of a different shape and area; for example square-to-round.
EXAMPLE 1 Develop the given square to square transition piece.
TLTL
1a
4
d
3
2
1
21,3
DEVELOPMENT
PLAN
ELEVATION
c
1
2
3
bab1,c1bcada1,d1
4
4
d c
ba
The rotation method is used to find the lengths of the sides.
TL
1a
4
d
3
2
1
21,3
DEVELOPMENT
PLAN
TL TREE
c
1
2
3
baa,b,c,dbcad
4
4
d c
ba
1,2,3,4
ELEVATION
The true length tree is used to find the true lengths of the sides.
EXAMPLE 2 Develop the given circle to rectangle transition piece.
78
910
11
121
2
34
56
a
ba
5
5 4
410
1
TL
TL
7
d
7
41,7
DEVELOPMENT
PLAN
ELEVATION
c
b,ca,d
10
d c
ba
The rotation method is used to find the true lengths of the lines.
78
910
11
121
2
34
56
a
ba
5
4,1,10,7
410
1
TL 2,3,5,6,8,9,11,12
TL
7
d
7
41,7
DEVELOPMENT
PLAN
ELEVATION
c
b,ca,d
10
d c
ba
TL TREE
The true length tree is used to find the true lengths.
bdcaba,bbf,gede
PLAN
ELEVATIONTRUE LENGTH TREE
a
1
g
d
e
f
4
c
3
2
b
a
2,1 3,4
32
1 4 g
f
e
dc
a,b
b
a
1
DEVELOPMENT
EXAMPLE 3
The true length tree is used to find the true lengths.
EXAMPLE 4 CIRCLE TO SQUARE
EXAMPLE 5 CIRCLE TO RECTANGLE
