Lecture 26
TA111
Engineering Graphics 2023-2024, Sem-II
By
Dr. Mukesh Sharma
Professor
DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KANPUR
KANPUR-208016, INDIA
Development of an Oblique Pyramid
Cr
Dr
A1
Seam line
O1
A1
Or
Bend line
Ar
Br
B1
Or
D1
Stretchout or girth
C1
Axis
BRCR
CRBR
AR,DR
Soldered lap seam
ARDR
8
9
8
12
11
9
7
12
1I
R’T
AT
7T
10
11
10
ST
1T
SI
RI
6
TI
5
4
2
6
5
TI
3
4
3
AI
RI
AF
2
SI
1I
TR
RF RR
SF
7F
3,11 2,12 IF
Development of Truncated Cone
This is called method of Triangulation – for Cone equal lengths triangle
YH
X
Path of
Revolution
Axis
XH
XF
F
ӨR
H
F
Y
YR
TL Axis
O
YHR
ӨH
YF
OBSERVATION
If axis is perpendicular to the plane, the hypotenuse of triangle like XOYR will
always give the TL of the line. Or, if perpendicular and base are known so is the TL
Base is seen in the TV. Eureka moment in TA101!!
YFR
Development of Oblique Cone – Elements are of different lengths
One half of development
OI
10T
9T
CT
1T
2T
3T 4
T
7
5T 6T T
8T
1I
OT,DT
2I
OF O
9
10I I
CF
1F
3F
5F
7F 9F 10
CI
DF D
9
7
5
3
8I
7I
6I
5I
4I
3I
1 C
Which line is seen in TL? O-10 in FV – begin development by laying off O-10
Is 10-9 seen in TL, if yes proceed and mark and arc.
Do we know TL of O-9? No we don’t.
In fact, no other element is in TL (except O-C). Find a smart way to find all lines in TL.
Recall if true altitude and base of line are known hypotenuse is the TL of line.
For line O-9 see altitude and base (in TV) and get TL.
Repeat the process for all lines and find TL diagram that gives all TLs.
Connect two hollow objects having different base
Three surface
Transition Pieces
Triangulation Method: Dividing
a surface into a number of
triangles and transfer them to
the development
Development of Transition Piece – Join Cylindrical Pipe to Rectangular Pipe
OI
C’
B’
D’
A’
E
A 1
2
3
B
4 5 6
7
½E
C
OT
OF
1 23 4 5
C’
9,P
8
VT
6 789 O
VF,P
B’
D’
V
B
1I 2 3
4
56
C
VI
D
½E
P
7
8
9I
7 5,8 9
342 51
For cone – B For cone – D
(TL)
(TL)
The piece is composed of:
(a) 4-triangular planes (bases are sides of rectangle) (b) 4-parts of oblique cone (bases are arc of circles)
Development of Cone – Triangulation method – divide the cone in parts
Make true length diagram for each cone
OI
A’
C’
C
B’
B
1I
½E
D’
VI
2
3
4
D
5
6
7
8
9I
½E
P