oblique cones
TRANSCRIPT
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1 3 5 7 9 11 13 15 17 19 21 23 1
3579
11
13
15
1719
21
23
1
*
9,17
Development of Truncated Cylinder – treated as a many-sided prism
Do not forget the true shape of truncated face
2
34
5
6
7T
8
910
11
12
1T
1I
2
3
4
5
6
7
89
AI
101112
1I
SI
RI
SIRI
AF
RFRRSF
7F IF
AT
R’T
ST
3,11
TR
TI
TI
2,12
Development of Truncated Cone
This is called method of Triangulation – for Cone equal lengths triangle
AxisPath of Revolution
F
HF
H
Y
YR
ӨR
XH
YH
YHR
XF
YFRYFTL
Axi
s TL
ӨH
X
OBSERVATIONIf 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.
O
CT
1T
2T 3T 4T 5T 6T7T
8T
9T10T
OT,DT
OI CI
1I
2I3I
4I5I6I7I8I9I10I
OF
CF1F 3F 5F 7F 9F DF D 9 7 5 3 1 C
O
True lengths
One half of development
Development of Oblique Cone – Elements are of different lengths
10
Which line is seen in TL? O-10 in FV – begin development by laying off O-10Is 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 and get TL.Repeat the process for all lines and find TL diagram that gives all TLs.
½ E
A’
B C C’
½ E D’
B’
D 1I 2 3 4 5 6
7 8
9I
OI
VI
V
7 5,8 934251
1 23 4 5 6 789 O
OFVF,P
OT VT
A
B’C’
D’E
12
34 5
C
6 789,P
B
Development of Transition Piece – Join Cylindrical Pipe to Rectangular PipeThe 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 partsMake true length diagram for each cone
For cone – B(TL)
For cone – D(TL)
P