Lecture -26

http://home.iitk.ac.in/~mukesh/

Development of Surfaces - II

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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)

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