MEM05 Metal and Engineering
Training Package
M
PL
E
MEM05037C
Perform geometric development
Learner guide
SA
Version 2
Training and Education Support
Industry Skills Unit
Meadowbank
Product code: 5404
MEM05037C Perform geometric development
Acknowledgement
The TAFE NSW Training and Education Support Industry Skills Unit, Meadowbank would like to
acknowledge the support and assistance of the following people in the production of this learner
resource guide:
Kockhams Industries
W.E. Smith Engineering Pty Ltd
Redimix concrete
Writers:
E
Paul Leete (North Coast Institute)
TAFE NSW
Reviewers:
PL
Neil Smith (Illwarra Institute)
Jim Miles (Contractor)
John Sharples (Illawarra Institute)
Murray McGregor (New England Institute)
Project Manager:
Enquiries
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Stephen Davies
Education Programs Manager
TAFE NSW
Enquiries about this and other publications can be made to:
Training and Education Support Industry Skills Unit, Meadowbank
Meadowbank TAFE
Level 3, Building J,
See Street,
MEADOWBANK NSW 2114
Tel: 02-9942 3200 Fax: 02-9942 3257
© The State of New South Wales, Department of Education and Training, TAFE NSW,
Training and Education Support Industry Skills Unit, Meadowbank, 2011
Copyright of this material is reserved to TAFE NSW Training and Education Support Industry Skills Unit,
Meadowbank. Reproduction or transmittal in whole or in part, other than for the purposes of private
study or research, and subject to the provisions of the Copyright Act, is prohibited without the written
authority of, TAFE NSW Training and Education Support Industry Skills Unit, Meadowbank.
ISBN 978 1 74236 228 1
Developed by Training & Education Support Industry Skills Unit, Meadowbank
© TAFE NSW 2011
MEM05037C Perform geometric development
Table of Contents
Topic 3: Radial line development ......................................................................... 55
1. General introduction ......................................................................................................... 5
Pattern development for conical sections ............................................................................... 58
2. Using this learner guide .................................................................................................... 5
Review questions ............................................................................................................... 61
3. Prior knowledge and experience ......................................................................................... 6
Pattern allowances ............................................................................................................. 63
4. Unit of competency overview ............................................................................................. 6
Pattern development using calculations ................................................................................. 67
5. Assessment ..................................................................................................................... 7
Calculating material sizes for patterns ................................................................................... 71
Introduction to unit .............................................................................................................. 8
Truncated right cones ......................................................................................................... 72
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Introduction .......................................................................................................... 5
Development of truncated right cone .................................................................................... 73
Topic 1 - Geometric methods and terminology .................................................... 11
Method 1: Parallel line development ..................................................................................... 11
Review questions ............................................................................................................... 81
Topic 4: Triangulation development ................................................................... 83
Method 3: Triangulation development ................................................................................... 12
How to develop a pattern for a square to round transition ........................................................ 86
Review questions ............................................................................................................... 13
Pattern allowance ............................................................................................................... 90
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Method 2: Radial line development ....................................................................................... 11
Triangulation for radius corner transitions .............................................................................. 94
Topic 2: Parallel line development ....................................................................... 15
Review questions ............................................................................................................. 104
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How to mark out a pattern .................................................................................................. 18
Labelling and storage of templates ....................................................................................... 23
Resource Evaluation Form ................................................................................. 107
Truncated rectangular prism ................................................................................................ 24
Truncated cylinder .............................................................................................................. 26
Pattern allowances ............................................................................................................ 29
Review questions ............................................................................................................... 31
True lengths .................................................................................................................... 32
Rectangular elbow .............................................................................................................. 34
45˚ Cylindrical elbow .......................................................................................................... 37
4 segment 90° lobsterback .................................................................................................. 40
Cylindrical branch connections ............................................................................................. 44
Pattern allowances for branch connections ............................................................................. 46
Inclined cylindrical branch connection ................................................................................... 49
Inclined rectangular branch connection ................................................................................. 51
Developed by Training & Education Support Industry Skills Unit, Meadowbank
© TAFE NSW 2011
MEM05037C Perform geometric development
Topic 1 - Geometric methods and terminology
Method 2: Radial line development
A tradesperson can develop true detailed patterns of geometric shapes using the principles of
mathematics and geometry in particular. Three of the most common geometric development methods
are:
•
•
•
parallel line
radial line
triangulation
It uses radial lines to develop patterns of pyramids and conical shapes. Generator lines radiate from the
apex of the pyramid or cone.
These lines are used to develop the pattern or stretch-out.
Pyramids
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It uses a series of parallel lines to develop a square, rectangular and cylindrical shapes. The patterns of
these shapes are shown when they are unfolded or rolled out flat. They are often referred to as "stretch
outs"
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Method 1: Parallel line development
Stretch out
Rectangular prisms
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Cones
Stretch out
Cylinders
Page 11 of 110
Apex
MEM05037C Perform geometric development
Method 3: Triangulation development
Terminology used for shapes
Uses a series of adjoining triangles to develop patterns of irregular shaped transition pieces.
Top
Curved surface
Axis
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Parallel
Generator
Line
Axis
Radial
Generator
Line
Curved
surface
Base
Base
Square to round transition
piece with round corners
Half transition
Cones
Apex
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Square to round
transition piece
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Cylinder
Half transition
Page 12 of 110
Slant edge
Axis
Triangular
curved surface
Triangular
surface
Flat triangular
surface
Base
Joint/Seam
Base edge
Pyramid
Base edge
Generator line
Transition piece
MEM05037C Perform geometric development
Review questions
8. What is the shape of each end of a typical transition piece?
These questions will help you revise what you have learnt in topic 1, geometric methods and
terminology.
_____________________________________________________________________________
Geometric development
1. List three (3) common methods of geometric development:
• ________________________________________________________________________
• ________________________________________________________________________
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• ________________________________________________________________________
2. Name a shape produced by each of these methods:
• ________________________________________________________________________
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• ________________________________________________________________________
• ________________________________________________________________________
3. Give one (1) example for each method of a finished article:
• ________________________________________________________________________
• ________________________________________________________________________
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• ________________________________________________________________________
4. Name a finished article that needed the use of more than one geometric development method:
__________________________________________________________________________
5. The unfolded or unrolled pattern is called the: (Circle your answer)
a. Prism
b. flat surface
c. stretch out
6. The generator lines on a cone radiate from the:
a. point
b. apex
c. base
d. cylinder
d. axis
7. Which statement best describes the term parallel:
a.
b.
c.
d.
starting from common point
series of adjoining triangles
two lines equal distance apart
generator lines
Page 13 of 110
MEM05037C Perform geometric development
Topic 2: Parallel line development
Drawing interpretation and calculations
To mark out a pattern for a rectangular prism or cylinder, we need to calculate the perimeter or
circumference of the article.
Parallel line development is used
to develop rectangular and cylindrical
shapes.
Remember, a pattern is simply the article unfolded or unrolled. This unfolded length is often called the
stretch-out length of the pattern blank. (See examples below)
The square prism stretch-out length is the sum of all 4 sides.
pr
ism
E
u
are
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sq
Seam
Square prism
(X = Y)
B
d
en
lin
e
B
d
en
lin
e
n
Be
in
dl
e
Cylinder stretch out length is equal to its circumference
Circumference = diameter x 3.1416 ( )
r
de
lin
Cy
Cir
Seam
St
Page 15 of 110
re
tch
-o
ut
cu
mf
er
en
ce
of
cy
lin
de
r
MEM05037C Perform geometric development
Student exercises - Drawing interpretation and calculations
Exercise 2.1
Calculate the stretch-out length of the square prism and fill in the other missing dimensions on the
stretch-out.
Exercise 2.2
Calculate the stretch-out length of the rectangular prism and fill in the other missing dimensions on the
stretch-out
Rectangular prism
Square Prism
200
ism
Seam
Top view
B
in
dl
en
e
Be
nd
l
ine
Front view
Right side view
e
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350
Be
lin
nd
Be
Stretch-out
Page 16 of 110
450
Front view
nd
lin
e
n
Be
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Top view
Square prism
(X = Y)
Seam
in
dl
e
Be
380
u
pr
E
200
sq
are
200
Right side view
Stretch-out
nd
lin
e