Module 2 - eCollege

Trade of Sheet Metalwork
Module 2: Geometry and Pattern
Development
Unit 9: Triangulation
Phase 2

Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Table of Contents
List of Figures.................................................................................................................... 4
List of Tables ..................................................................................................................... 4
Document Release History ............................................................................................... 5
Module 2 – Geometry and Pattern Development........................................................... 6
Unit 9 – Triangulation..................................................................................................... 6
Learning Outcome: ..................................................................................................... 6
Key Learning Points: .................................................................................................. 6
Training Resources: .................................................................................................... 7
Key Learning Points Code:......................................................................................... 7
Transformers................................................................................................................... 11
False Length .................................................................................................................... 11
Ellipse............................................................................................................................... 11
Process of Triangulation................................................................................................. 11
Self Assessment................................................................................................................ 13
Answers to Questions 1-4. Module 2.Unit 9.................................................................. 15
Index................................................................................................................................. 16
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
List of Figures
Figure 1 - Triangulation 1................................................................................................... 8
Figure 2 - Triangulation 2................................................................................................... 9
Figure 3 - Triangulation 3................................................................................................. 10
List of Tables
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Document Release History
Date Version Comments
01/08/06 First draft
09/10/06 Implemented edits from
Brendan Deasy.
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Module 2 – Geometry and Pattern Development
Unit 9 – Triangulation
Duration – 30 Hours
Learning Outcome:
By the end of this unit each apprentice will be able to:
• Define the terms used in triangulation
• State the "golden rule" of triangulation
• Develop transformers between parallel planes
• Identify joint line positions
• Construct elliptical and oval shapes
Key Learning Points:
D Golden rule of triangulation.
D Pattern development using the triangulation
method.
D Methods used to find the true length of a line.
D True length diagram.
Rk Types and shapes of transformers.
D Determination of joint line positions.
D Elliptical construction.
D Major and minor areas.
M Calculate the surface area and perimeters of the
eclipse.
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Training Resources:
• Drawing instruments, equipment and materials
• Textbook: The Geometry of Sheet Metalwork
• Instructor handouts, drawings
Key Learning Points Code:
M = Maths D= Drawing RK = Related Knowledge Sc = Science
P = Personal Skills Sk = Skill H = Hazards
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Figure 1 - Triangulation 1
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Figure 2 - Triangulation 2
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Figure 3 - Triangulation 3
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Transformers
Sheet metal workers use the terms ‘transformer’ and ‘reducer’ often. A transformer alters
or modifies the shape of the cross section. The cross sectional area remains the same. A
reducer, as its name implies, cuts down the area.
The above items come in various shapes, examples being Equal Taper as in Fig. 1, Off
Centre as in Fig. 2, Twisted as in Fig. 3 and Flat Backed as the name implies.
False Length
A false length is a line that can’t be represented properly on a flat sheet of paper/metal.
Examples are sloping sides on transformers and reducers.
Ellipse
The formula for the surface area of an ellipse is = πRr.
The perimeter may be got by placing a light piece of metal around the edge of the ellipse
and measuring.
It can also be calculated by dividing the ellipse into its four different curves and
calculating the length of each curve.
Process of Triangulation
The golden rule in triangulation is Plan Length against Vertical Height.
Triangulation is a process of building up the pattern piece by piece in the form of
triangles.
Plan length refers to any length in the plan.
Vertical height is the finished height of the job and is gotten from the elevation.
The apprentice will come across true lengths and false lengths during their career. It is
important to recognise the difference.
To obtain the true length of any line place the plan length against the vertical height at
right angles and measure the diagonal.
If a line has a plan length but no vertical height then the true length is the plan length,
gotten from the plan.
If a line has a vertical height but no plan length then its true length is gotten from the
elevation.
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Self Assessment
Questions on Background Notes – Module 2.Unit 9
1. What is the golden rule of Triangulation?
2. What is the formula for the surface area of an ellipse?
3. Which view from a drawing gives us the vertical height?
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
4. Are all lines in an elevation drawing necessarily true lengths?
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Answers to Questions 1-4. Module 2.Unit 9
1.
2.
3.
4.
Plan length against vertical height and measure the resulting
diagonal.
Formula for surface area of an ellipse = π R . R
The Elevation
No, you must check to see if the line has a plan length in the
drawing if not, that particular line is a true length.
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Trade of Sheet Metalwork – Phase 2
Module 2 Unit 9
Index
E
Ellipse, 11
F
False Length, 11
P
Process of Triangulation, 11
S
Self Assessment, 13
T
Transformers, 11
Unit 9 16