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2Using drawing tools
& applied geometry
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Contents
Applied Geometry(or geometrical constructions)
Using of tools
Preparation of tools
Problem solving steps
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Preparation ofTools
Contents
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1. Paper
2. Pencils
3. Compass
Fastening a sheet to a drafting board
Sharpening the lead
Sharpening the lead
Tools to be prepared
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Paper
1. Place a paper close to the left edge of atable where a drafter can work conveniently.
3. Move the paper until its lower edge lies
close to the top edge of a T-square.
4. Align the top edge of the paper with
T-square blade.
5. Attach the papers corners with tape.
6. Move T-square down to smooth the paper.
7. Attach the remaining papers corners
with tape.
2. Place a T-square.
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1. Remove the wood with penknife while expose a lead
about 8-10 mm.
2. Polish the lead into a conical shape with a sandpaper.
3. Clean the lead with tissue paper.
Pencil
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Compass
2. Adjust the needleand theleadso that the tip of
the needle extends slightly more than the lead.
1. Sharpen the lead with a sandpaper.
needle lead
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Using the Tools
Contents
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Straight line
Arc, Circle4. Circle template
1. T-square
2. Triangles
3. Compass
Tools
Shape to be drawn
Function of the tools
T-square and triangles can be used together to draw
an inclined line with 15oincrement, i.e. 15o, 30o, 45o,
60o, 75o, 90o, 105o, 120o, 135o, 150o, 165o, 180oetc.
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To keep your drawing clean
Do Dont
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Using a compass
1. Locate the center of the circle to be drawn.
Draw two intersecting lines.
2. Adjust the distance between a needle and a lead
to be a radius of the circle.
3. Set the needle point at the circles center.
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4. Start circle.Apply enough pressure to the needle,
holding the compass handle between thumb and index
fingers.
5. Complete circle.Revolve the handle clockwise.
Using a compass
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1. Draw two perpendicular lines that pass through center of
a circle to be drawn.
Construction line
Visible line
2. Align all markings on template with the center lines.
3. Tracing the circle.
GivenCenter of a circle to be drawn
Using a template
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A
B
Draw a line through the given points
1. Place the pencil tip at one of the
given points.
2. Place the triangle against the
pencil tip.
3. Swing the triangle around the
pencil tip until its edge aligns with
the second point.
4. Draw a line.
Given
play
Explanations
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Draw a horizontal line
1. Press the T-square head against the left edge
of the table.
2. Smooth the blade to the right.
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Draw a horizontal line3. Lean the pencil at an angle about 60owith the paper
in the direction of the line and slightly toed in.
4. Rotate the pencil slowlywhile moving the pencil
from left to right.
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Draw a horizontal line
5. Move T-square up or down to draw another
horizontal line.
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Draw a vertical line1. Set T-square as before.
Place any triangle on T-square edge.
2. Use your left hand to hold both T-square and triangle
in position.
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Draw a vertical line
3. Lean the pencil to the triangle.
4. Draw the line upward while rotating the pencil slowly.
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1. Place 30o-60otriangle on the T-square edge and press
them firmly against the paper.
2. Draw the line in the direction as shown below.
Draw a line at 30owith horizontal
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Draw a line at 45owith horizontal
2. Draw the line in the direction as shown below.
1. Place 45otriangle on the T-square edge and press
them firmly against the paper.
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Draw a line at 60owith horizontal
1. Place 30o-60otriangle on the T-square edge and press
them firmly against the paper.
2. Draw the line in the direction as shown below.
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Draw a line at 15o with horizontal
1
2
+-30o
45o
= 15oCCW
+60o
(-45o)
= 15oCCW
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Draw a line at 75o with horizontal
1
2
+30o
45o
= 75oCCW
+45o 30o = 75oCCW
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Draw a line at 105o with horizontal
1
2
+60o
45o
= 105oCCW
+45o 60o = 105oCCW
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Practice by Yourself
Arrange the triangles to draw a line at
a) 120o
b) 135o
c) 150
o
with a horizontal.
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Applied Geometry
Contents
r
Bisecting Parallel line
Perpendicular
line
Inclined line
Tangent line
Tangent arc
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Bisecting a lineand an angle
Applied Geometry Contents
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To bisect a given line
1. Swing two arcs having a radius
greater than half-length of the
line with the centers at the
ends of the line.
2. Join the intersection points of
the arcs with a line.
A
B
r1r1
3. Locate the midpoint.
Given
play
Explanations
Applied Geometry
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To bisect a given angle
2. Swing the arcs of any radiusfrom the intersection points
between the previous arc and
the lines.
3. Draw the line.
1. Swing an arc of any radius
whose centers at the vertex.
r1
A
B
C
r2
r2
Given
play
Applied Geometry
Explanations
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Drawing a parallel line
Applied Geometry Contents
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+C
Line parallel to a given line
through a given point
Given
play
Applied Geometry
Explanations
3. Slide the first triangle until its
edge passes through the
given point.
1. Line an edge of a triangle up
to a given line.
2. Support the triangle with
another one.
4. Draw a line.
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r
Line parallel to a given line
at a given distance
Given
play
Explanations
3. Draw a line parallel to a given
line and tangent to the arc.
1. Choose a convenient point on
a given line.
2. Use that point as center of an
arc with a radius equal to a
given distance.
Applied Geometry
r
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Drawing a perpendicular line
Applied Geometry Contents
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+C
Line perpendicular to a point in a line
Revolv e method
Given
play
Explanations
3. Flip the first triangle and slide
until its edge passes through
the given point.
1. Line an oppositeedge of a 45o
triangle up to a given line.
2. Support the triangle with another
one.
4. Draw a line.
Applied Geometry
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+C
Ad jacent-s ides method
Given
play
Line perpendicular to a point in a line
Explanations
3. Slide the first triangle until
another adjacent edge passes
through the given point.
1. Line an adjacentedge of a 45o
triangle up to a given line.
2. Support the triangle with another
one.
4. Draw a line.
Applied Geometry
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r1
+C
r2
r2 > r1
A
B
D
Given
play
Line perpendicular to a point in a line
Compass method
Explanations1. Use a given point as center,
draw the arc with any radius.
2. Bisect the distance between the
intersection points between anarc and a given line.
3. Draw a line.
Applied Geometry
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Line perpendicular to a given line
through a point outside the line
+C
Given
play
Ad jacent-s ides methodExplanations
3. Slide the first triangle until
another adjacent edge passes
through the given point.
1. Line an adjacentedge of a 45o
triangle up to a given line.
2. Support the triangle with another
one.
4. Draw a line.
Applied Geometry
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Given
play
r2
+C
r2
r1
B
A
D
Line perpendicular to a given line
through a point outside the line
Compass method Explanations
1. Use a given point as a center,
draw the arc with any radius that
intersect the given line.
2. Bisect the distance between the
intersection points between an
arc and a given line.
3. Draw a line.
Applied Geometry
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Practice by Yourself
Draw a line perpendicular to a given line and passthrough a point lies outside using revolvedmethod.
Applied Geometry
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Drawing an inclined line
Applied Geometry Contents
Li ki 15o ith i li
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Line making 15owith a given line
through a given point
+C
+C
Given
play
Given
play
Applied Geometry
Li ki 30o ith i li
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Line making 30owith a given line
through a given point
+C
+C
Given
play
Given
play
Applied Geometry
Li ki 75o ith i li
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Line making 75owith a given line
through a given point
+
C
Given
play
Given
play
+
C
Applied Geometry
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Drawing a Tangent lineto an arc (or a circle)
Applied Geometry Contents
T t li t i ( i l )
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C
Tangent line to a given arc (or circle)
play
Case 1 : A given po int l ies on an arc
Applied Geometry
Given Explanations
3. Slide the first triangle until
another adjacent edge passesthrough the given point.
1. Line an adjacentedge of a 45o
triangle up to the center of an
arc and a given given.
2. Support the triangle with another
one.
4. Draw a line.
T t li t i ( i l )
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Tangent line to a given arc (or circle)
play
C
play
C
Applied Geometry
Case 2 : A given po int l ies outs ide an arc
Given Given1stmethod
2ndmethod
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Drawing a tangent curveto the given lines
Applied Geometry Contents
K C t
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Key Concept
1. its center, C.
To draw a tangent arc (of a specified radius, R),
it is necessary to locate
2. the startand end points
(or tangent points) of the arc.
It places outside a line for a distance
equal to a radius of an arc.
It lies on a given line in the way
that the line passing through this
point and the center of an arc be
perpendicular to a given line.
R
R R
T t t th i li
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Tangent arc to the given lines
R
R
play
Given 1. Locate the center of an arc
Applied Geometry
Continue
T t t th i li
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TP.1TP.2
Tangent arc to the given lines
2. Locate the tangent points
Applied Geometry
Replay
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Drawing a tangent curveto the given curves
Applied Geometry Contents
Key Concept
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Tangent point lies on the line passes through the centers
of each arc (or circle).
Key Concept
R1
R2
R3
Tangent arc to a gi en arcs (or circles)
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Tangent arc to a given arcs (or circles)
C2C1
C
C1 C2
C
1. its center, C.
To draw a tangent arc (of a specified radius, R),
it is necessary to locate
Case 1 : External Case 2 : Internal
2. the startand end points(or tangent points) of the arc.
R1R
R
R2 R1
R-R1 R-R2
R2
External tangent arc
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++C
1
C2
R+ R1
R+ R2
R1
R2C
External tangent arc
R
play
Applied Geometry
Given
Internal tangent arc (Type 1)
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++
C1C2
RR2
Internal tangent arc (Type 1)
RR1
R1
R2
C
R
play
Applied Geometry
Given
Internal tangent arc (Type 2)
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R+ R2
RR1C
Internal tangent arc (Type 2)
++C1 C
2
R1
R2
play
R
Applied Geometry
Given
Problem solving steps
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Problem solving steps
1. Calculate the required space
2. Understand the drawing type and information to be required
3. Choose suitable scale
4. Start drawing
Drawing Tools to be Purchased
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Drawing Tools to be Purchased
1. Transparent T-Square
2. Drawing board (optional)
3. Lead Pencil / Clutch Pencil
4. Sharpener, Eraser
5. 30o60oTriangle & 45oTriangle (Set Squares)
6. Compass and Divider
7. Paper Tape (0.5 inch wide)
8. Pocket size tissue pack
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