Using Drawing Tools

Chapter 2 Using drawing tools & applied geometry

Applied Geometry (or geometrical constructions)
Using of tools
Preparation of tools
Problem solving steps

Contents

Contents

Preparation of Tools

1. Paper
2. Pencils
3. Compass
Fastening a sheet to a drafting board
Sharpening the lead
Sharpening the lead
Tools to be prepared

Paper

1. Place a paper close to the left edge of a table 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 paper’s corners with tape. 6. Move T-square down to smooth the paper.
7. Attach the remaining paper’s corners with tape. 2. Place a T-square.

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

Compass

2. Adjust the needle and the lead so that the tip of the needle extends slightly more than the lead.
1. Sharpen the lead with a sandpaper.
needle
lead

Contents

Using the Tools

Straight line

Arc, Circle
4. 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 15o increment, i.e. 15o, 30o, 45o, 60o, 75o, 90o, 105o, 120o, 135o, 150o, 165o, 180o etc.

To keep your drawing clean

Do
Don’t


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 circle’s center.

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

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.
Given
Center of a circle to be drawn
Using a template


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

Draw a horizontal line

1. Press the T-square head against the left edge of the table.
2. Smooth the blade to the right.

Draw a horizontal line

3. Lean the pencil at an angle about 60o with the paper in the direction of the line and slightly “toed in”. 4. Rotate the pencil slowly while moving the pencil from left to right.

Draw a horizontal line

5. Move T-square up or down to draw another horizontal line.

Draw a vertical line

1. 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.

Draw a vertical line

3. Lean the pencil to the triangle.
4. Draw the line upward while rotating the pencil slowly.


1. Place 30o-60o triangle 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 30o with horizontal

Draw a line at 45o with horizontal

2. Draw the line in the direction as shown below.
1. Place 45o triangle on the T-square edge and press them firmly against the paper.

Draw a line at 60o with horizontal

1. Place 30o-60o triangle 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 15o with horizontal

1
2
+
-30o
45o
= 15o CCW
+
60o
(-45o)
= 15o CCW

Draw a line at 75o with horizontal

1
2
+
30o
45o
= 75o CCW
+
45o
30o
= 75o CCW

Draw a line at 105o with horizontal

1
2
+
60o
45o
= 105o CCW
+
45o
60o
= 105o CCW

Practice by Yourself

Arrange the triangles to draw a line at 120o 135o 150o with a horizontal.

Contents

r
Bisecting
Parallel line
Perpendicular line
Inclined line
Tangent line
Tangent arc

Applied Geometry

Applied Geometry
Contents

Bisecting a lineand an angle

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
r1
r1
3. Locate the midpoint.
Given
play
Explanations
Applied Geometry

To bisect a given angle

2. Swing the arcs of any radius from 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

Applied Geometry

Contents

Drawing a parallel line

+
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.



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

Applied Geometry

Contents

Drawing a perpendicular line

+
C
Line perpendicular to a point in a line
Revolve method
Given
play
Explanations
3. Flip the first triangle and slide until its edge passes through the given point.
1. Line an opposite edge of a 45o  triangle up to a given line.
2. Support the triangle with another  one.
4. Draw a line.
Applied Geometry



+
C
Adjacent-sides 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 adjacent edge of a 45o  triangle up to a given line.
2. Support the triangle with another  one.
4. Draw a line.
Applied Geometry


r1
r2
+
C
r2
r2 > r1
A
B
D
Given
play
Line perpendicular to a point in a line
Compass method
Explanations
1. Use a given point as center, draw the arc with any radius.
2. Bisect the distance between the  intersection points between an  arc and a given line.
3. Draw a line.
Applied Geometry

Line perpendicular to a given line through a point outside the line

+
C
Given
play
Adjacent-sides method
Explanations
3. Slide the first triangle until  another adjacent edge passes  through the given point.
1. Line an adjacent edge of a 45o  triangle up to a given line.
2. Support the triangle with another  one.
4. Draw a line.
Applied Geometry

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

Practice by Yourself

Draw a line perpendicular to a given line and pass through a point lies outside using revolved method.
Applied Geometry

Applied Geometry

Contents

Drawing an inclined line

Line making 15o with a given line through a given point
+
C
+
C
Given
play
Given
play
Applied Geometry

Line making 30o with a given line through a given point

+
C
+
C
Given
play
Given
play
Applied Geometry

Line making 75o with a given line through a given point

+
C
Given
play
Given
play
+
C
Applied Geometry

Applied Geometry

Contents

Drawing a Tangent lineto an arc (or a circle)

C
Tangent line to a given arc (or circle)
play
Case 1 : A given point lies on an arc
Applied Geometry
Given
Explanations
3. Slide the first triangle until  another adjacent edge passes  through the given point.
1. Line an adjacent edge 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.



Tangent line to a given arc (or circle)
play
C
play
C
Applied Geometry
Case 2 : A given point lies outside an arc
Given
Given
1st method
2nd method

Applied Geometry

Contents

Drawing a tangent curveto the given lines

Key Concept
1. its center, C.
To draw a tangent arc (of a specified radius, R), it is necessary to locate
2. the start and 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

Tangent arc to the given lines

R
R
play
Given
1. Locate the center of an arc
Applied Geometry
Continue

TP.1

TP.2
Tangent arc to the given lines
2. Locate the tangent points
Applied Geometry
Replay

Applied Geometry

Contents

Drawing a tangent curveto the given curves

Tangent point lies on the line passes through the centers of each arc (or circle).
Key Concept
R1
R2
R3

Tangent arc to a given arcs (or circles)

C2
C1
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 start and end points (or tangent points) of the arc.
R1
R
R
R2
R1
R-R1
R-R2
R2



+
+
C1
C2
R + R1
R + R2
R1
R2
C
External tangent arc
R
play
Applied Geometry
Given


+
+
C1
C2
R – R2 Internal tangent arc (Type 1)
R – R1 R1
R2
C
R
play
Applied Geometry
Given

R + R2

R – R1 C
Internal tangent arc (Type 2)
+
+
C1
C2
R1
R2
play
R
Applied Geometry
Given

Problem solving steps

1. Calculate the required space.
2. Layout the drawing steps.
3. Match the construction techniques to each drawing step.
4. Start drawing.
Always use a construction line if the information to draw a line or a curve is incomplete.

Example

Drawing steps VDO