TECHNICAL DRAWING Lecture notes
MET.BME.hu
Dr. Annamaria DUDÁS, PhD, MSc. civ. eng.
Department of Architectural Engineering
Faculty of Civil Engineering
Budapest University of Technology and Economics
MET.BME.hu
TECHNICAL DRAWING
Civil engineering representation preparatory course
Technical drawing
Short program of the subject
Intro
G2
G4
G6
T1
T3
T5
T7
T9
T11
T13
T15
16
AP2
Lectures ( 2 classes / week ) & Practice lessons ( 2 classes / week )
Mondays 8-10 K blg. 138.
Thursdays 8-10 K blg. 138.
Introduction
G1
Basics of geometry: positions of lines,
Types of technical drawing tools, list
angles, planes
of necessary tools
Types of rulers and pencils,
G3
Types of lines, meanings and
applications, methods, drawing,
application
redrawing, coloured pencils, patterns
Practice: construction lines
Drawing of parallels, perpendiculars
Construction of angles: bases
Hand out of 1st H.A. drawing task
Parallel ruler: fixing
G5
Topic on next practices: Construction of
angles (135, 225, etc.) Technical
Angles: measuring, using compass,
construction of angles:
writing, technical letters: introduction,
60, 90, 120, 30, 45
application, importance, practice
Parallel ruler: application
G7
Construction of geometrical forms:
Drawing of text frame, namebox on
triangles, rectangles, squares,
parallelograms, circle  ellipse
a drawing paper, Technical writing
Hand out of 2nd H.A. drawing task
practice
st
HAND IN of 1 H.A. drawing task
Construction of cover folder;
T2
2D, 3D representation
CONTROL TEST 30 minutes
Technical writing practice; Copy task
– magnifying
Test review
System of orthogonal projection
T4
3D, axonometric views, Practicing
HAND IN of 2nd H.A. drawing task
drawing tasks
Hand out of 3rd H.A.
drawing task
System of orthogonal projection
T6
System of orthogonal projection (simple
examples, practicing)
Repetition of control test
Scales: representation of a room or
T8
Copying of a ground plan and an
flat in sketch (small scale), in
elevation view of a small building
construction (1:50, 1:100)
(techniques)
HAND IN of 3rd H.A. drawing task
CONTROL TEST 30 minutes
Hand out of 4th H.A. drawing task
Copying of a ground plan of a small T10
Furnishing plan
traditional living house in scale 1:100
Representation of diagrams, figures
Ground plan of a small building
T12
Ground plan of a small building
Repetition of control test
2D  3D special reasoning exercises T14
2D  3D special reasoning exercises.
Basics of descriptive geometry
2D  3D special reasoning exercises. AP1
Picture mount (passe-partout)
Basics of descriptive geometry
(construction, cutting out, sticking on an
HAND IN of 4th H.A. drawing task
optional picture)
SEMESTER TEST 90 minutes
Practice, test review
Envelope (construction, cutting out,
sticking, addressing)
Repetition of semester test
Representation of plans at the corridors
of K. blg., Preparation for other subjects
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TECHNICAL DRAWING
GEOMETRY
G1
1. Basics of Geometry, Positions of Lines, Angles, Planes
1.1.
a.
b.
c.
Positions of Lines
Horizontal
Vertical
Inclined
1.2.
Relative Positions of Two Lines
a. Intersecting lines
Figure 1: Intersecting lines
 The two lines are in the same plane (they define a plane).
 They have one common point (the point of intersection).
b. Parallel lines
Figure 2: Parallel Lines
 The two lines are in the same plane (they define a plane).
 They do not have a point of intersection.
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TECHNICAL DRAWING
c. Skew lines
Figure 3: Skew lines
 The two lines are not in the same plane (two lines within the same plane
have to be either intersecting or parallel).
 They do not have a point of intersection.
1.3.
Definition of a Plane
a. Three points
Figure 4: Definition of a plane using three points
 The three points cannot be on the same line.
 The three points create a triangle, which defines the plane.
b. One point and a line
Figure 5: Definition of a plane using one point and a line
 The point cannot be on the line.
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c. Two intersecting lines
Figure 6: Definition of a plane using two intersecting lines
d. Two parallel lines
Figure 7: Definition of a plane using two parallel lines
In class, we usually use polygons to define a plane. This is the easiest method to
understand and visualize it.
1.4.
Relative Positions of Two Planes
a. Intersecting planes
Figure 8: Intersecting planes
 If there is a single point of intersection of the planes, consequently there
is also a line of intersection.
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b. Parallel planes
Figure 9: Parallel planes
 If two planes do not have a point of intersection, consequently they are
parallel.
 A line on the first plane and a line on the second plane are skew lines.
1.5.
Angle of Inclination of Two Lines
Figure 10: Angle of inclination of two lines
 Two intersecting lines divide their plane into four parts.
 The two angles opposite to each other are equal.
 The smaller angle created by the intersection is the angle of inclination.
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TECHNICAL DRAWING
2. Types of Technical Drawing Tools, List of Necessary Tools
2.1.
Using a Compass
To draw an arc with the compass, first mark the center point. Then draw a line from
the center point, and measure the radius on this line.
Place the compass point onto the marked center point. Open the compass so that
the lead points to the radius mark.
While drawing the arc, incline the compass slightly forward (see figure 11). Draw over
the arc again if it is not dark enough.
Figure 11: Using a compass [2]
2.2. Using a Curve Ruler
A curve ruler is used to draw irregular curves that are not a combination of circle
arcs.
1. Locate as many points on the curve as you need to define it.
2. Find the part of the ruler that fits on at least three points (A, 1, 2 for the first
segment).
3. Draw the curve segment, but stop before you reach the third point.
4. Find the part on the ruler that fits on the next three points (1, 2, 3 for the second
segment).
5. Keep going like this until you reach the end of the curve. Make sure you have a
smooth transition between the curve segments.
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Figure 12: Using a curve ruler [2]
2.2.
Triangles
Right triangles with 45° and 30° + 60° angles are used to make engineering drawings
(see figure 13).
Using triangles can help reduce the required movement of parallel rulers (and thus
avoid smudging the drawing).
Figure 13: Basic triangle types [2]
Triangles should be protected from damage.
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TECHNICAL DRAWING
GEOMETRY
G2
1. Drawing of Parallels, Perpendiculars
1.1. Drawing Horizontal Lines
 Place a triangle onto the vertical edge of the paper.
 Place a straight ruler against the perpendicular side of the triangle.
 Draw the line from left to right on the top edge of the straight ruler, holding the
pencil at 60° angle with the paper.
Figure 14: Drawing horizontal lines [2]
1.2. Drawing Vertical Lines
 Place the triangle onto the horizontal edge of the paper.
 Place a straight ruler against the perpendicular side of the triangle.
 Draw the line upward.
Figure 15: Drawing vertical lines [2]
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1.3. Drawing Inclined Lines
 Use a triangle, or the combination of a 45° and a 30-60° triangles to find the
desired angle from the horizontal or vertical edge of the paper.
Figure 16: Drawing inclined lines [2]
1.4. Drawing Parallel Lines
 Use two triangles, or a triangle and a straight ruler.
 Place the edge of the triangle along the given line.
 To draw a parallel, place the guiding triangle or straight ruler against the other
side of the triangle, and slide the triangle to a new position.
 Draw the new line along the same edge of the triangle as before.
Figure 17: Drawing parallel lines [2]
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TECHNICAL DRAWING
1.5. Drawing Perpendicular Lines




Use two triangles, or a triangle and a straight ruler.
Place the side of the triangle next to the right angle onto the given line.
Guide the other side of the triangle by another triangle or straight ruler.
Slide the first triangle along the guiding ruler until the right position draw the
line perpendicular to the given line.
Figure 18: Drawing perpendicular lines [2]
1.6. Divide a Straight Line into a Given Number of Equal Parts
 To divide LM, draw a skew line from L below LM.
 Using a compass, measure equal distances on the skew line from L, as many
times as many parts you want to divide LM into.
 Connect M to the last point of this line from P.
 Draw parallels LP line at every point on the line from B.
 The intersections of LM and the parallel lines are divided into equal distances.
Figure 19: Dividing a line into equal parts [2]
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1.7. Divide a Line Proportionally
 Given AB, draw BC perpendicular to AB.
 Place a ruler from A through BC so that the number on the ruler at the
intersection with BC is equal to the sum of the numbers representing the
proportions.
 Draw lines parallel to BC at the proportions.
 The illustrated proportions are 1:2:3.
Figure 20: Dividing a line proportionally [2]
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TECHNICAL DRAWING
G3
1. Construction of Lines
 Draw continuous lines with smooth, continuous movements.
 Avoid the corners that do not touch. Slight overlap is OK.
1.1.
Types of Lines
 Two widths of lines are recommended: thick and thin.
 The thick line should be twice as thick as the thin one.
1.2.
Line Types and Meanings
Line type
continuous thick line
continuous thin line
dashed thin line
dash-dot thin line
dashed thick line
etc.
Figure 21: Basic line types [1]
Meaning
section line
visible line
hidden line
center line, axis line
cutting plane
Figure 22: Line types and meanings [4]
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1.3. Practice: thin lines, thick lines, construction lines, colored pencils, erasure, felttip pen, ink pen, ink over something
Figure 23: Lineweight practice [3]
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2. Construction of Angles: Basics
 An angle is formed by two intersecting lines.
 Types of angles:
o
full circle: 360°
o
straight angle: 180°
o
right angle: 90°
o
acute angle: less than 90°
o
obtuse angle: more than 90°
o
complementary angles: two angles that add up to 90°
o
supplementary angles: two angles that add up to 180°
Figure 24.: Types of angles [1]
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TECHNICAL DRAWING
G4
1. Angles: Measuring, Using a Compass, Construction of Angles: 90°, 60°, 120°, 30°,
45°
1.1.
Transferring an Angle
 Use any radius to draw arcs with A and A’ as their center.
 Measure CB and use the same arc to find C’.
Figure 25: Transferring an angle [1]
1.2. Bisecting an Angle
 Use any radius to draw an arc from the center of the given angle (A).
 Draw arcs from B and C with the same radius ‘r’.
 Connect the intersection of the arcs (D) with A to draw the bisectors.
Figure 26: Bisecting an angle [1]
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1.3. Drawing a Line Through a Point and Perpendicular to a Line (Construction of a 90°
Angle)
1.3.1. When the point is not on the line
 With P as the center, draw an arc that intersects the line in 2 points (C and D).
 Find the midpoint between the two intersections (E).
 The line through P and E is perpendicular to the original line.
Figure 27: Drawing a perpendicular to AB line through a point
being not on the line [1]
1.3.2. When the point is on the line
 With P as the center, draw an arc that intersects the line in 2 points (D and G).
 Draw equal arcs from D and G on one side of the line.
 Connect the intersection of the arcs with P to draw the perpendicular line.
Figure 28: Drawing a perpendicular to AB line through a point of
the line [1]
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1.3.3. Drawing perpendicular line with rulers
 Use a triangle and a parallel ruler or a second triangle or T square.
 Align one edge of the triangle with the line, and align the second ruler with
the long side.
 Slide the triangle until the other side aligns with P, then draw the perpendicular
line ‘PR’.
Figure 29: Drawing a perpendicular to AB line [1]
1.4. Drawing a 60° Angle
 Draw a line; it will be one side of the angle.
 From the center point of the angle, draw an arc with any radius.
 Measure the same radius from the intersection of the line and the arc onto the
arc.
 Connect the intersection of the two arcs with the center point to draw the
other side of the angle.
(For explanation see figure : Geometry Practice Guides, Task 3, page: 33)
1.5. Drawing a 120° Angle
 Repeat the process of drawing a 60° angle, but measure the radius onto the
arc twice, instead of once.
1.6. Drawing a 30° Angle
 Repeat steps of drawing a 60° angle.
 Bisect the 60° angle.
1.7. Drawing a 45° Angle
 Draw a 90° angle, then bisect it.
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G5
1. Construction of Angles (135°, 225°, etc.)
1.1.
Drawing a 135° Angle
 Construct a 90° angle.
 Construct the bisector of the angle to create one side of the 135° angle.
 The other side of the angle is the extension of one of the sides of the original
90° angle.
 The 135° angle is the smaller angle defined by these two sides.
1.2.
Drawing a 225° Angle
 construct a 90° angle
 construct the bisector of the angle to create one side of the a 135° angle
 the other side of the angle is the extension of one of the sides of the original
90° angle
 the 225° angle is the larger angle defined by these two sides
2. Technical Writing, Technical Letters: Introduction, Application, Importance,
Practice
A technical drawing always includes text in addition to figures. The text is necessary
to completely describe an object. It includes descriptions of the structure, sizes, and
other notes.
The text has to be lettered in a plain, legible style. This lesson explains the lettering
and how to create it. Most engineering lettering is Gothic font.
Figure 30: Pencil lettering [1]
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Technical writing lettering is similar to freehand drawing. It has little to do with writing
ability; one can learn to letter neatly even if their handwriting is not neat.
2.1. The three main aspects of learning to letter
1. The proportions and shapes of the letters
Figure 31: The proportions and shapes of the letters [2]
Uniformity in height, width, spacing, inclination, and line thickness are important for
technical writing lettering.
Letters narrower than normal are compressed letters, wider than normal letters are
called extended letters.
Figure 32: Compressed and extended letters [2]
2. Composition and spacing of letters and words
The space between letters in a word should be half of the area of the letter M for
standard lettering.
3. Practice
The lettering of technical drawing requires practice, constant repetition. At the
beginning, focus on the form not the speed. Avoid sketching, because it results in
variable darkness and width.
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1.2.
Capital Letters
Vertical capital letters and numerals are 6 units high. The letter I and the number 1
are each 1 unit wide. The widest letter in the alphabet, W, is 8 units wide. Six unit
letters are the ones that spell TOM Q. VAXY, all other letters are 5 units wide.
The following figures show the proper technique for vertical and inclined capital
letters and numerals.
Figure 33: Vertical uppercase letters [1]
Figure 34: Inclined uppercase letters [1]
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1.3. Lowercase Letters
Lowercase letters are only used in technical drawings for longer notes. The height of
the lower part of the letter is 2/3 the height of the capital letter.
Figure 35: Vertical lowercase letters [1]
Figure 36: Inclined lowercase letters [1]
1.4. Large and Small Caps in Combination
When using this style, make the height
of the small capital letters about 3/5
the height of the large capital letters.
Figure 37: Combined letters [2]
1.5. Fractions
The height of numbers in a fraction is ¾
of the height of a non-fractional
number. The division bar is horizontal
and centered. The axis of the fraction
should be parallel to the axis of the
whole number.
Figure 38: Height of a fraction [2]
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1.6. Titles
Titles should be all large caps. The important items should be titled with more
prominent, larger lettering and thicker lines.
A title should be symmetrically placed. To ensure this, count the number of letters
and spaces, and then sketch the title lightly with a pencil, starting from the middle,
before you draw the final version with pen.
All the important information about a technical drawing should be represented in a
title block. The block should include the title of the drawing, the drawer, and date,
and any other important data.
Figure 39: Titles [2]
1.7. Text Alignment
Text on a technical drawing should be legible from no more than two directions.
Most of the text should be horizontal. The vertical text should be legible from the
right. Any slanted text should be easily legible from the same two directions.
Figure 40: Text alignment [2]
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TECHNICAL DRAWING
G6
1.
Parallel Ruler
1.1.
Fixing, Application
Figure 41: Parallel ruler application
1–4
Place 4 tacks on the long side of the drawing board.
5
Fix the end of the plastic cable provided in the package with the ruler to the
1st tack.
Place the ruler horizontally, in the middle of the board.
6
Run the cable down to the ruler (parallel with the side of the board), wrap it
around the left screw from the bottom, then around the right screw from the
top.
7
Run the cable down to the 4th tack. Do not fix.
8
Run the cable from the 4th to the 3rd tack.
9 – 10 Run the cable up to the ruler (parallel with the side of the board), wrap it
around the left screw from the top, then across the board and around the
right screw from the bottom
11
Run the cable up to the 2nd tack, and fix it.
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1.2. Fundamentals of using the ruler
Technical drawing requires a sitting position. Make sure you don’t slouch or bend
your back, you should maintain an ergonomic posture. This is crucial because
technical drawing requires long hours of sitting. Make sure that your chair is adjusted
to the proper height.
Purchase a good quality table light that is adjustable, so you can find its best position
above your work.
Use the parallel ruler to draw horizontal lines. Align the appropriate side of a triangle
ruler with the edge of your parallel ruler in order to draw vertical lines, as well as lines
with 45°, 30° and 60° degree inclination.
2. Drawing of Text Box, Namebox
Every technical drawing homework submitted to the Department of Architectural
Engineering has to include a namebox in the bottom right corner of the paper.
The dimensions of the namebox and the necessary information written in the
appropriate fields are shown below.
Figure 42: Namebox of the Department of Architectural Engineering
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G7
1. Construction of geometrical forms: triangles, rectangles, squares, parallelograms,
circle, ellipse
1.1.
Triangles
1.1.1. Basic types of triangles
 equilateral
 isosceles
 scalene
 right triangle
Figure 43: Basic types of triangles [1]
1.1.2. Construction of a triangle with known sides
 Draw a line and measure the length of side C onto it using a compass.
 Draw an arc from the left end of the line section C using a radius equal to the
length of side A.
 Draw an arc from the right end of the line section C using a radius equal to
the length of side B.
 Connect the intersection of the arcs with the ends of the line section C.
Figure 44: Construction of a triangle with known sides [1]
1.2. Quadrilaterals
Quadrilaterals are polygons with four sides.
1.2.1. Basic types of quadrilaterals
 Square – all sides are equal, all angles are 90°.
 Rectangle – opposite sides are equal, all angles are 90°.
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 Rhombus – all sides are equal, opposite sides are parallel, opposite angles are
equal.
 Rhomboid – opposite sides are equal and parallel, opposite angles are equal.
 Trapezoid – two sides are parallel.
 Trapezium – no sides are parallel.
Figure 45: Types of quadrilaterals [1]
1.2.2. Construction of a Square
Method I: given the side AB
 Using a parallel ruler and a triangle draw perpendiculars to AB through A and
B.
 Locate point D by drawing a 45° line from A.
 Draw a parallel to AB through D.
Method II: given the diagonal length
 Draw the diagonal horizontally.
 Using a parallel ruler and a 45° triangle draw the sides of the square.
Figure 46: Construction of a square - Method I and II [2]
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1.3. Circle
1.3.1. Definition
A circle is a closed curve. All of its points are equidistant from the center point.
The following figure shows the definition of the basic characteristics of circles:
Figure 47: Basic characteristics of circles [1]
1.3.2. To find the center of a circle through three given points not in a straight line
 Connect A, B, and C with straight lines, and draw the perpendicular bisectors
of the lines.
 The intersection point of the bisectors is the center of the circle (O).
1. Figure: Construction of a circle from 3 given points not on a line [2]
1.4. Conic Sections
When a right circular revolution cone is cut by planes at different angles, four
different types of intersection curves are created, called conic sections.
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 The result of the intersection with a horizontal plane is a circle.
 The result of the intersection with a plane at a greater angle to the axis than
the cut form is an ellipse.
 The result of the intersection with a plane at the same angle to the axis as the
cut form is a parabola.
 The result of the intersection with a plane at a smaller angle to the axis than
the cut form is a hyperbola.
Figure 49: Conic sections [2]
1.5. Ellipse
1.5.1. Mathematical definition
An ellipse is a curve generated by a moving point whose total distance from the two
focal points is constant (equal to the major diameter).
In technical drawings ellipses appear when oblique circles (pipe sections, etc.) are
drawn in orthographic drawings.
1.5.2. Construction of an ellipse
 Draw concentric circles with diameters
equal to the major axis (AB) and the
minor axis (CD).
 Divide the circles into equal central
angles, and draw the diameters (for
example P1P2).
 From point P1 draw a line parallel to CD,
from point P1’ draw a line parallel to AB.
 The intersection point (E) is part of the
ellipse.
 Repeat the process with different
diameters until you get enough points
to draw the ellipse smoothly.
Figure 50: Construction of an ellipse [2]
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1.6. Regular Polygons
1.6.1. Construction of a Regular Pentagon Given the Circumscribing Circle
 Draw the circle and the perpendicular diameters AB and CD.
 Bisect OB straight line: the center point is E.
 Mark point F on AB from point E with CO as the radius.
 Using C as the center and CF as the radius, draw an arc to mark G.
 Locate the remaining vertices by measuring the same radius along the circle.
Figure 51: Construction of a regular pentagon [2]
1.6.2. Construction of a Regular Hexagon
Method I
 Draw a circle with AB as the diameter (the radius of the circle is equal to the
length of the side of the regular hexagon).
 Using the same radius draw arcs from points A and B.
 Connect the resulting intersections points (C, D, E, F) to A and B in the right
order to draw the hexagon.
Method II
 Draw line AB.
 Using a 30° and 60° draw the lines indicated on (b).
Figure 52: Construction methods of a regular hexagon [2]
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1.6.3. Construction of a Regular Octagon
 Draw a square and its diagonals. The sides of the square have the same
length as the distance of opposite sides of the octagon.
 Using the corners draw circles with the radius equal to half of the diagonal.
 The intersection points of the circles and the sides of the square are the
corners of the octagon.
Figure 53: Construction of a regular octagon [2]
1.6.4. Construction of Any Regular Polygon Given One Side
 Draw LM, then a semicircle with radius LM.
 Divide the circle into as many equal parts as the sides of the polygon using
radial lines.
 Using M as the center and radius LM draw an arc through the first radial line to
find point N.
 Using N as the center and the same radius strike an arc to find O on the
second radial line, repeat until you arrive back to point L.
Figure 54: Construction of a regular polygon [2]
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G8
1.
Construction of cover folder
2.
Copy task – magnifying
2.1. Squares Method of Magnifying
Figure 55: The squares method of magnifying [1]
The squares method is an easy way to magnify an image, or redraw in a different
smaller or larger scale. First create a grid on the original image. It is best to choose a
convenient equal spacing, like 5 mm or 10 mm. To create the second image in a
different scale, first draw the grid, enlarging or reducing the spacing between the
lines to fit the change in scale (for example: if you are going from 1:100 to 1:10,
increase the grid spacing by 10 times to the original). Then redraw the image square
by square, drawing the lines in and across the grid lines the same way as the original.
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Geometry Practice Guide (Source of figures [3])
1. To Construct Parallel Lines
2. To Bisect an Angle
- align the edge of a triangle ruler with
the first line
- draw arcs from S (as center point) to
intersect the two sides of the angle
- align a second guiding triangle or
straight ruler with the other side of the
triangle
- from the new points of intersection draw
intersecting arcs with the same radius to
create point II
- slide the triangle along the edge of the
guiding ruler
- connect S and II. to draw the bisector line
- draw the parallel line along the same
edge of the triangle
3. To Construct a 60° Angle
4. To Bisect a Line
compass
- draw an arc from S (as center point)
- draw a new arc with the same radius
from the intersection of the arc and the
horizontal line
- connect S with the intersection of the
two arcs to create the other side of the
angle
- draw arcs with the same radius (that is
larger than half of the line’s length) from
point A and B
- make sure to draw the arcs long enough
that they intersect in two points on either
side of the line
- connect the intersections of the arcs to
draw the bisector of the line
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TECHNICAL DRAWING
5. To Construct a Perpendicular line from a
Given Point Not On a Line
6. To Construct a Perpendicular line at a
Point On a Line
compass
compass
- draw an arc from P (as center point)
- make sure that the radius is large enough
so the arc intersects the line in two points
- from each of the intersections, draw arcs
with the same radius
- connect the intersection of the arcs with
P to draw the perpendicular to the given
line
- draw arcs from P (as center point) on
either sides of P
- draw arcs with equal radius from both
intersections of the arcs and the line
- connect the intersection of the arcs
with P to draw the perpendicular to the
given line
7. To Construct a 90° Angle
8. To Draw the Tangent of a Circle at a
Given Point
- draw an arc with a 3 cm radius and P as
its center point
- connect the center of the circle (M)
with the point on the circumference,
and extend the line
- from point P, use a compass to measure 4
cm on the horizontal line
- draw an arc with a 5 cm radius and this
new point as its center
- connect P with the intersection of the
arcs to create the other side of the 90°
angle at P
- use a compass to measure equal
distances on the line on both sides
- draw the bisector of the line segment
between the points marked II.
- this bisector line is also the tangent line
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9. To Trisect a 90° Angle (3*30°)
10. To Divide a Line into a Number of
Equal Parts
- draw an arch from S as center point
- to divide AB, draw a skew line from B
above AB
- using the same radius, draw arcs from
both intersections of the sides of the angle
and the arc
- connect the intersections of the first and
the two new arcs with S to get the
trisectors of the angle
- using a compass, measure equal
distances onto the skew line from B, as
many times as many parts you want to
divide AB into
- connect A to the last point of the skew
line and draw parallels to this
connecting line at every point of the
skew line
- the intersections of AB and the parallel
lines are equidistant
11. To Find the Golden Ratio
12. To Draw a Hexagon
compass
- draw a vertical line at point B, and
measure half the distance between A and
B (a) using a compass to create point C
- connect C to A and draw an arc with
the radius of a/2 and C as the center point
- use a compass to measure the distance
of A and the intersection of AC and the
arc
- draw a horizontal and a vertical line
through the center of a circle
- from the intersection points of the lines
and the circle, draw arcs with the radius
of the circle
- connect the intersections of the arcs
and the circle to draw the hexagon
- measure the same distance onto the
horizontal line from A
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13. To Draw an Equilateral Triangle
MET.BME.hu
14. To Draw a Spiral
compass
compass
- draw a vertical line through the
center of a circle
- from the intersection of this line and
the circle, draw an arc with the radius
of the circle
- connect the intersections of the arc
and the circle as well as the
intersection of the vertical line and the
circle
- draw points A, B, C, D (the corners of a
square), then draw vertical lines through A
and B, and horizontal lines through B and C
- start the spiral with A as the center point
and AD as the radius.
- draw the arc until you reach the
horizontal line from A
- switch to B as the center point, increase
the radius to continue the arc and draw
the arc until the vertical line at B
- continue with C as the center point, etc.
15. To Draw the Circumference Circle
of a Triangle
16. To Draw the Incircle of a Triangle
- construct the bisectors of the two
sides of a right triangle that are
adjacent to the right angle
- construct the bisectors of two angles of a
triangle
- the intersection of the bisectors is the
center of the circumference circle
- the intersection of the angle bisectors is
the center of the incircle of the triangle
- use the intersection point of an angle
bisector with the opposite side of the
triangle to measure the radius of the
incircle
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MET.BME.hu
T1
1.
2D, 3D representation
1.1. Basics
Buildings are traditionally described by using an orthogonal two dimensional system.
Ortho is a Greek word meaning right angle. Orthographic projection is the transfer of
images using perpendicular projector rays. The rays are parallel to each other, as if
the observer was at infinity (see figure 56.).
Figure 56: Transfer of images using perpendicular projector rays [2]
Each object is shown in three views, since no single image shows the thickness of the
object.
1.2. Principal planes
 The horizontal plane is parallel to the ground.
 The frontal elevation plane is vertical.
 The profile elevation plane is perpendicular to the other two planes.
The lines of sight and the projection lines are perpendicular to the principal planes.
(See figures 57, 58, 59.)
The folding plane line is the intersection of principal planes. The plan and profile
elevation planes are rotated into the plane of the frontal elevation.
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Figure 57: Projector lines are perpendicular to the principal planes I [2]
Figure 58: Projector lines are perpendicular to the principal planes II [2]
Figure 59: Orthographic views and the arrangement of the planes of projections [6]
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TECHNICAL DRAWING
T2-T5
1.
First-Angle Projection
The planes of projection form four 90° angles. First-angle projection is shown on the
following figures:
Figure 60: First-angle projection [2]
Figure61: First-angle projection [5]
The lines of intersection between the planes of projection are called coordinate
axes, the point of their intersection is called the origin.
2.
System of Orthogonal Projection
Definition of multiview projection: a method by which the exact shape of an object is
represented by two or more views produced by orthogonal projection planes.
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2.1. The Glass Box Method of Obtaining the Views of an Object
The projection planes placed around an object form a ‘glass box’. The observer
views the object from outside. The views are obtained by running projectors from
points on the object to the planes of projection.
Figure 62: The ’Glass Box' and unfolding the ’glass box’ [2]
Let’s assume that the ‘glass box’ is hinged so its sides can be folded down into a
single plane, thus creating a two dimensional representation of the original three
dimensional objects.
The figure shows the six views of an object created by the ‘glass box method’. Usually
only three of these views (front, top and right side views) are necessary.
Figure 63: The arrangement of the six views created by the ’glass box method’ [2]
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TECHNICAL DRAWING
2.1.1.
Examples for the six views of objects
Figure 64: Six views of a complex object [1]
Figure 65: Six views of a house [1]
Figure 66: Six views of a car [1]
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TECHNICAL DRAWING
2.2. Methods of orthogonal projection
There are several different methods to obtain additional views in orthogonal
projection.
The depth of an object can be transferred to the side view from the top view using a
compass (radial projection), using 45° lines (45° projection) or using a diagonal or
miter line. The miter line method is explained in detail in the following point.
Figure 67: Orthogonal projection methods [3]
2.3. Using a Miter Line
A miter line is a 45° line drawn next to the top view that can be used to help transfer
distances from the top and front views onto the side view. The technique is
demonstrated on a modified example from [5].
Step 1. Draw the miter line at a convenient distance on the right
side of the top view.
Step 2. Draw the lines from important points on the top view to
the miter line and then up to the side view quadrant.
Step 3. Connect the appropriate points to draw the vertex of
each surface on the side view
Figure 68: Steps of using a miter line [5]
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TECHNICAL DRAWING
2.4. Views of Surfaces
Surfaces that are perpendicular to a plane of projection appear a straight line,
parallel surfaces appear with their real size, and skew surfaces are shortened.
Figure 69: Views of surfaces [5]
Surfaces are defined based on their angle to the planes of projection. There are
three main types of surfaces:
A normal surface is parallel to a plane of
projection. Depending on the plane of projection
it appears either as a line or in its true size.
Figure 70: Normal surface [5]
Inclined surfaces are perpendicular to one plane
of projection, but inclined in the other direction.
Figure 71: Inclined surface [5]
Oblique surfaces are neither parallel nor
perpendicular to any of the planes of projection.
Figure 72: Oblique surface [5]
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TECHNICAL DRAWING
2.5. Views of Edges
The intersection of two plane surfaces produces an edge, which is represented by a
line in the drawing.
A normal edge is a line that is perpendicular to a plane of projection. It appears as a
point on that plane, and as a true length line on the other planes of projection.
Figure 73: View of a normal edge [5]
An inclined edge is parallel to one plane of projection, and inclined in the other
directions.
Figure 74: View of an inclined edge [5]
An oblique edge is neither parallel nor perpendicular to any of the planes of
projection.
Figure 75: View of an oblique edge [5]
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TECHNICAL DRAWING
2.6. Angles
An angle will be shown in its real size if it is in a normal plane. If an angle is in an
inclined or oblique plane, it may be projected with a different angle than in reality,
either larger or smaller.
Figure 76: Angles in different planes [5]
3.
Necessary views for representing an object
Usually not all the six views are necessary to describe an object adequately. Choose
the views that have the smallest amount of hidden lines so it is easier to understand.
The right and left side views are mirror images of each other when using hidden lines
so the images represent the same information. The same is true for top and bottom
views.
3.1. Representation of objects using two views
Many objects can be represented with only two views. In this case choose the right
side view over the left side view and choose the top view above the bottom view.
Figure 77: Porper arrangement of different views on a paper [5]
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TECHNICAL DRAWING
3.2. Representation of objects using three views
The following figure shows six views of an object. In most engineering drawings, three
views are enough. The following figure shows the three views that can be eliminated
without losing information.
Figure 78: Eliminating unnecessary views [5]
4.
Technical drawing details
4.1. Centerlines and hidden lines
Centerlines are used to indicate the axes of symmetry of objects and bolts.
Centerlines are useful in dimensioning. Centerlines are represented by dash-point
lines.
The proper way to draw the hidden lines in different situations is shown on the figures
below.
Figure 79: The proper way to draw hidden lines [1]
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4.2. Fillets and rounded edges
A rounded interior corner is called a fillet. A rounded exterior corner is called a round.
Fillets that connect with plane surfaces tangent to cylinders are called runouts.
Figure 80: Representation of rough and finished surfaces [5]
4.3. Suggested layout for engineering drawings
Figure 81: Suggested layout for freehand drawings [5]
Figure 82: Suggested layout for engineering drawings [5]
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TECHNICAL DRAWING
5.
3D, axonometric views
5.1. Types of projection
Figure 83: Types of projection [1]
5.2. (Representation of )Paraline Perspective
In paraline systems, the edges of parallel surfaces remain parallel. Verticals remain
vertical and the other axes slope at specified angles.
Figure 84: Paraline perspective[4]
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TECHNICAL DRAWING
5.3. Choosing the Appropriate Axonometric View
An object that you naturally view from below should be shown in perspective from
below.
Figure 85: Choosing the Axonometric View [5]
5.4. Three Dimensional Solids
Figure 86: 3D Solids [1]
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TECHNICAL DRAWING
T6
1.
Representation of a building
An elevation is the image of the building projected onto a vertical plane.
A
A
Figure 87: Projection of an elevation and its view[4]
A ground plan (floor plan) is created by cutting the building with a horizontal plane.
See the position of A-A horizontal cutting plane in Figure 87.
Figure 88: Cutting plane for ground plan and its view[4]
Sections are created by slicing the building with vertical planes. See the position of
B-B vertical cutting plane on Figure 88.
B
B
Figure 89: Cutting plane for a longitudinal section and its view[4]
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Buildings are usually represented by two sections that are created by vertical planes
that are perpendicular to each other. The planes should be placed at representative
parts of the building to show the roof structure, the supporting walls, and other
important structural elements (doors, windows, staircases).
Figure 90: The principle and the representation of a longitudinal section [4]
Figure 91: The principle and the representation of a cross section [4]
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2.
MET.BME.hu
Practice task
Copy the architectural drawing of a room or a small building in a given scale
1:50 (construction plan), or
1:100(permission plan)
Figure 92: Ground plan of a holiday house in scale 1:50
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T7
Copying of a Ground Plan of a Small Building (technique, pencils, thickness of lines)
Figure 93: Ground plan of a traditional countryard house in scale 1:100
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T8
Copying of an elevation view of a small building (techniques)
Figure 95: Elevation of a historical train station [7]
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AP1
Picture mount (passe-partout)
(construction, cutting out, sticking on an optional picture)
Figure 96: Pattern for a handmade paper picture mount
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AP2
Envelope
(construction, cutting out, sticking, addressing)
Figure 97: Pattern for a handmade postcarde
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Aknowledgement:
The author would like to say special thanks to Máté OROSZ MSc. civil engineer for his
feedback and review and to Luca NAGY demonstrator student for technical help.
References:
[1] Frederick E. Giesecke, Alva Mitchell, Heny Cecil Spencer, Ivan Leroy Hill, John
Thomas Dygdon, James E. Novak: Technical Drawing
Pearson Prentice Hall, 2003
[2] Warren J. Luzadder, P.E., Jon M. Duff, Ph.D.: Fundamentals of Engineering Drawing
Prentice-Hall International, Inc., 1989
[3] Heinrich-Jürgen Dahmlos, Dr. Karl-Hermann Witte: Bauzeichnen
ISBN 3-507-91042-X, 1977 Schroedel Schulbuchverlag GmbH, Hannover
[4] Rendow Yee: Architectural drawing, A Visual Compendium of Types and Methods
SBN 978-0-471-79366-3, John Wiley&Sons, 2007
[5] Frederick E. Giesecke, Alva Mitchell, Heny Cecil Spencer, Ivan Leroy Hill, John
Thomas Dygdon, James E. Novak: Modern Graphic Communication
[6] D. V. Jude: Civil Engineering Drawing, Second edition, Granada Publishing, 1983
[7] M. Kubinszky, T. Nagy, L. Túróczy: Ez a vonat elment, (in Hungarian) Topic:
Architecture of railways
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