Technical Drawing 1st Term 1st ESO

8/10/2019 Technical Drawing 1st Term 1st ESO

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Engineering Drawing 1

st

Term 1

st

ESO

2014/2015

Tools, Symbols and Basic Geometry

Technical drawing, also known as drafting, is the technique of creating engineeringdrawings done with compasses, rulers, and computers for business and industry.

Tools

Paper

The drawing paper for technical drawings is

classified as:Opaque paper- It can be white or coloured, butit is opaque.

Tracing paper- It is a translucent thick paper,suitable for leads and pens.

The most common paper sizes are:

A3- 420x297 mm

A4- 297x210 mm

A5- 210x148 mm

Pencil-Many pencils across the world, and almost all in Europe, are graded on theEuropean system using a continuum from H (for hardness) to B (for blackness).

The standard writing pencil is graded HB.

A set of pencils ranging from a very hard, light-marking pencil to a very soft, black-

marking pencil usually ranges from hardest to softest as follows:

9H 8H 7H 6H 5H 4H 3H 2H H F HB B 2B 3B 4B 5B 6B 7B 8B 9B

Hardest Medium Softest
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For technical drawing the best graphite pencilsare hard ones, from 2H to 3H

Calibrated felt pens-Disposable black felt penscome in different thicknesses. In the classroom

we are going to use 0,2 0,4 and 0,8 black feltpens.

Rubber or Eraser: It is a correcting tool toeliminate incorrect or extra lines. It is importantto have an appropriate eraser for technicaldrawing. Harder erasers are for harder leads.

Graduated Ruler: It is a precision tool we use tomeasure distances. Measurements are marked in millimeters.

Compass- It is a tool used to make arched lines and circles.Cheap compasses tend to slip on the paper and break quiteeasily. A good, quality compass set will last a life time.

How to use a compass

1st-Sharpen thelead with sandpaper until you

get a chiseled point.

2ndThe sharp point of the compassmust be slightly longer than the lead

3rdWhen drawing the arc or circle,

the graphite lead and the compasspoint must both be perpendicular tothe paper.

4thHold the handle of the compassbetween your thumb and finger androtate it gently in a clockwisedirection.

A protractor is used to measure angles. Atypical protractor is a semi-circular piece of

plastic with 180 degrees printed around its

curve. This piece of equipment is not only


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used in graphics for constructing accurate drawings but is also used in subjects like

Mathematics.

Set Squaresare used to draw accurate angles,parallel and perpendicular lines. They are calledthe 60 degree or the 45 degree triangle.

TRIANGULAR SET OF SQUARES

The triangular set of squares consists of two triangles:the 45 set square, and the 60 set square.

THE 45 SET SQUARE is a right isosceles triangle.The legs make a 90 angle and its hypotenuse forms a45 angle with each leg.

THE 60 SET SQUAREis a right scalene triangle. The legs make a 90 angle andits hypotenuse forms a 30 angle with the bigger leg and a 60 angle with the other.

The 45 and 60 triangular set squares form a set when the longest side of the 60triangle is the same as the hypotenuse of the 45 triangle.

DRAWING STRAIGHT PARALLEL AND PERPENDICULAR LINES:

See how the triangles are placed to draw exactly parallel, horizontal lines andexactly parallel, vertical lines. As you can see, the vertical lines are alsoperpendicular to the horizontal ones.


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Symbols and lines

Symbol Symbol Name Meaning / definition Example

angle formed by two rays ABC = 30

right angle = 90 = 90 degree 1 turn = 360 = 60

t,r,s.. Straight line

A line is one-dimensional. Thatis, a line haslength, but nowidth or height. Ingeometry, a lineextends forever inboth directions.

A line is uniquelydetermined by twopoints.

AE segment

A line segmentconnects twoendpoints. A linesegment with twoendpointsAand B

is denoted by .

Points A point has nolength, width, orheight - it justspecifies an exactlocation. It is zero-dimensional.

In geometry we usually

identify this point witha number or letter.

| perpendicularperpendicular lines(90 angle)

AC |

|| parallel parallel lines AB || CD

> Greater than > < Less than

Pairs oflinescan relate to each other in four different ways:intersecting lines,parallel lines,perpendicular linesandskew lines.These concepts are useful forunderstanding and solving various geometry problems.

Intersecting Lines

Intersecting lines are lines that meet at apoint.When two lines intersect, theydefineanglesat the point of intersection.
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at point C

Parallel Lines

Parallel lines are lines that never intersect. The distance between the two lines isfixed and the two lines are going in the same direction.

Two parallel lines

can be written as

Perpendicular Lines

Perpendicular lines are lines thatintersectat one point and form a 90 angle.

Two perpendicular lines

can be written as

Skew Lines

The above relationships between lines take place on the sameplane.However,skew lines only happen inspace.Skew lines never intersect because they are noton the same plane. Skew lines are difficult to draw because they exist in the threedimensional space. Lets consider a cube.
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Imagine the linesrunningalong the edges of a cube as shown,

and line running on the frontsurface of the cube.

They are lines in different planesand will never intersect.

To watch a video with the explanation go to:http://www.onlinemathlearning.com/pairs-of-lines.html

THE CIRCUMFERENCE

Formally, a circumferenceis defined as the locus of points from the planeequidistant to another point, called the center of the circumference.

We must never confuse the concept of a circle with the concept of circumference,circumference is actually a curve that encloses a circle (the circumference is acurve, the circle is an area.)

Basic Elements of the Circumference

chord Diameter

Here you can see all the elements we are going to introduce.

- Center: center point that is equidistant to all points belonging to thecircumference.- Radius: line connecting the center with any point belonging to the circumference.- Chord:line connecting any two points of the circumference.- Diameter:longer string connecting two points of the circumference. There are

infinite diameters and all pass through the centerof the circumference.
http://www.onlinemathlearning.com/pairs-of-lines.htmlhttp://www.onlinemathlearning.com/pairs-of-lines.htmlhttp://www.onlinemathlearning.com/pairs-of-lines.html


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- Secant line:line that cuts through any two points of the circumference.- Tangent line:line touching the circle at just one point and perpendicular to aradius.

Basic Geometry Constructions

Construct the perpendicular bisector of a line segment.

Or construct the midpoint of a line segment.

1. Begin with line segment XY.

2. Place the compass at point X. Adjust the compassradius so that it is more than (1/2)XY. Draw two arcs asshown here.

3. Without changing the compass radius, place thecompass on point Y. Draw two arcs intersecting thepreviously drawn arcs. Label the intersection pointsA and B.

4. Using the straightedge, draw lineAB. Label theintersection point M. Point Mis the midpoint of linesegment XY, and lineABis perpendicular to linesegment XY.

Given point P on line k construct a line through P perpendicular to k.

1. Begin with line k, containing point P.

2. Place the compass on point P. Using an arbitraryradius, draw arcs intersecting line kat two points.Label the intersection points Xand Y.


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3. Place the compass at point X. Adjust the compassradius so that it is more than (1/2)XY. Draw an arc asshown here.

4. Without changing the compass radius, place thecompass on point Y. Draw an arc intersecting thepreviously drawn arc. Label the intersection pointA.

5. Use the straightedge to draw lineAP. LineAPisperpendicular to line k.

Given point R not on line k construct a line through R perpendicular to k.

1. Begin with point line kand point R, not on the line.

2. Place the compass on point R. Using an arbitraryradius, draw arcs intersecting line kat two points.

Label the intersection points Xand Y.3. Place the compass at point X. Adjust the compassradius so that it is more than (1/2)XY. Draw an arc asshown here.

4. Without changing the compass radius, place thecompass on point Y. Draw an arc intersecting thepreviously drawn arc. Label the intersection point B.

5. Use the straightedge to draw line RB. Line RBisperpendicular to line k.


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Angles

An angle is the part of a plane defined by two straight lines that cross at the samepoint called vertex(V). There are different ways to label an angle. The one we aregoing to use is a capiltal letter with a little angle on top of it. Example: .

Angles are measured using a sexagesimal system. Using degrees(o), minutes () andseconds().

Two equal angles are called congruent angles.


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ANGLE BISECTOR

The angle bisector is a ray that divides the angle into two smaller angles withequal measure.

CONSTRUCTION


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Scalene Triangle Noequal sidesNoequal angles

What Type of angle?

Triangles can also have names that tell you what type of angleis inside:

Acute Triangle

All angles are less than 90

Right Triangle

Has a right angle (90)

Obtuse Triangle

Has an angle more than 90

Combining the Names

Sometimes a triangle will have two names, for example:

Right Isosceles Triangle

Has a right angle (90), and also two equal angles

Can you guess what the equal angles are?

Constructing a Triangle given Three Sides

Using a ruler andcompass,construct a triangleABC withAB= 3 cm, BC = 4 cmandAC= 5 cm.

Solution:

Step 1: Draw a line,AB, 3 cm long.Step 2: Draw anarcofradius4 cm with Bas the centre.
http://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#compasshttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#compasshttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#compasshttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#archttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#archttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#archttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#radiushttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#radiushttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#radiushttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#radiushttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#archttp://www.mathsteacher.com.au/year8/ch10_geomcons/03_circles/comp.htm#compass


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Step 3:

Draw an arc of radius 5 cm withAas the centre to cut the arc drawn inStep 2 at C.Step 4:

Join, C, the point of intersection of the two arcs to the pointsAand B.Step 5: Erase the arcs to obtain the required triangleABC.

REGULAR POLYGONS

INTRODUCTION:

A POLYGON is a closed, flat surface with strait sides. We can classify thenaccording to shape:

Equilateral polygon:This is a polygon whose sides are all the same length.

Equiangular polygon:This is a polygon whose angles are all the same size.

Regular polygon:This is a polygon with equal sides and angles.

Irregular polygon:This is a polygon whose sides and angles are not equal.

Inscribed polygon:This is a polygon that is inside a circumference. In otherwords, its vertex angles are in contact with the circumference and the centreof the polygon is also the centre of the circumference.

Circumscribed polygon: This is a polygon whose sides are tangent to acircumference. This means that the circumference must be inscribed insidethe polygon.

Star polygon:This is a polygon whose angles alternate outwards and inwards

and whose sides form a closed, continuous interrupted line.

HOW TO INSCRIBE POLYGONS IN A CIRCUMFERENCE:

Inscribing an EQUILATERAL TRIANGLE in a Circumference:

1. Draw a circumference with the given radius and the centre at O.


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2. Draw the diameter, AP, of the circumference. With your compass on one ofthe endpoints (for example at point P), open it to the width of the

circumferences radiusand draw an arc thatintersects it at points B

and C.3. Join points A, Band C to get the trianglewe are looking for.

Inscribing a SQUARE in a Circumference:

1. Draw a circumference with thegiven radius (r). Draw two diameters thatare perpendicular to each other tointersect the circumference, giving us thefour vertex A, B, C and D.

2.

Join these points to make thepolygon.


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Inscribing a PENTAGON in a Circumference:

1. Draw a circumference with the given radius and the centre on point O. Nextdraw two perpendicular diameters (MN) and (PJ).2. With your compass on point J, open to the width of the circumferences

radius and draw an arc that intersects it at points 1 and 2. Join these two pointsto get point H along radius OJ.3. With your compass on point H, open to the length of the radius of HM anddraw an arc until it intersects radius PO at point G. Segment MG is one of thesides of the pentagon.4. Now starting at point M, open your compass to the length of MG andconstruct this length onto the circumference, giving us in this way, the vertex ofour polygon (points A, B,C and D). We get our pentagon by joining all thesevertexes.

Inscribing a HEXAGON in a Circumference:

The hexagon is the only regular polygon whose sides are equal to the radius of thecircumference circumscribing it.

1. Draw the circumference of radius r and diameter AD.2. With your compass at point A, open it to the radius of AO and drawan arc that intersects the circumference at points B and F.


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3. Place your compass at point D, open it to the radius of DO and drawand arc that intersects the circumference at points E and C.4. Join these points to get our hexagon.

Inscribing a HEPTAGON in a Circumference:

1. Draw the circumference with the givenradius and point O as its centre.

2. The first steps in drawing a heptagonare the same for drawing an equilateraltriangle to get points M and N.

3. We join M and N, and half of its lengthJM is equal to the heptagons sides.

4. Use the length of JM seven timesaround the circumference with your compass toget the vertex of our polygon.


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Inscribing an OCTAGON in a Circumference:

It is so easy to draw an inscribed octagon that you can follow the steps shown in

the illustration:

A star polygonis a non-convex polygon which looks in some way like a star.

We can create different starts connecting the alternative vertexes of any regularpolygon.

A six-pointed star, like a hexagon, can be createdusing a compass and a straight edge:

Make a circle of any size with the compass. Without changing the radius of the compass,

set its pivot on the circle's circumference, and findone of the two points where a new circle wouldintersect the first circle. With the pivot on the last point found,

similarly find a third point on the circumference, andrepeat until six such points have been marked.

With a straight edge, join alternate points on the circumference to form twooverlapping equilateral triangles.

Approximate Division of a Circle into Equal Parts General Instructions)

You are given a circle with the center point of O.

1. Divide diameterAL into as manyequal parts as you are going to divide thecircumference, using Thales Theorem. The example drawn below is down in11 equal parts.

2. Open the compass so its points are onA and L, the endpoints of thediameter, and draw two arcs. The arcs should have a radius equal in lengthto the diameter. Label the point where they intersect M.

3. Draw a ray from point Mthrough point 2 on lineAL and intersects thecircle on the other side. This intersection becomes point B.
http://upload.wikimedia.org/wikipedia/commons/6/67/Star_polygon_6-2.svghttp://upload.wikimedia.org/wikipedia/commons/6/67/Star_polygon_6-2.svg


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4. Use the compass to measure between pointsA and B. Use thismeasurement to draw points C, D, E, F, G, H, I, J, and K. Connect pointsAthrough Kto draw the polygon.

Technical Drawing 1st Term 1st ESO

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