SCALES

Usually the word scale is used for an instrument used for drawing straight lines. But actually in Engineer’s language scale means the proportion or ratio between the dimensions adopted for the drawing and the corresponding dimensions of the object. It can be indicated in two different ways. Example: The actual dimensions of the room say 10m x 8m cannot be adopted on the drawing. In suitable proportion the dimensions should be reduced in order to adopt conveniently on the drawing sheet. If the room is represented by a rectangle of 10cm x 8cm size on the drawing sheet that means the actual size is reduced by 100 times. 

Representing scales: The proportion between the drawing and the object can be represented by two ways as follows:

a) Scale: - 1cm = 1m or 1cm=100cm or 1:100

b) Representative Fraction: - (RF) = 1/100 (less than one) i.e. the ratio between the size of the drawing and the object.

There are three types of scales depending upon the proportion it indicates as

1. Reducing scale: When the dimensions on the drawing are smaller than the actual dimensions of the object. It is represented by the scale and RF as

Scale: - 1cm=100cm or 1:100 and by RF=1/100 (less than one)

2. Full scale: Some times the actual dimensions of the object will be adopted on the drawing then in that case it is represented by the scale and RF as

Scale: - 1cm = 1cm or 1:1 and by R.F=1/1 (equal to one).

3. Enlarging scale: In some cases when the objects are very small like inside parts of a wrist watch, the dimensions adopted on the drawing will be bigger than the actual dimensions of the objects then in that case it is represented by scale and RF as

Scale: - 10cm=1cm or 10:1 and by R.F= 10/1 (greater than one)

Note: The scale or R.F of a drawing is given usually below the drawing. If the scale adopted is common for all drawings on that particular sheet, then it is given commonly for all figures under the title of sheet.

1.7 Types of Scales and their constructions:

When an unusual proportion is to be adopted and when the ready made scales are not available then the required scale is to be constructed on the drawing sheet itself. To construct the scale the data required is 1) the R.F of the scale 2) The units which it has to represent i.e. millimetres or centimetres or metres or kilometres in M.K.S or inches or feet or yards or miles in F.P.S) The maximum length which it should measure. If the maximum length is not given, some suitable length can be assumed.

The maximum length of the scale to be constructed on the drawing sheet =

R.F X maximum length the scale should measure.

This should be generally of 15 to 20 cms length.

 Table: Metric Units Table: FPS Units

1 Kilometre (km) =10 Hecta metres (hm)                     1 Mile =8 Furlongs

1 Hectametere(hm) =10 Decametres(dam)or  0.1km         1 Furlong =220 Yards

1 Decametre(dam) =10 Metres (m) or  0.1hm                    1Yard =3 Feet

1 Metre(m) =10Decimetres(dm) or  0.1dam                       1 Feet =12 Inches

1 Decimetre(dm) =10 Centimetres(cm) or  0.1m

1 Centimetre(cm) =10 Millimetres (mm) or  0.1dm

The various types of scales used in practice are 1. Plain scales, 2. Diagonal scales, 3. Vernier scales, 4. Comparative scales and 5. Scale of chords.

1.7.1 Plain Scales: Plain scales read or measure upto two units or a unit and its sub-division, for example centimetres (cm) and millimetres (mm). When measurements are required upto first decimal, for example 2.3 m or 4.6 cm etc. It consists of a line divided into number of equal main parts and the first main part is sub-divided into smaller parts. Mark zero (O) at the end of the first main part. From zero mark numbers to the main parts or units towards right and give numbers to the sub-divisions or smaller parts towards left. Give the names of the units and sub-units below clearly. Indicate below the name of the scale and its R.F clearly.

The construction of the plain scale is explained below by a worked example.

W E 1.1 A 3 cm long line represents a length of 4.5 metres. Extend this line to measure upto 30 metres and show on it units of metre and 5 metre. Show the length of 22 metres on this line. Fig 1.10

i) The scale has to represent metre and 5 metres, hence it is a Plain scale.

ii) Given that 3cm represents 4.5metres or 450cm, Hence 1cm represents 450/3=150cm, hence scale is 1cm=150cm or 1:150: R.F=1/150

iii) Maximum length to read is 30metres; Length of the scale is 20cm. i.e. (1/150)x30x100 = 20cm

Construction:

Draw a straight line of 20cm length and divide into 6 equal parts.

Divide again first part into 5 equal parts. Give numbers as shown. To represent 22 metres, take 4 main parts to represent 20 metres and 2 small parts to represent 2metres. Give names as A and B so that the distance between A and B is 22 metres as shown.

Note: Assume height of the plain scale as 1 cm.

 Construct a plain scale of 1:5 to show decimeters and centimeters and to read upto 1 metre. Show the length of 7.4 decimetres on it. 

i) The scale has to represent decimetre and 1/10 of decimeter.

ii) Given that the scale is 1:5 that is R.F=1/5

iii) Maximum length to read is 1 metre; Length of the scale=(1/5)x1x100=20cm

Construction:

Draw a straight line of 20cm length and divide into 10 equal parts.

Divide again first part into 10 equal parts. Give numbers as shown. To represent 7.4 decimetres, take 7 main parts to represent 7 decimetres and 4 small parts to represen0t 0.4 decimetres. Give names as A and B so that the distance between A and B is 7.4 decimetres as shown.

 Diagonal Scales:

Diagonal scales are used to read or measure upto three units.

For example: decimetres (dm), centimetres (cm) and millimetres (mm) or miles, furlon

gs and yards etc. This scale is used when very small distances such as 0.1 mm are to be accurately measured or when measurements are required upto second decimal.

For example: 2.35dm or 4.68km etc.

Small divisions of short lines are obtained by the principle of diagonal division, as explained below:

Principle of diagonal scale: To divide a given line AB into small divisions in multiples of 1/10 its length for example 0.1AB; 0.2AB etc. as shown in 

Procedure: 

i) Draw AB of given length

ii) At one end, say at B draw a line perpendicular to AB.

iii) Mark 10 equal divisions by taking some convenient length starting from B and ending with C.

iv) Give numbers from 9, 8, 7----1 as shown.

v) Join C to A and from 9 to 1, draw parallels to AB, cutting AC at 9′, 8′, ------ 1′ etc.

vi) From the similar triangles 1′1C, 2′2C ------- 9′9C and ABC, C5=(1/2)BC=0.5BC and 5′5=(1/2)AB=0.5AB. Similarly 1′1=0.1AB, 2′2=0.2AB etc 

Thus each horizontal line below AB will be shorter by (1/10)AB, giving lengths in multiples of 0.1AB

: An area of 144 sqcm on a map represents an area of 9 sqkm on the field. Find the R.F.of the scale for this map and draw a diagonal scale to show kilometers, hectametres and decameters and to measure upto 5 kilometres. Indicate on the scale a distance of 3 kilometres, 5 hectametres and 6 decametres or 3.56km. 

The area on the map is 144 sqcm and the area on the field is 9 sqkm.

Take square root on both sides. Then 12cm=3 km or Scale is 1 cm= 0.25km or 2.5x10⁴ cm; RF=1/(2.5x10⁴)

Length of the scale to read upto 5 km is RF X 5 km= 1/(2.5x10⁴) X 5x10⁵ =20cm

Construction:

Draw a line AB of 20 cm and construct a rectangle on it, by taking AD 5cm as shown. Divide AB into 5 equal parts and number them from second part starting with 0 to 4 towards right side to indicate kilometers (km). Divide 0A into 10 equal parts, each part represents a hectametre (hm). Divide AD into 10 equal parts, each part represents one decametre (dam). Join diagonals as shown.

To mark 3.56km, take it as sum of 3.50km and 0.06km. On the plain scale take 3.5km and on the diagonal at 5 upto 6 parts diagonally which is equal to 0.06km, giving a total of 3.56km as shown by MN.

Note: Assume the height of the diagonal scale AD as 5cm for dividing it into 10 equal parts conveniently.

INVOLUTES and their CONSTRUCTION

INVOLUTE

• An involute is a curve that is traced by a point on a taut cord unwinding from a circle or regular polygon, which is called a base or (plane figures for part of this unit which includes a line, triangle, square, hexagon) The involute is a form of spiral, the curvature of which becomes straighter as it is drawn from a base circle and becomes a straight line at infinity.
• An involute drawn from a small base circle is more curved than one drawn from a larger base circle
• The involute of a circle has a property that makes it important to the gear industry: if the teeth of two mating gears have the shape of an involute, their relative rates of rotation are constant while the teeth are engaged. 
• With teeth of other shapes, the relative speeds rise and fall as successive teeth engage, resulting in vibration, noise, and excessive wear
• 
  

PARABOLA by TRIANGLE METHOD

A parabola is a curve traced by a point, moving such that, at any position ,its distance from the fixed point  (focus) is always equal to its distance from a fixed straight line (directrix)

  parabola can be constructed in many ways.. like eccentricity method,  triangle method, oblong or rectangle method etc....

 Triangle method

triangle method of construction is based on tangents.. 

• Draw the base AB and axis CD , such that CD is perpendicular bisector to AB.

• produce CD to E such that DE = CD.
• join E,A and E, B. these are the tangents to the parabola at A and B.

• Divide AE and BE in to the same number of the equal parts and number the points as shown.

• join 1,1' ; 2,2' ; 3,3'; etc.... forming the tangents to the required parabola

• A smooth curve passing through A,D and B tangential to the above lines is the required parabola

hence the required parabola through triangle method

PARABOLA and its CONSTRUCTION by ECCENTRICITY METHOD

The parabola  is a conic section, the intersection of a right circular conical surface and a plane to a generating straight line of that surface. Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola

OR SIMPLY

A parabola is a curve traced by a point, moving such that, at any position ,its distance from the fixed point  (focus) is always equal to its distance from a fixed straight line (directrix)

Construction

Draw the axis AB and the directrix CD, at right to each other.

Mark the focus F on the axis with given length for suppose AF=50 or 40 etc..

Locate the vertex V on AB such that AV=VF= ½(AF)

Draw a line VE, perpendicular to AB such that VE=VF

Join A,E and extend , by construction VE/VA=VF/VA=1, the eccentricity.

Locate a number of points 1,2,3, etc . to the right of V on the axis, which need not be equidistant.

Through the points 1,2,3 etc, draw  lines perpendicular to the axis and to meet the line AE extended at 1’,2’,3’, etc.

With the center F and radius 1-1’, draw arcs intersecting the line through 1 at P1 and P1’. P1 and P1’ are the points on the parabola, because, the distance of P1(P1’) from Fis 1-1’and from CD. It is A-1 and

1-1’/A-1=VE/VA=VF/VA=1

Similarly locate the points P2,P2’;P3,P3’; etc.. on either side of the axis.

Join the points by a smooth curve, forming the required parabola

NOTE

OUR REQUIRED ONE ( PARABOLA) SHOULD BE DARK

hence our final figure is

TO draw the tangent and normal

To draw the tangent and normal to the parabola , locate the point M. which at a given distance from directrix

Then join M and  F and draw a line through F, perpendicular to MF, meeting the directrix at T.

The line joining T and M and extended (T-T) is the tangent and line N-N , through M and perpendicular to TM is the normal to the curve

this is the construction of parabola by eccentricity method

CONIC SECTION

CONIC SECTION

CONIC SECTION mainly consists of three major parts they are

Ellipse

Parabola

Hyperbola

Conic sections are the intersections of a right regular cone, by a cutting plane in different positions, relative to the axis of the cone.

PARABOLA

The parabola  is a conic section, the intersection of a right circular conical surface and a plane to a generating straight line of that surface. Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola.

CONSTRUCTION 

READ MORE??????

ELLIPSE

an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is perpendicular to the axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant.

Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex; the other two (open and unbounded) cases are parabolas and hyperbolas. Ellipses can also arise as images of a circle under parallel projection and some cases of perspective projection.

CONSTRUCTION 

READ MORE ?????

HYPERBOLA

It is similar to parabola which has he eccentricity greater than 1

READ MORE ABOUT HYPERBOLA

HYPOCYCLOIDS AND THEIR CONSTRUCTION

HYPOCYCLOIDS

construction of hypocycloid

• The curve traced by a point on a circle which rolls on the inside of a circular base surface.

• Step 1: Divide the rolling circle in to 12 equal divisions.
• Step 2: Transfer the 12 divisions on to the base surface.

• Step 3: Mark the 12 positions of the circle - center (C1,C2,C3..) as the circle rolls on the base surface.
• Step 4: project the positions of the point from the circle.

• Step 5: Using the radius of the circle and from the marked centers step off the position of the point.
• Step 6: Darken the curve.

EPICYCLOIDS AND THEIR CONSTRUCTION

EPICYCLOIDS

What is Epicycloid?

• The cycloid is called the epicycloid when the generating circle rolls along another circle outside(directing circle)

• The curve traced by a point on a circle which rolls on the out side of a circular base surface

CONSTRUCTION OF EPICYCLOID

• Step1: Draw and divide the circle in to 12 equal divisions.
• Step 2: Transfer the 12 divisions on to the base surface.

• step3: Mark the 12 positions of the circle- centers (C1,C2,C3,C4..) as the circle rolls on the base surface.
• Step 4: Project the positions of the point from the circle.

• Step 5: Using the radius of the circle and from the marked centers C1,C2,C3,C4.. etc cut off the arcs through 1,2,3.. etc
• Step 6: Darken the curve

CYCLOIDS AND THEIR CONSTRUCTION

What is a Cycloid?

• A cycloid is a curve generated by a point on the circumference of the circle as the circle rolls along a straight line with out slipping..
• The moving circle is called the "Generating circle" and the straight line is called the "Directing line" or the "Base line".
• The point on the Generating circle which generates the curve is called the "Generating point"

Construction of a Cycloid

• Step1: Draw the generating circle and the base line equal to the circumference of the generating circle

• Step 2 : Divide the circle and the base line in to equal number of parts. also erect the perpendicular lines from the division of the line

• Step 3: with your compass set to the radius of the circle and centers as C1,C2,C3,.... etc cut the arcs on the lines from circle through 1,2,3, .. etc.

• Step 4: locate the points which are produced by cutting arcs and joining by a smooth curve.

• By joining these new points you will have created the locus of the point P for the circle as it rotates along the straight line with out slipping

• As our final result is a cycloid

BASICS OF Engineering drawing

Creating a drawing
Drawing  instruments are used to draw straight lines ,circles , and curves accurately  concisely 

                   

The drawing tools are  like drawing board, mini drafter, instrument box containing compass,divider etc,.. set squares,protractor,french curves, drawing sheet,pencils,erasers..... 


DRAWING STANDARDS

• Drawing standards are set of rules that govern how the technical drawings are represented
• these are used so that every one can commonly understand the meaning of drawn picture

  Drawing sheet

we have many types and sizes of drawing sheets..  like A4,A3,A2,A1,A0 etc

while in the drawing sheet .. first we have to draw border lines and title box and then we have to start drawing

lettering

lettering and numbering should be in a perfect manner.. for example in this figure.. the upper and lower case letters  are neatly draw

    lines and its types 

basically lines which are used in the representation of the diagrams are of mainly 4 types they are

• Visible line : represent features that can be seen in the current view
• Dimension line ;Extension line;Leader line: indicate the sizes and location of features
• Hidden line : represent features that can not be seen in the current view
• Center line: represents symmetry, path of motion, centers of circles, axis of axisymmetrical parts

In this way we use different types of lines in the drawing