A. Lettering, Dimensioning, Scales

**INTRODUCTION**

Before manufacturing any product, it goes through many stages like drawing, designing.

Thus, Engineering drawing is the graphical representation of the product to be manufactured or designed. It must contain all the information required to understand its physical appearance.

To draw any of given dimension, some instruments are required. Drawing instruments are those instruments which are used to prepare drawings easily and accurately. With good quality of instruments, required accuracy can be achieved.

Thus

Below is the list of some drawing instruments

- Drawing board
- Set-squares — 45° and 30°- 60°
- Scales
- French curves
- Drawing pencils
- Drafting machine
- T-square
- Drawing instrument box
- Protractor
- Eraser (Rubber)
- Drawing pins, clips or adhesive tapes
- Roll-n-draw.
- Divider

**DRAWING PAPERS **

Good quality of paper with smooth surface and having uniform are considered as Drawing Paper.

The standard sizes of drawing papers recommended by the Bureau of India Standards (B.I.S.). are given in table

Area of A0 size is 1m^{2}. Successive format sizes (from A0 to A5) can obtained by multiplying the size by .

**DRAWING PENCILS**

The pencils used for drawing is little bit different from the ordinary pencils. Depending upon the shade and thickness of lines to be draw, pencils can be divide in number of category. The grade of a pencil lead is usually shown by figures and letters marked at one of its ends.

The hardness is shown by H, its hardness can is described by putting some numeric values depending upon the hardness viz. 2H, 3H, 4H etc.

Similarly, the grade becomes softer according to the figure placed in front of the letter B, viz. 2B, 38, 48 etc.

Letters HB denote the medium grade.

Beginning of a drawing should be made with H or 2H pencil using it very lightly, so that the lines are faint, and unnecessary or extra lines can be easily erased. The final fair work may be done with harder pencils, e.g. 3H and upwards.

Lines of uniform thickness and darkness can be more easily drawn with hard-grade pencils.

H and HB pencils are more suitable for lettering and dimensioning.

For freehand sketching, soft-grade pencils should be used.

**Drawing Pins or Clips**

These are used to fix the drawing paper on the drawing board. Clips or adhesive tapes are often used instead of the pins.

** **

**DRAFTING MACHINE or Drafter**

It is an instrument which can fullfill all the task performed by using T-square, set-squares, scales and the protractor.

It’s one end is clamped by means of a screw, to the distant longer edge of the drawing board & at its other end, an adjustable head having protractor markings is fitted. Two blades of transparent celluloid accurately set at right angles to each other are attached to the head.

**LINES**

Different lines are used in engineering drawing to define their application. The thicknesses of lines are varied according to the drawing and are finalized either by ink or by pencil.

Some of them are given in tabular form.

**TYPES OF LINES **

**(1) Outlines:** Lines drawn to represent visible edges and surface boundaries of objects are called as outlines. They are continuous thick or wide lines.

**(2) Margin lines:** They are continuous thick lines along which the sheets are trimmed.

**(3) Dimension lines:** They are terminated at the outer ends by pointed arrowheads touching the outlines, extension lines or centre lines.

**(4) Projection lines:** These lines also are continuous thin lines. They extend by about 3 mm beyond the dimension lines.

**(5) Hatching or section lines:** These lines are drawn to make the section visible. They are continuous thin lines and are drawn generally at an angle of 45° to the main outline of the section. They are uniformly spaced about 1 mm to 2 mm apart.

**(6) Border lines:** Perfectly rectangular working space is determined by drawing the border lines.

**(7) Short-break lines:** These lines are continuous, thin and wavy. They are drawn freehand and are used to show a short break, or irregular boundaries.

**(8) Long-break lines:** These lines are thin ruled lines with short zigzags within them. They are drawn to show long breaks.

**(9) dotted lines:** Interior or hidden edges and surfaces are shown by dotted lines. They are made up of short dashes of approximately equal lengths of about 2 mm spaced at equal distances of about 1 mm.

**(10) Centre lines (G):** Centre lines are drawn to indicate the axes of cylindrical, conical or spherical objects or details, and also to show the centres of circles and arcs.

**LETTERING (IS 9609-2001) **

Every drawing requires some description which includes writing of titles, dimensions, notes and other important particulars is known as lettering.

It should be in plain and simple style so that it could be done freehand and speedily.

**(1) Single-stroke letters:** The Bureau of Indian Standards (BIS : 9609-2001) recommends single-stroke lettering for use in engineering drawing.

Single Stroke means that the thickness of the line of the letter obtained in one stroke of the pencil without redraw.

The horizontal lines of letters should be drawn from left to right and vertical or inclined lines, from top to bottom.

Single-stroke letters are of two types:

(i) vertical and

(ii) inclined.

Inclined letters lean to the right, the slope being 75° with the horizontal.

The size of a letter is described by its height. According to the height of letters, they are classified as:

(i) Lettering 'A'

(ii) Lettering 'B'

**DIMENSIONING **

In a Drawing, to give the information about the actual size & characteristics of the object, some notations are used, which are known as dimensioning.

Every drawing, whether a scale drawing or actual size, its exact length, breadth, height, sizes and various required information regarding the object must be given in the drawing itself.

Lines, figures, arcs, numerals, symbols, are used for the dimensioning.

**DIMENSIONING TERMS AND NOTATIONS **

**(1) Dimension line:** Dimension lines are thin continuous lines & it is drawn parallel to the surface whose dimension is to shown. These lines are terminated by arrowheads.

**(2) Extension line:** Extension lines are thin & continuous line drawn in extension of an outline. It extends by about 3 mm beyond the dimension line.

**(3) Arrowhead:** An arrowhead is placed at each end of a dimension line. Its pointed end touches an outline, an extension line or a centre line. The size of an arrowhead should be proportional to the thickness of the outlines.

**GENERAL RULES FOR DIMENSIONING **

(1) Dimensioning of all the required length should be done so that assumption or measurement of any dimension is not required.

(2) Dimensioning of any part should not be repeated.

(3) A dimension should be placed on the view where its use is shown more clearly.

(4) Dimensions should be placed outside the views, unless they are clearer and more easily read inside.

(5) Crossing of dimension lines and dimensioning between hidden lines should be avoided.

(6) Dimension lines should not cross any other line of the drawing.

(7) An outline or a centre line should never be used as a dimension line.

**SCALES**

Drawings of some objects can be made by considering their actual dimension whereas when the size of object is very small or very large then drawing the objects of actual dimension is not possible.

In that case, all the dimension of the drawing is reduced or enlarged by some amount (Times). This process is known as scaling.

Thus, “A scale is defined as the ratio of the linear dimensions of element of the object as represented in a drawing to the actual dimensions of the same element of the object itself”.

Depending upon this, scale can be of 3 types.

(1) Drawings whose dimension is same as that of the objects, are known as **full-size drawings**.

For full scale drawing, Scale is 1:1.

(2) Drawings Whose dimensions are smaller than the actual size of the objects then scale used is called as **Reducing Scale**.

The actual objects in this case is very large.

For Reducing Scale drawing, Scale < 1.

(3) Drawings Whose dimensions are larger than the actual size of the objects then scale used is called as **Enlarging Scale**.

For Enlarging Scale drawing, Scale > 1.

**(3) Representative fraction:** The ratio of the length of the object represented on drawing to the actual length of the object represented is called the Representative Fraction (i.e. R.F.).

RF = (LENGTH OF DRAWING)/(ACTUAL LENGTH OF OBJECT)

**NOTE – **While calculating RF, units of dimension in numerator and denominator must be same**. **

**SCALES ON DRAWINGS **

When an unusual scale is used, it is constructed on the drawing sheet.

To construct a scale the following information is required,

(1) The R.F. of the scale.

(2) The units which it must represent, for example, millimetres and centimetres, or feet and inches etc.

(3) The maximum length which it can show.

The length of the scale is determined by the formula:

** Length of the scale = R.F. × maximum length required to be measured**

**B. CONIC SECTION & ENGINEERING CURVES**

**1. ****CONIC SECTIONS**

The sections obtained by the intersection of a right circular cone by a plane in different positions relative to the axis of the cone are called conics.

By cutting the cones, we can obtain different curves like circle, ellipse, parabola, hyperbola etc.

The conic may also be defined as the locus of a point moving in a plane in such a way that the ratio of its distances from a fixed point and a fixed straight line is always constant. The fixed point is called the focus and the fixed line, the directrix & the ratio Is called as eccentricity and is denoted by e.

The line passing through the focus and perpendicular to directrix is called as axis and the point at which the conic cuts its axis is called as vertex.

α = Angle between one of the generators and base of the cone.

β = Angle between Section plane and base of the cone.

θ = Angle between both the generators. it is also known as vertex angle

** 2. CYCLOIDAL CURVES**

These curves are generated by a fixed point on the circumference of a circle, which rolls without slipping along a fixed straight line or a circle.

**Generating Circle-** Circle which rolls on the line or another circle is called as generating circle

**Directing Line/Circle – **Line or circle in which Generating circle rolls is termed directing line or directing circle.

Cycloidal curves are used in tooth profile of gears.

**2.1. Cycloid**

Cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line.

Mathematically it can be expressed as,

y = a (1 – cos θ) or x = a (θ – sin θ)

**2.1.1 Trochoid**

Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line.

**(a) Inferior Trochoid:**

When the point is within the circle, the curve is called as **inferior trochoid**

** Fig: Inferior Trochoid**

**(b) Superior Trochoid:**

When the point is outside the circle, the curve is called as **Superior trochoid**

** Fig: Superior Trochoid**

**(c)**** Epitrochoid**

Epitrochoid is a curve generated by a point fixed to a circle (within or outside its circumference, but in the same plane) rolling on the outside of another circle.

The curve is termed inferior or superior, according to the position of the point being inside or outside the rolling circle.

** Fig: Inferior & Superior ****Epitrochoid**

**(d) Hypotrochoid**

When the circle rolls inside another circle, the curve is called a hypotrochoid.

** **

**2.2. Involute**

The involute is a curve traced out by an end of a piece of thread unwound from a circle or a polygon, the thread being kept tight.

Thread will always be tangent to the circle thus normal to an involute of a circle is tangent to that circle.

It may also be defined as a curve traced out by a point in a straight line which rolls without slipping along a circle or a polygon.

Involute of a circle is used as teeth profile of gear wheel.

Mathematically it can be described by

x = rcosθ + rθsinθ,

y = rsinθ - rθcosθ,

where "r" is the radius of a circle.

**2.3. Spirals**

If a line rotates in a plane about one of its ends and if at the same time, a point moves along the line continuously in one direction, the curve traced out by the moving point is called a spiral.

The point about which the line rotates is called a **pole**.

The line joining any point on the curve with the pole is called the radius vector and the angle between this line and the line in its initial position is called the **vectorial angle**.

Each complete revolution of the curve is termed the **convolution**.

A spiral may make any number of convolutions before reaching the pole.

**2.3.1. Archemedian Spiral**

It is a curve traced out by a point moving in such a way that its movement towards or away from the pole is uniform with the increase of the vectorial angle from the starting line.

The use of this curve is made in teeth profiles of helical gears, profiles of cams etc.

** Fig: Archemedian Spiral**

**2.3.2. Logarithmic or Equiangular spiral**

In a logarithmic spiral, the ratio of the lengths of consecutive radius vectors enclosing equal angles is always constant.

In other words, the values of vectorial angles are in arithmetical progression and the corresponding values of radius vectors are in geometrical progression.

The logarithmic spiral is also known as equiangular spiral because of its property that the angle which the tangent at any point on the curve makes with the radius vector at that point is constant.

** Fig: Logarithmic** **Spiral**

**3.HELIX**

Helix is defined as a curve, generated by a point, moving around the surface of a right circular cylinder or a right circular cone in such a way that, its axial movement in the direction of the axis of the cylinder or the cone is uniform with its movement around the surface of the cylinder or the cone.

The axial advance of the point during one complete revolution is called the pitch of the helix.

** Fig: Helix**

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