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# Engineering graphics pdf

To achieve these objectives, IS 'Code of practice for general engineering drawing' was originally issued in and revised twice in and Engineering graphics is the method for documenting a design. • Mechanical engineering students must be familiar with standards of. Textbook of. Engineering Drawing. Second Edition. K. Venkata Reddy. Prof. & HOD of Mechanical Engineering Dept. C.R. Engineering College,. Tirupati - . Author: PARTHENIA DEMENT Language: English, Spanish, Japanese Country: Syria Genre: Art Pages: 761 Published (Last): 23.05.2016 ISBN: 229-6-66934-935-9 ePub File Size: 20.75 MB PDF File Size: 16.37 MB Distribution: Free* [*Regsitration Required] Downloads: 45080 Uploaded by: ABBIE

Each smaller part will represent distance traveled in one minute. Sectioning of above solids in simple vertical position when the cutting plane is inclined to the one of the principal planes and perpendicular to the other - obtaining true shape of section. Join B1 with O. Draw the projections of the line. First quadrant problem: P the projection on the AVP as seen from the left of the object and drawn on the right hand of the front view, is called left side view. Conics - Construction ellipse, parabola and hyperbola by eccentricity method - Construction of cycloid - construct of involutes of square and circle - Drawing of tangents and normal to the above curves, Sea Construction of Diagonal and Vernier scales.

Used to show the edges of a cutting plane. Thin continuous lines. Terminate with an arrow head.

Are continuous lines used in dimension lines. A gap of about should be maintain these lines and the visible lines of an object. ABC 8 Reg: All dimensions are in mm.

Size in drawing Actual size: Geometrical drawing by N. Door will be locked after 5 minutes. It should make approximately a 60o angle with the paper. In some cases, like the "W", the ratio is actually greater than 1. Tanzila Younas meager and unsatisfactory. The numerical value that defines the size, shape, location, geometric characteristic of a feature. Basic dimensions: A numerical value defining the theoretically exact size, location, profile or orientation of a feature.

Identified by enclosing the dimension in a box. Reference dimension: A numerical value enclosed in parenthesis, providing for info only and not directly used in the fabrication of the part. Dimension line: A thin, solid line that shows the extent and direction of a dimensions.

Symbols placed at the ends of dimension lines to show the limits of the dimension, leaders and cutting plane lines. Visible gap: There should be a visible gap of 1. Leader line: A thin, solid line used to indicate the feature with which a dimensions, note, or symbol is associated.

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Limits of size: The largest acceptable size and the minimum acceptable size of a feature. Maximum material condition MMC 2. Least material condition LMC P and below H P Sign Conventions: P and in front of the V. The distance of the point A from the H. P is h and that from the V.

The line joining the views a and a' meet XY at right angles. First quadrant problem: Draw the reference line X Y.

## Engineering Drawing Books

Draw a projector line perpendicular to X Y somewhere at the middle of the reference line X Y. Mark a point a' at a distance of 30 mm above X Y, Which is the front view of the point A.

On the same projector mark a at a distance of 15 mm below X Y, which is the top view of the point A. So mark b at the point of intersection of the projector and the XY line. So mark c' at the point of intersection of the projector and the XY line. So a point on XY line itself is the front view d' and the top view d of the point D. The distance of the point B from H P is h and that from the V P is d, b' is the front view or elevation of a point B and b is the top view or plan of a point B. Now the H. The plan top view above XY and is at a distance of d from XY. Projections of a point in third quadrant Fig shows a point C located in space in the third quadrant it is below the H P and behind the V P. The front view is below XY and is at a distance of h from XY. The line joining the views c and c' meet XY at right angles. Draw the reference the XY. Draw a projector some where in the middle of the XY line. Mark a point g' at a distance of 30 mm below XY, which is the front view of the point G.

On the same projector mark g at a distance of 15 mm above XY which is the top view of the point G. So mark h' at point of intersection of the projector and the XY line. Now the HP is rotated in the clockwise direction through and obtained in vertical position. The distance between end projectors is 60 mm. The distance between end projector is 70 mm. Draw straight lines joining the top view and front views.

The line joining their top views makes an angle with XY. Find the horizontal distance between the two points. The line joining their front views makes an angle of with XY while the line joining their top views makes an angle of with XY. Find the distance of point R from HP. Mark the intersecting point on top view of point R vi Draw a projector from r which intersects the inclined lines.

Draw the projections of the following points, keeping the distance between the projectors as 25 on the same reference line. A - 25 above H. P and 45 In front of V. B - 35 above H. P and 5O behind V. C - 40 below H. P and 30 behind V. D - 30 below H. P and 40 in front of V.

E - 50 above H. P and on V. F - 45 below H. P and 35 in front of V. P and 25 behind V. P and V. State the quadrants in which the following points are located: A - Front and top views are above XY. D - Front and top views are below XY. Mention the relative positions of the projections of the following points with respect to XY.

A - in the fourth quadrant. B - in the second quadrant. C - in the third quadrant. D- in the first quadrant. An engineering drawing not only shows the shape of the object but also describes the size and other specifications necessary for its constructions in the form of dimensions and notes.

Writing of the specifications and important particulars includes name of the drawing, title block etc on a drawing is called Lettering. Features of lettering: The main features of lettering are, 1. Legibility 2. Uniformity 3. Ease and rapidity of execution 4. Suitability for micro filming tracing , Photographic re-production, Ammonia printing etc.

Need for legible lettering and numbering in drawing: Lettering plays a major role in Engineering Drawing. However accurate and neat a drawing may be drawn, its appearance is spoiled and sometimes its usefulness is impaired by poor lettering. Therefore lettering should be done properly in clear, legible and uniform style. Good lettering improves the clarity and appearance of drawing.

Lettering should be in plain and simple style so that it can be done easily either by free hand or by using stencils. Therefore all the notes, dimensions, title blocks etc in the drawing should be lettered freehand like printing by Engineering Script and not as manuscript handwriting. Scope - This section specifies the characteristics of lettering used on technical drawings, and associated documents.

It concerns primarily letters written with the aid of stencils, but is equally applicable for free hand lettering. Use of instruments stencils for lettering is not preferred, as it will consume more time. Free hand, single stroke engineering script with proper strokes should be used to faster and proper lettering.

Efficiency in the art of lettering can be achieved by careful and continuous practice.

An example dimension is shown below. Dimensions are always drawn using continuous thin lines. Two projection lines indicate where the dimension starts and finishes. Projection lines do not touch the object and are drawn perpendicular to the element you are dimensioning.

In general units can be omitted from dimensions if a statement of the units is included on your drawing. The general convention is to dimension in mm's. All dimensions less than 1 should have a leading zero. In general all notes should be written in capital letters to aid legibility. All lettering should be of the same size and preferably no smaller than 3mm. An example typeface is shown below. Superimposed Running Dimensions Superimposed running dimensioning simplifies parallel dimensions in order to reduce the space used on a drawing.

The common origin for the dimension lines is indicated by a small circle at the intersection of the first dimension and the projection line. In general all other dimension lines are broken. The dimension note can appear above the dimension line or in-line with the projection line Chain Dimensioning Chains of dimension should only be used if the function of the object won't be affected by the accumulation of the tolerances.

A tolerance is an indication of the accuracy the product has to be made to. Tolerance will be covered later in this chapter. Dimensioning by Co-ordinates Two sets of superimposed running dimensions running at right angles can be used with any features which need their centre points defined, such as holes. Simplified dimensioning by co-ordinates It is also possible to simplify co-ordinate dimensions by using a table to identify features and positions.

In order to clarify dimensions on small features any of the above methods can be used. Dimensioning circles All dimensions of circles are proceeded by this symbol;. There are several conventions used for dimensioning circles: One method dimensions the circle between two lines projected from two diametrically opposite points. The second method dimensions the circle internally.

A leader line is used to display the dimension. The first method using projection lines is the least used method. But the choice is up to you as to which you use. Dimensioning Radii All radial dimensions are proceeded by the capital R. All dimension arrows and lines should be drawn perpendicular to the radius so that the line passes through the centre of the arc. All dimensions should only have one arrowhead which should point to the line being dimensioned.

There are two methods for dimensioning radii. Spherical dimensions The radius of a spherical surface i. Dimensioning Holes When dimensioning holes the method of manufacture is not specified unless they necessary for the function of the product.

The word hole doesn't have to be added unless it is considered necessary. The depth of the hole is usually indicated if it is isn't indicated on another view. The depth of the hole refers to the depth of the cylindrical portion of the hole and not the bit of the hole caused by the tip of the drip. Tolerance It is not possible in practice to manufacture products to the exact figures displayed on an engineering drawing. A tolerance value shows the manufacturing department the maximum permissible variation from the dimension.

Each dimension on a drawing must include a tolerance value. This can appear either as: Note the larger size limit is placed above the lower limit. All tolerances should be expressed to the appropriate number to the decimal points for the degree of accuracy intended from manufacturing, even if the value is limit is a zero.

Engineering drawing is a two dimensional representation of a three dimensional object. It is the graphic language, from which a trained person can visualize the object. As an engineering drawing displays a precise picture of the object to be produced, it conveys the same picture to every trained eye. Drawings prepared in one country may be utilized in any other country, irrespective of the language spoken there. Hence, engineering drawing is called the universal language of engineers. Knowledge in engineering drawing is equally essential for the persons holding responsible positions in engineering field. An engineer without adequate knowledge of this language is considered to be professionally illiterate.

Role of drawing in engineering education: The ability to read drawings is the most important requirement of all technical people in engineering profession. The classifications of engineering drawings include: Building drawing, machine drawing, Electrical drawing etc While teaching majority of subjects; figures or sketches of related objects, machines or systems are made use of, to explain the principles of operation, relation between the parts etc.

Unless the figures are presented, following the norms of drafting practice, the required information cannot be fully conveyed. Hence, the knowledge in engineering drawing is useful in understanding the other subjects as well. Need for preparing drawing as per standards: For the purpose of proper communication, every language has to obey its own rules of grammar. Similarly Engineering Drawing also has its own rules grammar.

These rules are laid down by certain standards and are governed by certain standard codes of practice. Keeping this objective in view, the codes of practice recommended by Bureau of Indian Standards BIS is given below The Relation of Drawing to Problem Solving The initial reduction of videotaped data taken of design engineers led to the publication of six uses of the act of drawing 1.

To archive the geometric form of the design. To communicate ideas between designers and between the designers and manufacturing personnel. To act as an analysis tool. Often, missing dimensions and tolerances are calculated on the drawing as it is developed. To simulate the design. To serve as a completeness checker. As sketches or other drawings are being made, the details left to be designed become apparent to the designer.

This, in effect, helps establish an agenda of design tasks left to accomplish. To act as an extension of the designer's short term memory. Designers often unconsciously make sketches to help them remember ideas that they might otherwise forget. Scope of Engineering Drawing: Writing — means preparing the drawing as per the standard rules Reading — means interpret and understand the idea or expression Reading is often more difficult than writing.

This is because the reader has to imagine a lot while interpreting a drawing. Every student of engineering drawing should study the language of engineers. Then only he can read and communicate technical information correctly.

Any error committed by an engineer in his drawings will lead to a lot of confusion to the operators, ultimately spoiling the product. Upon Successful completion of this module, the student should be able to: To a greater extent, the ac- curacy of the Drawings depends on the quality of instruments used to prepare them. The following is the list of Drawing Instruments and other materials required. Drawing board is made from strips of well seasoned soft wood generally 25 mm thick.

It is cleated at the back by two battens to prevent warping. One of the shorter edges of the rectangular board is pro-vided with perfectly straight ebony edge which is used as working edge on which the T-square is moved while making Drawings. Battens Fig.

Drawing boards are made in various sizes. The selection of Drawing board depends on the size of drawing paper used. T-squares are made from hard wood. A T-square consists of two parts namely the stock and the blade joined together at right angles to each other by means of screws and Pins as shown in figure.

The stock is made to slide along the working edge and the Blade moves on the Drawing board. Working edge Stock Blade Screws Fig. Drafting machine or Drafter: In a Drafting machine, the uses and advantages of T-square, set square, scales, and protractors are combined.

One end of the Drafter is clamped at the left top end of the Drawing board by a screw provided in the drafter.

These blades are used to draw parallel, horizontal, vertical and inclined lines. The blades always move parallel to the edges of the board.

Use of drafting machine helps in reducing the time required to prepare Drawing. Set squares are generally made from Plastic or celluloid material. They are triangular in shape with one corner, a right angle triangle. They are semicircular in shape of diameter mm and are made of Plastic or celluloid which has more life.

It consists of the following a Large size compasses, b Large size divider, c Small size bow pen, bow divider, and d Lengthening bar f Drawing sheet: They are available in many varieties and good quality paper with smooth surface should be selected for Drawings which are to be preserved for longer time.

The accuracy and appearance of a Drawing depends on the quality of Pencil used to make Drawing. The grade of a Pencil lead is marked on the Pencil. HB denotes medium grade. Increase in hardness is shown by value put in front of H such as 2H, 3H etc. Beginning of a Drawing may be made with H or 2H.

For lettering and dimensioning, H and HB Pencils are used. These are used to fix the Drawing sheet on the Drawing board. Board clips i Compass: Compass is used for drawing circles and arcs of circles. The compass has two legs hinged at one end. One of the legs has a pointed needle fitted at the lower end where as the other end has provision for inserting pencil lead.

Circles up to mm diameters are drawn by keeping the legs of compass straight. For drawing circles more than mm radius, a lengthening bar is used. It is advisable to keep the needle end about 1mm long compared to that of pencil end so that while drawing circles, when the needle end is pressed it goes inside the drawing sheet by a small distance approximately 1mm. Refer fig. Conics — Construction of ellipse, parabola and hyperbola by eccentricity method — Construction of cycloid — construction of involutes of square and circle — Drawing of tangents and normal to the above curves, Scales: Construction of Diagonal and Vernier scales.

Visualization concepts and Free Hand sketching: Projection of straight lines only First angle projections inclined to both the principal planes - Determination of true lengths and true inclinations by rotating line method and traces Projection of planes polygonal and circular surfaces inclined to both the principal planes by rotating object method.

Development of lateral surfaces of simple and sectioned solids — Prisms, pyramids cylinders and cones. Perspective projection of simple solids- Prisms, pyramids and cylinders by visual ray method.

Luzzader, Warren. Natrajan K. Basant Agarwal and Agarwal C. Publication of Bureau of Indian Standards: IS — Technical products Documentation — Size and lay out of drawing sheets. Technical products Documentation — Lettering. IS Parts 1 to 4 — Technical drawings — Projection Methods.

All questions will carry equal marks of 20 each making a total of The students will be permitted to use appropriate scale to fit solution within A3 size. The examination will be conducted in appropriate sessions on the same day. This chapter deals the problems on geometric construction which are mostly based on plane geometry and which are very essential in the preparation of engineering drawings.

These constructions use only compass, straightedge i. This is the "pure" form of geometric construction - no numbers involved! What is the main image, which we are using in all our projects, designs, drawings? It is a line! And in Graphics Communications practice there is the whole bunch of different lines, which are used for drawing purposes Drawings convey the following critical information: For example, a mass-marketed product usually requires a much higher surface quality than, say, a component that goes inside industrial machinery.

Line styles and types A variety of line styles graphically represent physical objects. Types of lines include the following: They are the thickest lines on a drawing and done with a pencil softer than HB.

A harder pencil should be used, such as a 2H. They are freehand drawn and only for short breaks. They are dotted lines. They are dotted lines, but a long line of 10—20 mm, then a gap, then a small line of 2 mm. They indicate the cutting plane of an object. They are drawn with a long line of 10—20 mm, then a small gap, then a small line of 2 mm, then a gap, then another small line.

Alternate exterior angles lie on opposite sides of the transversal, and on the exterior of the space between the two lines. Alternate interior angles lie on opposite sides of the transversal, and on the interior of the space between the two lines. That is, they lie between the two lines that intersect with the transversal.

Angle trisectors come in pairs. Each angle in the pair is the other's complement. Angles can be congruent to other angles and segments can be congruent to other segments.

Each angle in the pair is on the same side of the transversal, but one is in the exterior of the space created between the lines, and one lies on the interior, between the lines. One full rotation is equal to degrees. A right angle is 90 degrees. One degree equals radians. Were one of the rays of an angle to be rotated until it met the other ray, an exterior angle is spanned by the greater rotation of the two possible rotations.

The measure of an exterior angle is always greater than degrees and is always degrees minus the measure of the interior angle that accompanies it. Together, an interior and exterior angle span the entire plane. Its measure is always less than degrees, and is equal to degrees minus the measure of the exterior angle. The distance from the endpoint of a segment to its midpoint is half the length of the whole segment.

A geometric figure line, segment, plane, etc. One radian is equal to degrees. It is the angle formed when perpendicular lines or segments intersect. Formed by two rays that shares a common vertex and point in opposite directions.

Each angle in the pair is the other's supplement. These angles are formed by rays pointing in opposite directions, and they are congruent. Vertical angles come in pairs. It is formed by two rays that share a vertex and point in the same direction.

Important Geometrical Terms 1. Triangles- equilateral, isosceles and scalene. Square- all sides are equal and all angles right angles. Rectangle or oblong- opposite side equal and all angles right angles. Rhombus- all sides equal, but angles are not right angles. Rhomboid- opposite sides equal and parallel, but angles are not right angles. Trapezoid- only two sides parallel. Trapezium-No sides parallel, but may have two of its sides equal.

When two of the sides are equal; it is called a trapezium or kite. Pentagon — 5sides; hexagon-6 sides; heptagon-7sides; Octagon -8 sides; nonagon -9 sides; decagon sides.

To bisect a given straight line AB. Draw the given straight line AB as shown in figure 1. Similarly, with the center B and the same radius, draw arcs to intersect the previous arcs at C and D. Problem 2: To bisect a given circular arc AB. Draw the given circular arc AB with center O.

Join CD to cut at M. Problem 4. To find the center of given arc AB. O is the required center of the given arc. To draw an arc passing through three given points not in straight line.

Mark the given points A, B and C. Join AB and BC. Problem 6. To bisect a given angle. Draw the given angle ABC. With D and E as centers and the same or any length as radius, draw two arcs to intersect each other at F. Problem 7. To divide a given straight line into any number of equal parts. Draw the given line AB of length L to be divided into, say, six parts.

Draw a line AC of any length inclined at some convenient acute angle, say, 30oor 45o to AB. From A and along AC, step-off six equal divisions of any convenient length, using the divider. Join B and 6. To draw a tangent to a given circle at any point at any point P on it. With O as center draw the given circle. Mark the given point P on the circumference of the circle. Join OP. RS is the required tangent at P. Problem 9. To draw a tangent to a given circle from a point Outside it 1.

Mark the given point P outside the circle. Join OP and bisect it. With OP as diameter, describe a semi circle to cut the given circle at the point C. Join PC, which is the required tangent. To construct regular pentagon given the side. First Method: Draw a line AB equal to the given length of a side. With A as center and AB as radius draw a semi-circle. Divide the semi-circle into 5 equal parts for pentagon by trial and error method and name the points as 1,2,3,4, and 5 starting from P.

Join A2. With E as center and same radius draw an arc to intersect the extension of A3 at D. ABCDE is the required pentagon. Second Method: Draw AB equal to one side of the pentagon. With B as center and BA as radius draw a semi-circle. Divide the semi-circle into 5 equal parts for pentagon by trial and error method and name the points as1, 2…5 Starting from P.

Join B2. The above two methods may be used for the construction of any polygon. Problem To construct a regular hexagon given length of a side. Refer fig10 when one side is drawn in horizontal position. Let AB be the given side.

## 47028604-Engineering-Graphics-for-Diploma.pdf

With O as center and AB as radius describe a circle. With the same radius and A and B as centers, draw arcs to cut the circumference of the circle at F and C respectively.

With the same radius and C and F as centers, draw arcs to cut the circle at D and E respectively. To construct a regular octagon given the length of a side. Draw perpendicular through A and B. The drawing must show clearly the main details of an object and be fully dimensioned. So what is orthographic projection? Copy the following information to your jotter; Orthographic means straight and perpendicular drawings or pictures. If we apply this to a drawing, then orthographic projection would be looking at o the surface at an object straight and perpendicular!

Imagine a piece of transparent material like glass being placed between our eyes and an object. We would look at the object through the glass with our eyes at right angles to the glass. We would draw a flat view of what we see of the object onto the glass. We now know that drawing true flat views i. When we start to draw orthographic views of an object, we would find that we could draw Designers and engineers would only draw enough views to give them all the information that they require.

They would also devise a method of putting the drawings in some order, to make them easy to understand. There are two main methods of drawing orthographic views in some order: We will be looking at 3rd Angle Projection only.

PLAN We normally draw on paper and not on glass. The of paper, of glass together it would look like Plan is drawn something above so that the Elevation and the End Elevation, is drawn to the left we are the drawing shown opposite. They are hinged This view at called would be the topthe and left side as shown opposite. The drawing opposite shows this symbol It would be placed discreetly on the sheet of paper as shown above. Three objects are shown below A - C.

What is orthographic projection? What is 3rd Angle Projection? What is an orthographic view? Give an example. Make a sketch of the symbol which shows that a drawing has been produced in 3rd Angle Projection. Task 3 The pictorial views of four shaped blocks are shown A-D. The three views of each block are drawn in 3rd Angle Projection below For each pictorial view, select the correct three views.

In each situation 1 -4 three views of the block are drawn but only one is drawn in 3rd Angle Projection. Which one is it? Three hours Maximum: Also draw a tangent and a normal to the ellipse. Or b Make free hand sketches of the front, top and left side view of the object shown in Fib.

P and 20 mm in front of V. The end B is 60 mm above H. The distance between the end projectors of the line is 55 mm. Draw the projections and find its inclination with V.

Or b A regular hexagonal lamina of 40 mm side is resting on one of its corner on H. The plan of the diagonal through the corner which is on H. Or b A pentagonal pyramid of base edge 25 mm and axis length 60 mm rests on one base side on HP such that the highest base corner is 20 mm above HP.

Its axis is parallel to VP. Draw its top and front views. A section plane perpendicular to V. P cuts the tetrahedron such that the true shape of section is an isosceles triangle of base 50 mm and altitude 36 mm. Draw the front view, sectional top view and the true shape of the section. Also find the inclination of the section plane. Or b A vertical cylinder of diameter 50 mm and height 80 mm is drilled by a hole of diameter 30 mm such that the axis of the hole is perpendicular toV.

Draw the lateral surface development of the solid. P cutting the axis of the prism at a height of 45 mm from its base. Draw the isometric view of the truncated prism. Or www. The nearest vertical edge of the solid is 20 mm behind PP and 25 mm to the left of the observer who is at a distance of mm in front of PP. The height of the observer above the ground is mm. Draw the perspective view of the prism. BB traces BB planes BB planes and perpendicular to the other plane Number of hours actually taken: Number of hours planned: BB method.

BB planes inclined to one plane - true shape of section BB BB truncated solids — Prisms, pyramids BB truncated solids - cylinders and cones Principles of isometric projection — isometric scale BB BB objects in simple vertical positions BB ray method BB General principles of orthographic projection LCD Prepared by: Approved by: Signature of HOD Date: What is Projection? A projection is defined as a view imagined on to a plane known as projection plane.

In graphic language shape of an object is described by projection, which is image of the object, formed by the rays of sight taken in some particular direction from the object into a picture plane. Depending upon the orientation of the object, location of the point of sight, and the direction of lines of sight relative to the picture plane, different types of projections such as orthographic, isometric, perspective, oblique etc. The point, from which the observer is assumed to view the object, is called station point or the center of projection and the lines of rays drawn from the object to the plane are called Projectors.

Orthographic projection 2. Isometric projection 3. Oblique projection 4. Perspective projection. Let us discuss small introduction of each one of these so that we can understand examples 1.

Orthographic projection-when the projectors are perpendicular to the plane of projection the projection is known as orthographic projection.

Isometric projection-when the projectors are parallel but inclined to one plane of projection, the projection thus obtained is known as isometric projection 3. Oblique projection-when the projectors are parallel to each other and oblique to the plane of projection, the projection drawn is known as oblique projection.

Perspective projection-when the projectors converge to a point, the projection thus obtained is known as perspective projection Now we will discuss the most important and widely used method by engineers. Yes, orthographic projection is the most important method out of these so will discuss this in detail.

Before starting orthographic projection we must discuss planes of references in which we have to draw projections. Planes of References In study of orthographic projection, two principle planes are used.

They are known as coordinate planes. One plane is horizontal and the other vertical and they intersect each other at right angles.

This can be drawn as you have seen the planes divide themselves into four angular spaces or dihedral angles. The horizontal plane is known as H. P and the vertical plane is known as V.

Their line of intersection is known as the ground line denoted by the line XY. The projection of an object on H. P is known as the plan and the projection on the V.

P is known as elevation. In this method the observer is assumed to be at infinite distance from the plane of projection, such that the projectors will be parallel to each other. P and another auxiliary vertical plane AVP. AVP is perpendicular to both V.