Join 3,3 1and also 5,5 1. Both will meet the vertical OR at a third point. Join 4,41 and it will meet the vertical OR at V.

Draw a tangent and a normal at any point on the curve. As the eccentricity is greater than 1; the curve is a hyperbola. This is the eccentricity scale, which gives the distances in the required ratio. Mark any point 1 on the axis and proceed further as explained in earlier to get the points PI’ P: ‘P3 ,etc. Tangent and normal at any point P on the hyperbola can be drawn as shown.

Problem: Two points F I and F2 are located on a plane sheet mm apart. A point P on the curve moves such that the difference of its distances from FI and F2 always remains 50 mm. Find the locus of the point and name the curve. Mark asymptotes and directrices. Hyperbola Fig.

A curve traced out by a point moving in the same plane in such a way that the difference of the distances from two fixed points is constant, is called a hyperbola. With centre 0 and radius equal to F draw a circle. Draw a line joining JOL and produce it and this line is one asymptote. The other asymptote is the line passingt through KOM. Mark any number of points 1,2,3, etc. Problem: Draw a hyperbola when its double ordinate is 90 m, abscissa is 3Smm and half the transverse axis is 4S mm.

Construct the rectangle ppi RIR. Problem: Construct a rectangular hyperbola when a point P on it is at a distance mm and 40 mm resepctively from the two asymptotes. Both intersect at P. Along BP mark 1, 2, and 3 at approximately equal intervals. Join 01, 02, and 03, and extend them to meet AX at 11,2 1 and 3 1 respectively. From 2 and 3 draw lines parallel to OR I. They intersect at P2 and P3 respectively. Then along PAmark points 41 and 51 at approximately equal inervals.

Join 04 1and 05 1and extend them to meet BY at 4 and 5 respectively. Also draw a normal and a tangent at any point M on the curve. Divide the rolling circle into any number of equal parts say Cb , Let Po be the initial position of the point P and it coincides with the point A.

Draw arcs through points 1,2,3, etc. Similarly obtain other intermediate points PI P2 P3 , etc. Draw a smooth curve passing through all these points to get the required epicycloid. To daw a tangent at any point M on the curve, with centre M draw an arc of radius equal to 25mm to cut the arc Ca Cb at S. From point S, Join NM which is the required normal to the curve. Now, TMT is the required tangent at M. Problem: Draw an epicycloid of rolling circle of diameter 40 mm which rolls outside another circle base circle of mm diameter for one revolution.

Draw a tangent and normal at any point an the curve. In one revolution of the generating circle, the generatin point P will move to a point Q, so that the arc PQ is equal to the circumference of the generating circle. Let P be the generating point. Taking centre C and radius r 20 mm draw the rolling circle. Divide the rolling circle into 12 equal prats and name them as 1,2,3, etc. With 0 as centre, draw concentric arcs passing through 1,2,3, With 0 as centre and OC as radius draw an arc to represent the locus of centre.

Divide the arc PQ into same number of equal parts 12 and name them as 1’2′.. Join 01′,02′ Taking C, as centre and radius equal to r, draw an arc cutting the arc through 1 at Pl’ Similarly obtain the other points and draw a smooth curve through them.

Also draw a normal and a tangent at any point M on tile curve. Here, the centre of the generating circle, Ca is inside the directing circle. The tangent and the normal drawn at the point M on the hypocycloid is shown in Fig. Draw a tangent and normal at any point on it. With C as centre and radius r 20 mm draw the rolling circle.

Divide the rolling circle into 12 equal parts as 1,2,3 etc. With 0 as centre, draw concentric arcs passing through 1, 2, 3 etc. Divide the arc PQ into same number of equal parts 12 as 3 1 etc.

Join OIl 02 1 etc. Similarly obtain the other points and draw a smooth curve through them. To draw a tangent and normal at a given point M: 1. Join ON and extend it to intersect the base circle at S. JoinMS, the normal. At M, draw a line perpendicular to MS to get the required tangent.

Measure its major and minor axes. What is the distance between the foci? The major and minor axes of an ellipse are SO mm and 50 mm respectively. Construct the curve. Draw an ellipse whose major and minor diameters are mm and mm respectively.

Use oblique method. The foci of an ellipse are 90 mm apart and minor axis is 60 mm. Determine the length of the major axes and draw the ellipse by a Concentric circle method, b oblong method, c trammel method. Draw a tangent and normal to the curve at a point on it 20 mm above the major axis. A plot of ground is in the shape ofa rectangle of size x 60m. Inscribe an elliptical lawn in it. Construct an ellipse, when a pair of conjugate diameters are equal to 90 mm and 60 mm respectively.

The angle between the conjugate diameters is Two points AB are mm apart. Draw an ellipse passing throughA,B and C. Draw a four centres approximate ellipse having a major axis of mm and a minor axis of SOmm. Draw an ellipse of having a major axis of mm and minor axis of 70 mm using the concentric circles method. Draw a tangent at any point on the ellipse.

Inscribe an ellipse in a parallelogram of sides mm and 80 mm. Parabola 1. Draw a parabola whose focus is at a distance of 50 mm from the directrix. A highway bridge of parabolic shape is to be constructed with a span of 10m and a rise of 5 m.

Make out a profile of the bridge by offset method. A ball thrown up in the air reaches a maximum height of 50 m. The horizontal distance traveled by the ball is 80 m.

Trace the path of the ball and name it. Construct a parabola if the distance between its focus and directrix is 60 mm. Also draw a tangent to the curve. Construct a parabola whose base is 90 mm and axis is 80 mm using the following methods: a Rectangular method b Tangent method, c Off-set method 6. Draw a parabola if the longest ordinate of it is 50 mm and abscissa is mm. Locate its focus and directrix. A cricket ball thrown reaches a maximum height of 9 m and falls on the ground at a distance of25 m from the point ofprojection.

Draw the path of the ball. What is the angle of projection? Water comes out of an orifice fitted on the vertical side of a tank and it falls on the ground.

The horizontal distance of the point where the water touches the ground, is 75 em when measured from the side of the tank.

If the vertical distance between the orifice and the point is 30 em, draw the path of the jet of water. Hyperbola 1. A vertex of a hyperbola is 50 mm from its focus. Two fixed point A and Bare mm apart.

Trace the locus of a point moving in such a way that the difference of its distances from the fixed points is 80 mm. Name the curve after plotting it. Construct a hyperbola if the distance between the foci is mm and the transverse axis is 70mm.

The asymptotes of a hyperbola are making with each other. A point P on the curve is at a distance of 40 mm from the horizontal asymptote and 50 mm from the inclined asymptote. Plot the curve.

Draw a tangent and normal to the curve at any point M. Draw a curve satisfying the above law, if0. Construct a cycloid having a rolling circle of 60 mm diameter. Also draw a tangent and normal at any point P on the curve. A circle of 40 mm diameter rolls along a straight line without slipping. Draw the curve traced by a point on the circumference, for a one complete revolution and b one and a half revolutions of the circle.

Draw a normal and tangent to the curve at a point 25 mm from the straight line. A circular wheel of diameter mm rolls over a straight surface without slipping. Draw the curve traced by a point P for one revolution of the wheel. Assume that the critical position of the point P is at the top of the vertical centre line of the wheel. Draw an epicycloid having a generating circle of diameter 75mm and a directing curve of radius mm.

Also draw a normal and a tangent at a point P on the curve. Draw a hypocycloid for a rolling circle of diameter 75 mm and a base circle of mm diameter. Draw an involutes of a hexagon mm side. The evolute of a curve is a circle of diameter 30mm. Trace the curve. Draw the curve traced out by the end of a straight line mm long as it rolls over the circumference of a circle 98 mm diameter. Draw the involute of an isosceles triangle of sides 20 mm, and the other side 15 mm for one turn.

Draw the involute of a semicircle of radius 25 mm. Engineering drawing, particularly solid geometry is the graphic language used in the industry to record the ideas and informations necessary in the form of blue prints to make machines, buildings, strutures etc. The size of the image formed in the retina depends on the distance of the observer from the object. If an imaginary transparent plane is introduced such that the object is in between the observer and the plane, the image obtained on the screen is as shown in Fig.

This is called perspective view of the object. Here, straight lines rays are drawn from various points on the contour of the object to meet the transparent plane, thus the object is said to be projected on that plane. Converging rays Observer Fig. The lines or rays drawn from the object to the plane are called projectors. The transparent plane on which the projections are drawn is known as plane of projection.

Pictorial projections i Perspective projection ii Isometric projection iii Oblique projection 2. Orthographic Projections 1. Pictorial Projections The Projections in which the description of the object is completely understood in one view is known as pictorial projection.

They have the advantage of conveying an immediate impression of the general shape and details ofthe object, but not its true dimensions or sizes. When the projectors are perpendicular to the plane on which the projection is obtained, it is known as orthographic projection. The rays are parallel to each other and perpendicular to both the front surface of the object and the plane.

When the observer is at a finite distance from the object, the rays converge to the eye as in the case of perspective projection. When the observer looks from the front surface F or the block, its true shape and size is seen.

When the rays or porjectors are extended further they meet the vertical plane Y. P located behind the object. By joining the projectors meeting the plane in correct sequence the Front view Fig.

Front view shows only two dimensions of the object, Viz. It does not show the breadth B. Thus one view or projection is insufficient for the complete description of the object. As Front view alone is insufficient for the complete description of the object, another plane called Horizontal plane H. P is assumed such that it is hinged and perpendicular to Y. P and the object is in front of the Y. P and above the H. P as shown in Fig. Both top surface and Top view are of exactly the same shape and size.

P ‘? Note 1 Each projection shows that surface ofthe object which is nearer to the observer. P is called the reference line and is denoted as xy. P through 90 0 in the clockwise direction about xy line so that it lies in the extension ofVP as shown in Fig. The two projections Front view and Top view may be drawn on the two dimensional drawing sheet as shown in Fig.

Thus, all details regarding the shape and size, Viz. Length L , Height H and Breadth B of any object may be represented by means of orthographic projections i.

Terms Used VP and H. P are called as Principal planes of projection or reference planes. They are always transparent and at right angles to each other. The projection on VP is designated as Front view and the projection on H. P as Top view. Four Quadrants When the planes of projections are extended beyond their line of intersection, they form Four Quadrants. These quadrants are numbered as I, II, ill and IV in clockwise direction when rotated about reference line xy as shown in Fig.

Horizontal plane Fig. Front view shows the length L and height H of the object, and Top view shows the length L and the breadth B of it. Orthographic Projections 5. P and above H. P in the first quadrant and so on. Figure 5. P and v. Front view is drawn by projecting the object on the v. Top view is drawn by projecting the object on the H.

The projection on the AVP as seen from the left of the object and drawn on the right of the front view, is called left side view. P, the projections obtained on these planes is called First angle projection. P coincides with xy line and in top view v.

The Planes ofporjection lie between the object and the observer. The front view comes below the xy line and the top view about it. Designation and Relative Position of Views An object in space may be imagined as surrounded by six mutually perpendicular planes. So, it is possible to obtain six different views by viewing the object along the six directions, normal to the six planes.

Note: A study of the Figure 5. Sc Fig. The positions of a point are: 1. First quadrant, when it lies above H. P and in front ofV. Second quadrant, when it lies above HP and behind v.

Third quadrant, when it lies below H. P and behind v. Fourth quadrant, when it lies below H. P and V. P, projections on H.

P and Y. P are found by extending the projections perpendicular to both the planes. Projection on H. P is called Top view and projection on Y.

P is called Front view Notation followed 1. Actual points in space are denoted by capital letters A, B, C. Their front views are denoted by their corresponding lower case letters with dashes ai, bl , d, etc.

Projectors are always drawn as continious thin lines. The model will facilitate developing a good concept of the relative position of the points lying in any of the four quadrants. Since the projections of points, lines and planes are the basic chapters for the subsequent topics on solids viz, projection of solids, development, pictorial drawings and conversion of pictorial to orthographic and vice versa, the students should follow these basic chapters carefully to draw the projections.

Problem: Point A is 40 mm above HP and 60 mm in front of v. Draw its front and top view. Looking from the front, the point lies 40 mm above H. A-al is the projector perpendicular to V. Hence a l is the front view. To obtain the top view of A, look from the top. Point A is 60mm in front ofV. Aa is the projector prependicular to H. P Hence, a is the top view of the point A and it is 60 mm in front ofxy. To convert the projections al and a obtained in the pictorial view into orthographic projections the following steps are needed.

P occupies the position verically below the V. P line. Also, the point a on H. P will trace a quadrant of a circle with 0 as centre and o-a as radius. Now a occupies the position just below o. The line joining al and a, called the projector, is perpendicular to xy Fig. To draw the orthographic projections. P in the front view and v. Therefore while drawing the front view on the drawing sheet, the squares or rectangles for individual planes are not necessary.

Only the orthographic projections shown in FigA. Point A is lying on H. P and so its front view allies on xy line in Fig. Therefore, mark a line xy in the orthographic projeciton and mark on it a l Fig.

Point A is 25mm in front ofV. P and its top view a lies on H. P itself and in front of xy. Rotate the H. In the orthograpl;tic projection a is 25 mm below xy on the projector drawn from a l.

Looking at the pictorial view from the front Fig. P and so a l is 70 mm above xy. Hence, mark a l the orthographic projection 70 mm above xy Fig. Looking at the pictorial view from the top, point a is on V. P and its view lies on xy itself. The top view a does not lie on the H.

So in this case the H. P need not be rotated. Therefore mark a on xy on the projector drawn from a l. It is 30 mm above H. P and b I is the front view ofB and is 30 mm above xy. Point B is 40 mm behind v. To obtain the orthographic projections from the pictorial view rotate H. Now the H. P coincides with v. P will trace a quadrant of a circle with 0 as centre and ob as radius. Now b occupies the position above o.

To draw the orthographic projections; draw xy line on which a projectior is drawn at any point. Mark on it b l 30 nun above xy on this projector. Mark b 40 nun above xy on the same projector.

Problem : A point C is 40 mm below HP and 30 mm behind v. Sulution : Fig. C is 40 nun below H. P Hence cl is 40 nun below xy. Draw xy and draw projector at any point on it.

Mark cl 40 nun below xy on the projector. Cis 30 nun behind v. So cl is 30 nun behind xy. Hence in the orthographic projections mark c 30 nun above xy on the above projector. Problem: A point D is 30 mm below HP and 40 mm in front of v. Draw its projeciton. Solution: F ig. Dis 30 nun below H. Hence, d l , is 30 nun below xy. Draw xy line and draw a projector perpendicular to it.

Mark d l 30 nun below xy on the projector. Dis 40nun in front ofV. P; so dis 40 nun in front ofxy. Therefore, mark d 40 mm below xy. Point Pis 30 mm. P and 40 mm. Point Q is 25 mm. P and 35 mm. Point R is 32 mm. P and 45 mm behind VP d. Point Sis 35 mm. P and 42 mm in front ofVP e. Point T is in H. P and 30 mm. Point U is in v.

Point V is in v. Point W is in H. P and 48 mm. The projectors of a straight line are drawn therefore by joining the projections of its end points. The possible projections of straight. P and H. P in the flrst quadrant are as follows: I.

Perpendicular to one plane and parallel to the other. Parallel to both the planes. Parallel to one plane and inclined to the other. Inclined to both the planes. Line perpendicular to H. P and parallel to V. Looking from the front; the front view of AB, which is parallel to v. Looking from the top; the top view ofAB, which is perpendicular to H. P is obtained a and b coincide.

The Position of the lineAB and its projections on H. P are shown in Fig. The H. P is rotated through in clock wise direction as shown in Fig. The projection of the line on V. P which is the front view and the projection on H. P, the top view are shown in Fig. Note: Only Fig. Line perpendicular to v.

Problem: A line AB 50 mm long is perpendicular to v. Its end A is 20 mm in front of v. Draw the projectons of the line. Solution Fig. Therefore the true length of the line is seen in the top view. So, top view is drawn fIrst. P and parallel to H. Draw xy line and draw a projector at any point on it. Point A is 20 mm in front ofY. Mark a which is the top view of A at a distance of 20 mm below xy on the projector.

Mark the point b on the same projector at a distance of 50 mm below a. To obtain the front view; mark b l at a distance 40mm above xy line on the same projector.

The line AB is perpendicular to Y. So, the front view of the line will be a point. Point A is hidden by B. Hence the front view is marked as bl al. The fmal projections are shown in Fig.

Line parallel to both the planes Problem : A line CD 30 mm long is parallel to both the planes. The line is 40 mm above HP and 20 mm in front of V. Draw its projection. Draw the xy line and draw a projector at any point on it. To obtain the front view mark c’ at a distance of 40mm abvoe xy H. The line CD is parallel to both the planes. Front view is true lenght and is parallel to xy.

Visible, cutting plane and short break lines are thick lines, on the other hand hidden, center, extension, dimension, leader, section, phantom and long break lines are thin. Table 2. They should end on both sides by touching the visible lines and should touch themselves at intersection if any.

Some geometric symbols are commonly used in almost every types of drawing while there are some special symbols used in specific types civil, mechanical, electrical etc. Make a table showing the conventional lines most commonly used in engineering drawing mentioning their specific applications. Why have you studied lines and symbols?

Why there is no specified proportion for dimension and extension line? What is difference between applicability of a section line and a break line? Which conventional lined are to be drawn with 2H pencils? Which conventional lined are to be drawn with HB pencils? Draw some electrical symbol for household weiring. The plainest and most legible style is the gothic from which our single-stroke engineering letters are derived. The term roman refers to any letter having wide down ward strokes and thin connecting strokes.

Roman letters include old romans and modern roman, and may be vertical or inclined. Inclined letters are also referred to as italic, regardless of the letter style; text letters are often referred to as old English. Letters having very thin stems are called Light Face Letters, while those having heavy stems are called Bold Face Letters.

In addition, light vertical or inclined guidelines are needed to keep the letters uniformly vertical or inclined. Guidelines are absolutely essential for good lettering and should be regarded as a welcome aid, not as an unnecessary requirement. Make guidelines light, so that they can be erased after the lettering has been completed. Use a relatively hard pencil such as a 4H to 6H, with a long, sharp, conical point. The vertical guidelines are not used to space the letters as this should always be done by eye while lettering , but only to keep the letters uniformly vertical, and they should accordingly be drawn at random.

A guideline for inclined capital letters is somewhat different. The spacing of horizontal guidelines is the same as for vertical capital lettering. The American Standard recommends slope of approximately Strokes of letters that extend up to the cap line are called ascenders, and those that extend down to the drop line, descenders.

Since there are only five letters p, q. But the width of the stroke is the width of the stem of the letter. In the following description an alphabet of slightly extended vertical capitals has-been arranged in-group. Study the slope of each letter with the order and direction of the storks forming it. The proportion of height and width of various letters must be known carefully to letter them perfectly. The top of T is drawn first to the full width of the square and the stem is started accurately at its midpoint.

The first two strokes of the E are the same for the L, the third or the upper stoke is lightly shorter than the lower and the last stroke is the third as long as the lower. The second stroke of K strikes stem one third up from the bottom and the third stroke branches from it. A large size C and G can be made more accurately with an extra stroke at the top. U is formed by two parallel strokes to which the bottom stroke be added.

J has the same construction as U, with the first stroke omitted. The middle line of P and R are on centerline of the vertical line. The background area between letters, not the distance between them, should be approximately equal. Some combinations, such as LT and VA, may even have to be slightly overlapped to secure good spacing. In some cases the width of a letter may be decreased.

For example, the lower stroke of the L may be shortened when followed by A. Words are spaced well apart, but letters with in words should be spaced closely. Make each word a compact unit well separated from the adjacent words. For either upper case or lower-case lettering, make the spaces between words approximately equal to a capital O. Avoid spacing letters too far apart and words too close together.

Most of the lettering is done in single stroke either in vertical or in inclined manner. Only one style of lettering should be used throughout the drawing. Lettering can be done either in free hand or using templates. Standard height of letters and numbers are 2. Review Questions: 1. Why have you studied lettering? What is the difference between Gothic and Roman letters? Which style of lettering is most commonly used in engineering drawing and why?

What do you mean by guidelines? Why is it used? What are the ISO rules for lettering? How do you maintain the spaces between letters, words and lines? Which letters have equal height and width? What are the standard heights of letters in engineering drawing?

These methods are illustrated in this chapter, and are basically simple principles of pure geometry. These simple principles are used to actually develop a drawing with complete accuracy, and in the fastest time possible, without wasted motion or any guesswork. Applying these geometric construction principles give drawings a finished, professional appearance. Strict interpretation of geometric construction allows use of only the compass and an instrument for drawing straight lines but in technical drawing, the principles of geometry are employed constantly, but instruments are not limited to the basic two as T-squares, triangles, scales, curves etc.

Since there is continual application of geometric principles, the methods given in this chapter should be mastered thoroughly.

It is assumed that students using this book understand the elements of plane geometry and will be able to apply their knowledge. It is actually represented on the drawing by a crisscross at its exact location.

Lines may be straight lines or curved lines. A straight line is the shortest distance between two points. There are three major kinds of angles: right angels, acute angles and obtuse angles. The various kinds of triangles: a right triangle, an equilateral triangle, an isosceles triangle, and an obtuse angled triangle.

When opposite sides are parallel, the quadrilateral is also considered to be a parallelogram. The most important of these polygons as they relate to drafting are probably the triangle with three sides, square with four sides, the hexagon with six sides, and the octagon with eight sides. Some helpful relations to be remembered for regular polygons are: 1.

The major components of a circle are the diameter, the radius and circumference. The surfaces are called faces, and if these are equal regular polygons, the solids are regular polyhedral. Thus, the remaining of this chapter is devoted to illustrate step-by-step geometric construction procedures used by drafters and technicians to develop various geometric forms. First of all we have to be well-expertise in using set squares particularly for drawing parallel and perpendicular lines. In the given process, a line will also be constructed at the exact center point at exactly Where this line intersects line A-B, it bisects line A-B.

Line D-E is also perpendicular to line A-B at the exact center point. This new line is longer than the given line and makes an angle preferably of not more than with it.

The original line AB will now be accurately divided. D C Fig. Draw a straight line from A to D. Point X is the exact center of the arc or circle. If all work is done correctly, the arc or circle should pass through each point. In this example, place the compass point at point A of the original shape and extend the lead to point B.

Swing a light arc at the new desired location. Letter the center point as A’ and add letter B’ at any convenient location on the arc. It is a good habit to lightly letter each point as you proceed. Place the compass point at letter B of the original shape and extend the compass lead to letter C of the original shape. Transfer this distance, B-C, to the layout.

Going back to the original object, place the compass point at letter A and extend the compass lead to letter C. Transfer the distance A-C as illustrated in Figure. Locate and letter each point. This completes the transfer of the object.

Recheck all work and, if correct, darken lines to the correct line weight. Use the longest line or any convenient line as a starting point. Line A-B is chosen here as the example. Lightly divide the shape into triangle divisions, using the baseline if possible. Transfer each triangle in the manner described in previous procedure.

Check all work and, if correct, darken in lines to correct line thickness. Letter a diameter as HB. Now set off distances DE around the circumference of the circle, and draw the sides through these points. Diagonals will intersect the circle at 4 points.

These tangents will meet the sides of square drawn in step 3. Now darken the obtained octagon. Given: Number of sides and the diameter of circle that will circumscribe the polygon.

Mark a diameter. As example let us draw a 7 sided polygon. Mark the diameter as Taking as radius of compass, cut the circumference in 7 equal segments to obtain the corners of the seven sided polygon and connect the points. Given: Length of one side and number of sides i. Thus the polygon will be drawn. Given: Number of sides and diameter of out scribing circle.

Then AB is the length of one side. Now set off distances AB around the circumference of the circle, and draw the sides through these points. Given: Number of sides and diameter of inscribing circle. At each point of intersection draw a tangent to the circle.

The tangents will meet each other at 1, 2, 3, 4…… etc. Then ….. Label the end points of the chord thus formed as A and B. Locate points C and D where these two lines pass through the circle.

Where these lines cross is the exact center of the given circle. Place a compass point on the center point; adjust the lead to the edge of the circle and swing an arc to check that the center is accurate. This arc will touch the line AB and the given arc.

Center locations given Radius given Fig. It forms a gentle curve that reverses itself in a neat symmetrical geometric form. In this example, from point B to point C. Draw a perpendicular from line C-D at point C to intersect the perpendicular bisector of C-X which locates the second required swing center.

Place the compass point on the second swing point and swing an arc from X to C. This completes the ogee curve. Note: point X is the tangent point between arcs. Check and. If r1 , r2 and AB are given draw them accordingly. If value of r1 , r2 are given simply draw the arc EF taking radius as r2- r1 and center as B. Then PQ will be the required tangent. Thus the ellipse will be completed. Divide a line of length 40mm into 7 equal parts. Draw a regular pentagon inscribing a circle of diameter 80mm.

Avoid use of protractor. Draw a regular pentagon out scribing a circle of diameter mm. Draw a regular pentagon having length of side as 45mm. Draw a regular hexagon inscribing a circle of diameter 80mm. Draw a regular hexagon out scribing a circle of diameter mm.

Draw a regular hexagon having length of side as 45mm. Draw a regular octagon inscribing a circle of diameter 80mm. Draw a regular octagon out scribing a circle of diameter mm. Draw a regular octagon having length of side as 45mm. Draw a 9 sided regular polygon inscribing a circle of radius 50mm.

A 80mm long horizontal straight line is located outside a circle of radius 30mm, such that a 50mm line drawn from center of the circle meets the mid-point of the straight line at right angle. Draw two arc tangents, each having a radius of 40mm touching the circle and one of the ends of the straight line.

Draw a common arc tangent of radius 70mm to the two circles having their centers 80mm apart and having diameters of 50mm and 30mm respectively. Draw an ogee curve to connect two parallel lines each of length 20mm and their mid-points spaced 30mm vertically and 70mm horizontally. Two wheels with diameters 3. Draw the line diagram of the arrangement. Use a reduced scale. Draw an ellipse having major and minor axis length as 90mm and 60mm.

Why have you studied geometric drawings? Name the geometric nomenclatures and draw a qualitative shape of them. Name and draw the different types of lines. What do you mean by isosceles, equilateral and scalene triangle? What are different types of quadrilaterals? Draw them. What is the difference between parallelogram, trapezoid, rectangle, square and rhombus?

What do you mean by regular polygon? How can you calculate summation of all internal angles of a polygon? A circle has a diameter of cm. Draw a circle showing chord, diameter, radius, arc, segment and sector.

Name some solid geometric form. Draw a parallel or perpendicular line to a given line at any point using set-square. Transfer a given polygon to other specified point. Locate the center of a given circle.

Draw a tangent to the two given circle. A complete set of dimensions will permit only one interpretation needed to construct the part. In some cases, engineering drawing becomes meaningless without dimensioning. Maintaining scale only does not make a drawing sufficient for manufacturer. By direct measurement from drawing according to the scale is very laborious, time-consuming and such a part cannot be manufactured accurately.

But for overcrowded drawing they can be drawn at an oblique angle as well. Correct Wrong Fig. They are usually drawn freehand. It must not be either away from the line or cross the line.

They are also used to present note, symbols, item number or part number etc. R3 Fig. Unidirectional system: All the dimensions are oriented to be read from the bottom of drawing. It is also known as horizontal system. This system is preferred to aligned system.

Aligned system: All the dimensions are oriented to be read from the bottom or right side of the drawing. These are dimensions which indicate the overall size of the object and the various features which make up the object. Locational dimensions are dimensions which locate various features of an object from some specified datum or surface.

Figure gives examples of size and location dimensions. Sometimes the space may be even too small to insert arrows, in such case dimensions as well as arrows can be provided on outside of the extension lines as shown in Fig. Sometimes smaller circular dots are used in place of arrowhead for space limitation. Portion to be enlarged Enlarged view of A Use of small dot Fig. The symbols used to depict degrees, minutes, and seconds are also shown in this figure.

Angular measurements may also be stated in decimal form. This is particularly advantageous when they must be entered into an electronic digital calculator.

The key to converting angular measurements to decimal form is in knowing that each degree contains 60 minutes, and each minute contains 60 seconds. If space is limited then leaders can be used comfortably. An arc symbol is placed above the dimension. Why have you studied dimensioning?

Which information are provided in dimensioning system? What are the conditions for a good dimension system? Name the elements of dimensioning system. What are the rules that must be followed while dimensioning? What is the purpose of extension line and what are the rules to be followed for extension line? What is the purpose of dimension line and what are the rules to be followed for dimension line?

What is the purpose of leaders and what are the rules to be followed for leaders? What are the uses of arrowheads in dimensioning and what are the rules to be followed for arrowheads? What is the proportion of width and length of an arrowhead? Draw a square out scribing a circle and complete dimensioning. What is the difference between aligned and unidirectional dimensioning?

Give examples. What will you do when the space between extension lines is too small to accommodate the dimension line with text at its middle? What will you do when the space between extension lines is too small to accommodate the dimension line with arrows? What will you do when the feature is too small to make the dimension visible?

What is the difference of dimensioning of chord, arc and angle? Give example. Draw a circular hole of 2cm deep and give dimensions to it. It is not possible always to make drawings of an object to its actual size as the extent of drawing paper is limited and also sometimes the objects are too small to make it clearly understandable by drawing its actual size in drawing paper.

Scale is the technique by which one can represent an object comfortably as well as precisely within the extent of drawing paper. In other words, a scale is a measuring stick, graduated with different divisions to represent the corresponding actual distance according to some proportion.

Numerically scales indicate the relation between the dimensions on drawing and actual dimensions of the objects. It is represented as scale. If possible, drawing should be done in full scale. Reducing Scale The scale in which the actual measurements of the object are reduced to some proportion is known as reducing scale. The standard formats of reducing proportions are: – drawing made to one-half of the actual size – drawing made to one-fifth of the actual size – drawing made to one-tenth of the actual size – drawing made to one-fiftieth of the actual size – drawing made to one-hundredth of the actual size Enlarging Scale The scale in which the actual measurements of the object are increased to some proportion is known as reducing scale.

The standard formats of enlarging proportions are: – drawing made to twice the actual size – drawing made to five times the actual size – drawing made to ten times the actual size Md. It is simply a line divided into a number of equal parts and the 1st part is further sub-divided into small parts. It is so named because the 2nd sub-unit or 2nd decimal of main unit is obtained by the principle of diagonal division.

Table 6. Scale is constructed by simply dividing the line Scale is constructed by dividing the line longitudinally.

For example let us consider a plan drawn in inch units and scale provided with drawing can measure in feet and inch. If we draw another scale taking same R. Also if we draw another scale that can measure in cm and mm with same R. It consists of a fixed main scale and a movable vernier scale. This scale is usually marked on a rectangular protractor.

Therefore, to get the actual measurements, it is a must to know the proportion using which the drawing is prepared. Sometimes the drawing may need to be prepared to an odd proportion like In such case individual scale construction is required for that specific drawing.

It is often found helpful and convenient to construct and draw the corresponding scale on the drawing than mentioning the proportion in language. On the other hand if a drawing is to be used after decades, the paper may shrink or Md. Taking measurements from such a drawing using the proportion mentioned will give some inaccurate result. But if a scale is constructed an drawn during the preparation of 1st time, the drawn scale will also shrink or expand in the same proportion to the drawing.

Thus if one take measurements with the help of the drawn scale, accurate measurements will be obtained. The ratio of the distance on drawing paper of an object to the corresponding actual distance of the object is known as the representative fraction R.

It is to be remembered that for finding RF the distances used for calculation must be in same unit. And being a ratio of same units, R. Calculation Example 6. Calculate R. Solution: Representative Fraction of the scale for this map,. Find out RF of the scale for this drawing. Solution: Representative Fraction of the scale,.

What will be the R. Solution: Here 1 sq. However, sometimes British system is also used. It is important to have clear understanding about unit conversion in both system. Avoid fractions, consider the next integer value. For instance, if maximum length to be measured is 6.

For instance if the scale need to measure in feet and inches, number of minor divisions will be If space is limited they can be marked after every 2 division like 0, 2,4,….. Find R. Solution: 2. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 1, 2, 3, 4 and 5.

The 1st division is further divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2 division as 2, 4, 6, 8 and 10 toward left.

Thus the scale is constructed and the required distances are indicated. In this publication we have put together a list of books about Drawing, all in PDF format. This is a topic worthy of our digital library, and today we share it with you. The art and technique of illustrating is what we know as drawing. Through the action of drawing, an image is captured on a surface such as a canvas or paper, using various techniques.

On the other hand, it can also be said that drawing is a style of graphic expression on a horizontal surface, that is, in two dimensions. Moreover, it is one of the known visual arts. Drawing is a tool that allows us to express both thoughts and objects. When something cannot be expressed in words, the best option is to draw it.

The list of books about drawing that we share today is made up of more than 30 texts in PDF format in which you can consult all the relevant information about this artistic expression. Additionally, we have integrated in our collection, books in Spanish and in Portuguese, so that you can enjoy this topic in any of these languages, if you wish.

Finally, it is important to note that each and every one of these books has been given for its publication and distribution, or are in the public domain. Drawing is often considered a hobby. Sometimes, parents give their children a sheet of paper and some crayons to entertain themselves with this activity; however, as adults, we can also draw to de-stress or simply for pleasure. Drawing can then be considered as an art or even as a profession, which is used by many in their jobs.

An example of this can be seen in painters, portrait artists, graphic designers, illustrators, etc. Therefore, if you want to learn how to draw, you can find good materials to do it through the Basic Drawing Books we have for you, so that you can learn the basics of this technique and, together with practice, become an excellent illustrator or cartoonist.

Cartoon Books usually provide readers or students with a good amount of exercises to learn how to do them by themselves, from how to do the feet to each of the parts of the body. It is worth mentioning that learning this art can open the doors to success, since it is quite commercialized, both by companies and independent cartoonists. Comic books can be made, as well as Japanese manga, among others. This type of drawings is also known as blueprints, and is usually used for construction, hence its great importance when it comes to making it, as well as the responsibility that runs on the part of the drafter.

If you are a student of architecture, or simply want to learn how to make this type of art, you can consult the Architectural Drawing Books, with which you will be able to learn and understand how to make them in a correct and practical way. Do you know who Leonardo Da Vinci was? This type of art is one of the most striking and used by painters and illustrators today, so you can learn everything about it by consulting the Artistic Drawing Books that we have available in PDF and that will surely be very useful for you.

According to this definition, geometric drawing is considered to be that which is made following the rules of this discipline. However, geometric drawing has a wide application, since it can be found not only in mathematics, but also in graphic design, architecture and other related disciplines.

In that sense, we have made a selection of Geometric Drawing Books that will help you better understand its use. You will learn how to draw circles, triangles, ovals and rectangles, and how to make compositions with them, including logos, faces and other more complex drawings. Mechanical drawing is quite similar to architectural drawing in terms of importance and responsibility since both are used as blueprints for later construction or, in this case, manufacturing.

 
 

Download Engineering Drawing Books – PDF Drive

 
To provide necessary information about an object to the manufacturer or to any other ebolk party, it is usual practice to provide projection s of that object.

 

[(PDF) Engineering Drawing for Beginners | Md. Roknuzzaman – replace.me

 
Construct a scale for this drawing showing meters, decimeters and centimeters and measure 2 meters, 5 decimeters and 8 centimeters on it. Thus, the remaining of this chapter is devoted to illustrate step-by-step geometric construction procedures used by drafters and technicians to develop various geometric forms. Bernd S. Sitting chair iii. Drawing paper 5.