Model engineers handbook pdf download

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. Draw a plain scale to show units of 10 miles and single miles. Thus we have to construct the scale for 70 miles of maximum distance. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 10, 20, 30, 40, 50 and On a scale one centimeter represents one third of a kilometer.

Construct the scale and show the distance travelled by the car in 3 minutes and 30 seconds. What is the R. Solution: 1 1. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 1, 2, 3 and 4. The 1st division is further divided into 6 divisions so that each minor division shows 10 seconds and starting at 0 mark placed earlier the sub-divisions are marked as 10, 20, 30, 40, 50 and 60 toward left.

Thus the scale is constructed and the required time is indicated. Let the given short line AB which is required to be divided into 12 equal parts. Thus dividing is complete indirectly. For instance if the scale need to measure in yards, feet and inches, number of horizontal sub-divisions will be 3. For instance if the scale need to measure in yards, feet and inches, number of vertical sub-divisions will be At every horizontal sub-division point draw a parallel line to this diagonal line.

At left end a perpendicular of length equal to one major division is drawn and a rectangle is completed considering the mutually perpendicular lines as two sides. The vertical line at left end is divided into 10 equal parts and at each division point a line parallel and equal length of the base line is drawn. Top left corner and the point corresponding to 9hm is connected with a diagonal line. At the remaining 9 horizontal sub-division points parallel lines are drawn to the 1st diagonal line.

Vertical divisions are marked sequentially from bottom toward top at every 2 division as 2, 4, 6, 8 and At all the horizontal major division points vertical lines are drawn. Also show 2 yds. The 1st division is further divided into 3 divisions and starting at 0 mark placed earlier the sub-divisions are marked as 1, 2 and 3 toward left.

The vertical line at left end is divided into 12 equal parts and at each division point a line parallel and equal length of the base line is drawn. Top left corner and the point corresponding to 2ft is connected with a diagonal line.

At the remaining two horizontal sub-division points parallel lines are drawn to the 1st diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as 2, 4, 6, 8, 10 and Construct a scale for this drawing showing meters, decimeters and centimeters and measure 2 meters, 5 decimeters and 8 centimeters on it.

Solution: 20 1. Assume the drawing scale length is 15 cm standard value. Both are acceptable as we have to show a distance only 2m 5dm 8cm on this scale. Let us take 7. Now a horizontal line 15cm long is drawn and is divided into 7 equal parts. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 1, 2, 3, 4, 5 and 6. Top left corner and the point corresponding to 9dm is connected with a diagonal line. Maximum measuring length is given here i.

Considering a drawing scale length as 15 cm. So our major unit should be th of meters, 1st sub-unit should be 10th of meter and 2nd sub-unit or diagonal sub-unit should be single meters. Now a horizontal line 15cm long is drawn and is divided into 3 equal parts. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 1, and 2. 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 20, 40, 60, 80 and toward left.

Top left corner and the point corresponding to 90m is connected with a diagonal line. Construct a scale to read miles, furlongs and minimum 20 yards distance and mark 4 miles 6 furlongs and yards on it. Let us assume the drawing scale length is 6 inch. The 1st division is further divided into 8 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2 division as 2, 4, 6 and 80 toward left.

The vertical line at left end is divided into 11 equal parts and at each division point a line parallel and equal length of the base line is drawn. Top left corner and the point corresponding to 7 furlongs is connected with a diagonal line. At the remaining 7 horizontal sub-division points parallel lines are drawn to the 1st diagonal line.

Vertical divisions are marked sequentially from bottom toward top at every 2 division as 20, 60, , , and The scale should be such that 4mm length is represented by 10cm and it should be able to measure upto 5mm. Construct the scale and measure 3.

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 0. Top left corner and the point corresponding to 0. Vertical divisions are marked sequentially from bottom toward top at every 2 division as 0. Draw a scale to represent 6 km by 1 cm and to show distance upto 60 km. From left staring 0 at 2nd division major units are marked sequentially toward right as 0, 1, 2, 3…… and 9.

The 1st division is further divided into 6 divisions so that each sub-division represents 10 seconds and starting at 0 mark placed earlier the sub-divisions are marked after every 2 division as 20, 40 and 60 toward left. Top left corner and the point corresponding to 50 seconds is connected with a diagonal line. At the remaining 5 horizontal sub-division points parallel lines are drawn to the 1st diagonal line. Construct a plain scale to show meters and decimeters, when 3 centimeters are equal to 2 meters and long enough to measure upto 5 meters.

Show a distance of 2 meters 7 decimeter and 4. Construct a plain scale that can measure 1m to 50m. Show a distance 38m on the scale. Construct a scale to show miles and furlongs, when 2. In a certain map 1 acre represents square kilometers of land area.

Construct a scale for a portion of that map which can measure in kilometers and its 1st decimal point. The scale should be long enough to measure upto 9.

Construct a plain scale to measure a maximum distance of 55 km and show the measurement of 42 km on it. The volume of a room is cubic metre. It is represented by a volume of 80 cubic cm.

By measuring R. Also show the measurement of 12 metre on it. The distance between Dinajpur and Joypurhat railway station is km and it is covered by the Drutajan Express in 4 hours. Draw a plain scale to measure the time upto single minute. Take R. Calculate and show the distance covered by the train in 45 minutes on the scale. Construct a diagonal scale to read meters, decimeters and centimeters and long enough to measure upto 5 meters when 1 meter is represented by 3 centimeters.

Indicate on the scale a distance of a. Construct a diagonal scale of R. A plan of a house 12 cm represents m. Construct a diagonal scale to read metres to one metre and show the measurement metres on it. The distance between two station is km. On a map it is represented by a 12 cm length line. Construct a diagonal scale to show kilometers and to measure a distance of km. Find the R. Also mark a distance 46 metres and 5 decimetres on it.

Ina drawing of machine parts, the original shapes are magnified 50 times. Construct a scale to measure upto 2nd decimal point of a single millimeter and long enough to measure upto 4mm. Show a length of 2. A person is running at a speed of 6 kmph.

Why have you studied scale? Define scale. When scale becomes necessary? Why have you learned to draw scale? In which situation scale is to be drawn along with the drawing? Classify scales according to scale size. Define each type and give practical examples. Classify scale according to measurement capacity. Define each type. Which scales are usually used by engineers? Differentiate between plain and diagonal scale.

Which information you think necessary to construct a scale? Define R. What is the unit of R. Give logic to your answer. What do you understand when an R. It is mentioned in a drawing that R. What is its meaning? On a map of Bangladesh you measured the distance from Dinajpur to Dhaka as 6 inch.

Actually the distance is miles. What should be the possible R. A 15 cm scale measures a maximum length of 10 km. What is its R. If 9 hectares of area is represented by 1mm2 in a map, what is the value of R. During the construction of scale why the zero notation placed at 2nd division?

How can you divide a 1mm line in 7 equal parts? To provide necessary information about an object to the manufacturer or to any other concerned party, it is usual practice to provide projection s of that object.

If straight lines rays are drawn from various points on the contour of the object to meet a transparent plane, thus the object is said to be projected on that plane. The figure or view formed by joining, in correct sequence, the points at which these lines meet the plane is called the projection of the object. Pictorial Projection 3. Perspective Projection 7. When the projectors are perpendicular to the plane on which the projection is obtained, it is known as orthographic projection.

Following six views are possible in orthographic projection of a solid object. Top View b. Front view c. Left View d. Right View e. Rear view f. Bottom view Fig. They have the advantage of conveying an immediate impression of the general shape and details of the object, but not its true dimensions or sizes. Pictorial projections may be of two types as a. Axonometric b. Oblique 7. Axonometric projections are classified according to how the principle axes are oriented relative to the projected surface.

There may be three types as: i. Isometric ii. Dimetric iii. Trimetric Fig. The angle is usually kept This may be of two types: i.

Cavalier Projection: In this case, the dimensions along all the axes are plotted in full scale. Cabinet Projection: In this case, the dimensions along the diagonal axis are plotted by reducing it to half of the actual value. Dimensions along other axes are plotted in full scale. In case of perspective projection observer is considered to be at finite distance where in case of any other type of projection observer is considered to be at infinity.

In short, orthographic projection is the method of representing the exact shape of an object by dropping perpendiculars from two or more sides of the object to planes, generally at right angles to each other; collectively, the views on these planes describe the object completely. Descriptive geometry is basically the use of orthographic projection in order to solve for advanced technical data involving the spatial relationship of points, lines, planes, and solid shapes.

The most common means of understanding these types of orthographic projection is - The Glass Box method. It can be suitably used for understanding the generation of orthographic views. The box is unfolded to obtain the arrangement of views. In figure 7. The line of sight is always perpendicular to the plane of projection, represented by the surfaces of the glass box top, front, and right side.

Projection lines C connect the same point on the plane of projection from view to view, always at right angle. A point is projected up on the plane of projection where its projector cuts that image plane.

In the figure 7. When it intersects the horizontal plane top plane of projection , it is identified as 1H, when it intersects the frontal plane front plane of projection , it is identified as 1F, and where it intersects the profile plane right side plane of projection , it is labeled 1P.

On these planes, views of the object can be obtained as is seen from the top, front, right side, left side, bottom and rear.

Consider the object and its projection in fig. In actual work, there is rarely an occasion when all six principal views are needed on one drawing. All these views are principal views. Each of the six views shows two of the three dimensions of height, width and depth. In general, when the glass box is opened, its six sides are revolved outward so that they lie in the plane of the paper.

And each image plane is perpendicular to its adjacent image plane and parallel to the image plane across from it. Before it is revolved around its hinged fold line reference line. A fold line is the line of intersection between any hinged adjacent image planes.

The left side, front, right side, and back are all elevation views. Each is vertical. The top and bottom planes are in the horizontal plane. But in most cases the top, front, and right sides are required. Sometimes the left- side view helps to describe an object more clearly than the light side view. Orthographic views are arranged in two techniques as a. First Quadrant Fig. When an inclined or oblique line is to be projected it is helpful to identify and draw the end points and then joining them to obtain the projection.

Parallel Inclined Fig. Oblique Fig. The edges, intersections, and surface limits of these hidden parts are indicated by a discontinuous line called a dashed line or hidden line. Particular attention should be paid to the execution of these dashed lines.

If carelessly drawn, they ruin the appearance of a drawing. All the center lines are the axes of symmetry. Hidden portions of the object may project to coincide with visible portions.

Center lines may occur where there is a visible or hidden out line of some part of the object. Since the physical features of the object must be represented full and dashed lines take precedence over all other lines since visible out line is more prominent by space position, full lines take precedence over dashed lines.

A full line could cover a dashed line, but a dashed line could not cover a full line. When any two lines coincide, the one that is more important to the readability of the drawing takes precedent over the other.

The following line gives the order of precedence of lines. Full line 2. Dashed line 3. Careful line or cutting — plane line 4. Break lines 5. Dimension and extension lines. Crosshatch lines. The points which are connected by lines in original object should be connected in the vertical plane. All other 5 views can be obtained in similar way. The plane of projection vertical, in case of front view should be parallel to the face for which views are being drawn. For example, in case of top view the plane will be horizontal.

In the projection there is a relationship of different views. It is usual practice to draw the front view first, then top and side views are drawn with the help of the vertical and horizontal projection lines. This can be done using T-square, set-squares and compasses. Here only the figure C requires the use of compass in addition to T-squares and set- squares.

The spacing between views has to be determined or decided beforehand and if equal spacing is needed then fig. A can be followed and if a different spacing is needed then fig.

B can be followed. Sufficient space should be provided in order to give dimensions avoiding any crowding and also excessive space should be avoided. If not mentioned or required otherwise 30mmmm spacing can be provided between two successive views.

Position of this line depends on the spacing requirement between side view and front view. If equal spacing is required then the line should originate at the corner of the front view.

These lines will cut the diagonal line. It is to be noted that for 1st angle projection the lines should be projected according to position of views. For example to draw top view, vertically downward lines need to be projected from front view so that the top view is generated below the front views; for getting right side view horizontal lines from front view are to be projected toward left and so on. The length along the third axis cannot be shown in same view.

This makes it difficult to understand them and only technically trained persons can understand the meaning of these orthographic views. As discussed in earlier editions of this handbook , such models and algorithms for their solutions have been the subject of study since the early s. Liptak Ed. See Mahomet's Successors , Q. As discussed in earlier editions of this handbook , such models and algorithms for their solutions have been the subject of intensive study since the early s when digital computing became practical.

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