In the first chapter you learnt the importance of engineering graphics as a means of communicating design ideas. Man can communicate through language, either in oral or in written form. Both the methods are, however, found to be unsuitable for conveying technical information regarding the shape, size, and internal features of even a relatively simple object. This information is essential for the manufacturing of the object. Engineering graphics can solve this problem very effectively as it involves visualisation and graphic representation (drawing) of the object(s) that has been visualised.
A technical (engineering) drawing, properly prepared, will communicate more accurate and vivid description of an object than a photograph or a verbal/written analysis. A photograph exhibits only the outward appearance of an object. It does not give an idea of the internal details. Also, it is not possible to photograph something that does not exist. The purpose of engineering drawing is to give an exact visual description of an object that may not even exist at this moment. The method of orthographic projection is universally accepted to serve this purpose completely. With this method, it is very convenient to describe the true shape and size of any three-dimensional object on a two-dimensional drawing sheet. In order to understand Orthographic Projection Drawing, you must consider a few elemental features of the projection system, namely, a plane of projection (also known as the picture plane), a point where the observer is situated, and a given object.
Let us concentrate on Fig. 2.1 that represents an object, a plane of projection, and a stationary point P where an observer is positioned. You know that an object is visible when light rays from the object strike the observer's eye. The size of the image formed on the retina depends on the distance of the observer from the object. In Fig. 2.1, the picture plane is an imaginary transparent plane placed in between the observer and the object. The visual rays, known as projectors, from various points on the contour of the object intersect the picture plane at different places and thus an image of the object is formed. This image is referred to as the projection of the object on the picture plane or a perspective view of the object. Though the perspective projection of a three-dimensional object results in a pictorial view for easy understanding, it contains distortions of linear and angular magnitudes. For example, the image formed on the plane of projection is much reduced in shape and size as compared to the original object. As a consequence, this method is not very useful so far as engineering graphics is concerned, since the primary intention of engineering graphics is to represent the true shape and size of an object to be manufactured in a workshop at a later stage.
FIG. 2.1 Perspective projection
FIG. 2.2a Parallel projection
If the observer is situated at infinity with respect to the picture plane or the object, it may be assumed that the visual rays or the projectors become parallel to one another and the image, thus formed on the picture plane is as shown in Fig. 2.2a. Following the principle, if we project the rectangular plane A'B'C'D' with a circular hole on the XY plane, it becomes ABCD where the length of the vertical sides (A'B' and C'D') remains unchanged and that of the horizontal side (A'D' and B'C') gets reduced. It may also be noted that the projected circle will become an ellipse.
The projection of a particular line or edge on the projection plane depends on the orientation of the line with respect to that projection plane. Before proceeding further, we should first explain the standard method of obtaining the parallel projection of a line with its geometrical significance. The line may be oriented to the projection plane in three possible ways as mentioned below.
- The line is parallel to the plane.
- The line is perpendicular to the plane.
- The line is inclined to the plane at an angle.
Fig. 2.2b depicts the line AB and its projection A'B' in all the three cases mentioned above. It may be noted that
- when the line is parallel to the projection plane, the generated projection will be equal in length to that of the original line [Fig. 2.2b(i)];
- when the line is perpendicular to the projection plane, its projection becomes a point [Fig. 2.2b(ii)]; and
- when the line is inclined to the plane of projection, its projected length is reduced depending on the angle of inclination [Fig. 2.2b(iii)].
FIG. 2.2b Relation between true length and projected length
The level of distortion of the image is considerably reduced as compared to perspective projection. In fact, if the object is oriented in such a fashion that certain surfaces are parallel to the plane of projection, their true shapes will be exhibited. But this is not sufficient as the surfaces inclined to the plane of projection do not show their true magnitude since the visual rays coming from these surfaces intersect the plane of projection at oblique angles.
The word orthogonal means ‘perpendicular to’. When the visual rays or projectors coming from an object are oriented at right angles to the projection plane, we obtain an orthogonal projection of the object. A careful observation indicates that if this system is followed, it is possible to obtain the true dimensions of the object on the plane of projection. This can be explained with the help of the following example.
FIG. 2.3 Orthographic projection
Let us consider an object and its projection view on a reference vertical plane R placed in front of the object and parallel to the surface A of the object. This projected view is obtained when the observer is situated at infinity but is viewing the object in a direction perpendicular to the vertical reference plane R. The entire arrangement is shown in Fig. 2.3. As mentioned before, visual rays from the contour of the object intersects the plane R at right angles to form an orthogonal projection of the object. Following the principle of projection explained earlier, the height ‘h’, width ‘w’ and so on available on plane R conform to the true lengths of the object.
FIG. 2.4 Orthographic pojection in two planes
However, even now, this view is not sufficient in order to represent the actual shape of the entire object because we cannot get any idea about the depth ‘d’ of the object. The easiest solution is to obtain another projection view on a horizontal reference plane, as shown in Fig. 2.4. This view is obtained when the observer is situated at infinity but is viewing the object in a direction perpendicular to the horizontal reference plane.
Very often, two views are not sufficient to obtain full information of a complicated object. To highlight this point, two objects are shown in Fig. 2.5. You may realise that the projected view on the frontal and horizontal planes are identical for both the cases yet the objects are not same. Therefore, it may be necessary to have additional views on planes placed parallel to the sides of the objects as illustrated in Fig. 2.6. Since most of the objects have six sides, six views may result. We can assume an object is placed within a transparent glass box centrally (Fig. 2.7) and we may obtain six projected views on the six walls of the glass box as shown in Fig. 2.8.
FIG. 2.5 Two possible interpretations of the object based on the views shown in Fig. 2.4
FIG. 2.6 Three orthogonal views
FIG. 2.7 Object placed inside a glass box
FIG. 2.8 Six projected views on the sides of the glass box
Unfortunately, all these projection planes are mutually perpendicular whereas the sheet of paper on which the object is to be represented is two-dimensional. By unfolding the sides of the glass box, it is possible to bring all the projected views on the plane of the paper as shown in Fig. 2.9.
FIG. 2.9 Glass box opened
The process of unfolding the sides of the glass box follows certain universally accepted drawing conventions and different methods of projection drawings result. Now, we shall discuss the different drawing conventions.
ANGLES OF PROJECTIONS
An orthographic projection involves the use of three orthogonal planes in general. These are—vertical plane (VP), horizontal plane (HP) and one of the profile planes (PP) in the case of most objects. The relative position of these three planes are shown in Fig. 2.10.
FIG. 2.10 Three orthogonal planes of projection
According to engineering drawing conventions, all these planes are imaginary, transparent, flat surfaces with no thickness and they are considered to be extended to infinity. The objects are projected on these planes in order to obtain their true shape and size. The horizontal and vertical planes (Fig. 2.11) divide the space into four quadrants (also known as dihedral angles) and the object has the option to occupy any one of the four quadrants resulting in different drawing options. As a convention they are called first angle projection, third angle projection, and so on. We shall deal with all the four options separately.
FIG. 2.11 The four quadrants
First Angle Projection
In first angle projection, the object is assumed to be situated in the first quadrant, in front of the vertical plane and above the horizontal plane. The observer is positioned at infinity so that the object lies between the observer and the respective plane. Therefore, the view of the side of the object closer to the observer is projected on the plane of projection situated on the other side of the object.
FIG. 2.12 First angle projections on three planes
Maintaining the above convention, the front view is projected on the vertical plane and the top view is projected on the horizontal plane (Fig. 2.12). The edges of the object which are hidden from the view of the observer, is represented by short dashed lines, also called hidden lines, and the respective views are obtained on different planes. The left-hand side view appears on the profile plane. By convention, a drawing sheet is assumed to be the vertical plane. Therefore, the horizontal and profile plane are rotated, as shown in Fig. 2.13, to bring them into the same plane as that of the drawing sheet.
FIG. 2.13 The first angle projection
FIG. 2.14 Inter-relation of projection in first angle projection
The front view (also known as elevation) comes above the top view (also known as plan) and the left-hand side view comes to the right of the front view and vice versa. The orthographic projection drawing of the object in first angle is illustrated in Fig. 2.14.
Third Angle Projection
Third angle projection follows the same principles as that of first angle projection. The only difference being, here the object is assumed to be situated in the third quadrant. As a result, the relative position of the object with respect to the principal plane changes. Here the projection plane comes in between the object and the observer and the view of the object nearer to the projection plane is projected on the projection plane. The hidden edges of the object are represented by hidden lines in respective views as in the first angle system. The front view is projected on the vertical plane and the top view comes on the horizontal plane. The right-side view is projected on the profile plane. When these planes are rotated into a single plane (vertical plane), the top view appears to be placed above the front view and the right-hand side view comes to the right side of the front view as shown in Fig. 2.15.
FIG. 2.15 Arrangement of views in third angle projection
Second and Fourth Angle Projection
In second and fourth angle projection, the object, as usual, is to be placed in the second and the fourth quadrant respectively, and the corresponding front and top views are projected on the vertical and horizontal planes. Following drawing conventions, the top views in both cases are to be brought in the vertical plane by a suitable rotation of the horizontal plane. It may be noted that the two views overlap over each other, resulting in utter confusion. Therefore, these two methods of projection drawings are not at all recommended in practice.
The relative positions of the different views on the drawing sheets are usually guided by the two methods of orthographic projections, namely, first angle projection and third angle projection. The drawing layout for both these methods are illustrated in Fig. 2.16. The lower case letters with arrows represent the different view directions.
FIG. 2.16 Designations of view directions in orthographic projections
FIG. 2.17 Relative position of views—first angle projection
First Angle Projection Method
The view from the top, ‘b’, is placed underneath ‘a’.
The view from the bottom, ‘e’, is placed above ‘a’.
The view from the left, ‘c’, is placed on the right of ‘a’.
The view from the right, ‘d’, is placed on the left of ‘a’.
The view from the rear, ‘f’, is placed either on the right or left of side view (whichever is convenient).
Third Angle Projection Method
The view from the top, ‘b’, is placed above ‘a’.
The view from the bottom, ‘e’, is placed underneath ‘a’.
The view from the left, ‘c’, is placed on the left of ‘a’.
The view from the right, ‘d’, is placed on the right of ‘a’
The view from the rear, ‘f’, is placed either on the left or right of side view, whichever is convenient.
FIG. 2.18 Relative position of views—third angle projection
Layout Using Reference Arrows
In case of Computer-Aided Drafting, it is sometimes more convenient to position the views without following the strict pattern of first or third angle projection. With the help of reference arrows, it is now possible to position your views in the drawing space according to your choice.
FIG. 2.19 Using reference arrows for views
In the principal view, arrows are drawn to indicate the direction of viewing for the relevant view. Each arrow is designated by capital letters that is repeated with the drawing of each view as shown in Fig. 2.19. The designated views may be located irrespective of the principal view. This has been adopted to facilitate Computer-Aided Drafting and may be considered as an important deviation from the convention being followed by the first and third angle projection. The capital letters identifying the respective view may be placed either immediately below or above the view. In a particular drawing, the references must be consistent all through.
Indication of Method
When a drawing is developed following either first angle or third angle projection method, it is essential to indicate the method of projection adopted by means of its distinguishing symbol. The symbol for the first and third angle projection methods are shown in Fig. 2.20.
FIG. 2.20 Symbols for projection views
In fact, these symbols are nothing but the projection views of a truncated cone of convenient dimensions. The symbol should be placed in a space provided for the purpose in the title block of the drawing. When the layout of views is created using reference arrows (a very common practice adopted by Computer-Aided Drafting), no distinguishing symbol is required.
DRAWING CONVENTION OF ORTHOGRAPHIC VIEWS—HIDDEN AND CENTER LINE
A pictorial view depicts an object as it appears to the observer viewing from one direction only. As a result, it fails to represent the true shape and size of its different surfaces or the contours of the object. All the hidden parts of the object are invisible to the observer and hence their details cannot be shown. For converting a pictorial view into an orthographic view, a sound knowledge of the principles of orthographic projection is essential.
It is very important to choose the proper orientation of the object with respect to the observer. It is customary to place the object in the simplest position so that the front view will show width and height, the top view width and depth, and the side view depth and height. All the visible edges, intersection of surfaces, and so on are represented by continuous lines. In any view, there may be some internal edges of the object that are not visible from the position of the observer due to obstruction. The edges, intersections and so on of the hidden parts are indicated by discontinuous lines called dashed lines. In Fig. 2.21, both the holes of the object are hidden in the front view and hence they are shown in dashed or hidden lines. Also, note that the viewing direction should be such that the orthographic views represent the true length and shape of the object.
FIG. 2.21 The application of hidden and center line
A careful observation of Fig. 2.21 reveals that apart from the continuous and dashed lines, another type of lines has been used as well. These lines are referred to as the center lines and are drawn first in the layout of an engineering drawing. The center lines represent the axes of symmetry for all symmetrical portions of views. The center lines are drawn in the following cases:
- Any part having an axis of symmetry, such as a cylinder or cone, will have its axis represented by a center line.
- Any circle having two axes of symmetry is represented by two intersecting, mutually perpendicular center lines drawn through the center of the circle.
The center lines are always extended slightly beyond the contour of the portion. In general, they form the basic structure of the drawing. Sometimes, important dimensions of the object are shown from the center line.
CONVERSION OF PICTORIAL VIEWS INTO ORTHOGRAPHIC VIEWS
Now that we have a thorough knowledge about the principles and conventions being followed in orthographic projection, we need to apply the same to develop orthographic views of objects from their pictorial views.
Most pieces have a characteristic view by which they can be recognised easily. This is the first view you should consider and draw. Let us consider the pictorial view of an object (Fig. 2.22) in the form of a plate having different shapes of grooves. In the front view (Fig. 2.23), two pairs of vertical lines will be visible to define the edges of the rectangular and semicircular grooves. In case of triangular groove, three vertical lines are essential to define its edges. However, from the front view, it is not possible to have an idea about the shape of the grooves. The top view clearly depicts the shape of the object and hence this view should be drawn first. In this case, a side view is quite unnecessary as it does not supply any additional information. The practical purpose of a drawing is to describe the shape of an object, and if more views than required are drawn, time is actually wasted both in producing the drawing as well as in reading it.
In the above example, the lines are continuous lines as the grooves are all visible. Fig. 2.24 shows another object having holes of different shapes. The orthographic views are also developed. You may observe that the hidden lines in the front view represent the edges of the holes since they are not visible from the front.
FIG. 2.22 Pictorial view
FIG. 2.23 Orthographic views
In the side view too, the holes will be represented by hidden lines although the view is necessary for this particular object.
FIG. 2.24 Object with holes of various shapes
In order to have a better understanding of projection drawing, a few problems are worked out below (Fig. 2.25). In each case, pictorial views of objects are shown along with the orthographic projection views.
Readers are advised to go through the solutions. The following sequential steps should be followed while constructing an orthographic view of an object.
|Step I||View selection Choose the view to be projected and drawn as the front view. Also choose the corresponding top view and, if essential, side views to be drawn.|
|Step II||Selection of scale Find the overall dimensions of the views and select a suitable scale so that the views may be conveniently arranged on the drawing sheet.|
|Step III||Layout of the views Draw rectangles on the sheet for the views to be drawn and arrange them in proper places as per the angle of projection, allowing sufficient space between them and at prescribed distances from the border of the sheet.|
|Step IV||Alignment and symmetry To align the views symmetrically, draw center lines in all the views. Remember to draw only one center line to represent the axis of any cylindrical object or hole when seen as a rectangle. However, when the hole is seen as a circle, draw two orthogonal intersecting center lines at its center. In case of an AutoCAD drawing, it may sometimes be essential to draw a few geometric lines to determine the correct position of some parts of the object. The lines should be drawn in this step also.|
|Step V||Construction of details and visibility Draw the details following the sequence given below.
While drawing the main outline or the minor details of one particular view, the feature of the object visible in that view and the feature that is not, needs to be kept in mind. Draw the lines and curves representing them as continuous or hidden lines accordingly.
OTHER TYPES OF PROJECTIONS
It is possible to represent any complex object by means of an orthographic projection. However, the short-coming of this type of representation is that a knowledge of the principles of orthographic projection is required to interpret the drawing.
To overcome this difficulty, a pictorial representation of an object is extensively used to convey the idea to a person who lacks technical knowledge. These projections represent several faces of an object seen in one view, as they tend to appear to the eye. There are three common types of pictorial projections in use, namely (i) axonometric, (ii) oblique, and (iii) perspective projections. Axonometric projection can be further classified into three types—isometric, dimetric, and trimetric. Isometric is the one that is most popular and widely used in engineering practices. We have already discussed perspective projection at the begining of this chapter. Now, we shall give a very brief overview of the isometric and oblique projections.
PRINCIPLES OF ISOMETRIC PROJECTION
In an isometric projection, the observer is supposed to be situated at infinity and hence the visual rays, or projectors, become parallel to one another. The plane of projection should be perpendicular to the projectors. In order to obtain an isometric projection, the object is assumed to be placed in such a manner that the principal axes or edges make equal angles with the plane of projection and their length is shortened in equal proportions. In other words, these edges would be projected equally and make equal angles of 120° with each other as can be seen from the isometric drawing of a cube with a hole shown in Fig. 2.26a.
Isometric projection has some characteristics that are listed below.
- All lines that are parallel on the object remain parallel on the isometric projection.
- Vertical lines on the object become vertical in the isometric projection.
- Horizontal lines on the object are drawn at an angle of 30° or 150° with the horizontal.
- The projected lengths of the object along the isometric axes are approximately 82 per cent of their true lengths.
- The rectangles in orthographic views become parallelograms. Similarly, circles become ellipses.
- Hidden lines are generally not shown.
FIG. 2.26 Isometric and other types of projections
In this projection, the view is generated by using projections that are parallel to one another but oblique to the plane of projection. The front face of the object is displayed in its true shape and size as it is placed parallel to the picture plane. The receding lines representing the other two sides are usually drawn at an angle of 45° to the horizontal plane. Fig. 2.26b shows the same cube in an oblique projection, showing its relation with orthographic projection.
There are mainly two types of oblique projection—cabinet and cavalier (Fig. 2.26c). The difference between them is in the length of the reduced lines.
FIG. 2.26c Oblique projection
- Explain clearly the difference between first angle and third angle projection method.
- Why are second and fourth angle projection not used in practice?
- What symbols are used to represent first and third angle projection drawing?
- Why is orthographic projection necessary to define an object properly?
- Differentiate clearly between pictorial projection and orthographic projection.
- Examine the drawings shown in Fig. 2.27 and Fig. 2.28. Add the lines missing on the views. Use sketches if necessary.
- Figs. 2.29 and 2.30 contain a number of pictorial views of objects of various shapes. Draw the orthographic views (three views) of the objects in freehand.