Unit - 2
Orthographic Projections and Projections of Points
If straight lines are drawn from various points on the contour of an object to meet a plane, the object is said to be projected on that plane. The figure formed by joining, in correct sequence, the points at which these lines meet the plane, is called the projection of the object. The lines from the object to the plane are called projectors.
Methods of Projection:
Following four methods of projection are commonly used,
1) Orthographic projection.
2) Isometric projection.
3) Oblique projection.
4) Perspective projection.
In the above methods 2, 3 and 4 represent the object by a pictorial view as eyes see it. In these methods of projection, a three-dimensional object is represented on a projection plane by one view only, while in the orthographic projection an object is represented by two or three views on the mutual perpendicular projection planes. Each projection view represents two dimensions of an object. For the complete description of the three-dimensional object at least two or three views are required.
Orthographic Projection:
Theory of orthographic projection:
Let us suppose that a transparent plane has been set up between an object and the station point of an observer's eye (Fig. 1). The intersection of this plane with the rays formed by lines of sight from the eye to all points of the object would give a picture that is practically the same as the image formed in the eye of the observer. This is perspective projection.
Figure Perspective projection. The rays of the projection converge at the station point from which the object is observed.
If the observer would then walk backward from the station point until he reached a theoretically infinite distance, the rays formed by lines of sight from his eye to the object would grow longer and finally become infinite in length, parallel to each other, and perpendicular to the picture plane. The image so formed on the picture plane is what is known as "orthographic projection." See Fig.
2.
Figure Orthographic projection.
Basically, orthographic projections could be defined as any single projection made by dropping perpendiculars to a plane. However, it has been accepted through long usage to mean the combination of two or more such views, hence the following definition has been put forward: 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. (The term "orthogonal" is sometimes used for this system of drawing.)
Orthographic views:
The rays from the picture plane to infinity may be discarded and the picture, or "view," thought of as being found by extending perpendiculars to the plane from all points of the object, as in Fig. 3. This picture, or projection on a frontal plane, shows the shape of the object when viewed from the front, but it does not tell the shape or distance from front to rear. Accordingly, more than one projection are required to describe the object.
Figure The frontal plane of projection. This produces the front view of the object.
In addition to the frontal plane, imagine another transparent plane placed horizontally above the object, as in Fig. 4. The projection on this plane, found by extending perpendiculars to it from the object, will give the appearance of the object as if viewed from directly above and will show the distance from front to rear.
Figure The frontal and horizontal planes of projections. Projection on the horizontal plane produces the top view of the object.
If this horizontal plane is now rotated into coincidence with the frontal plane, as in Fig., the two views of the object will be in the same plane, as if on a sheet of paper.
Figure The horizontal plane rotated into the same plane as the frontal plane.
Now imagine a third plane, perpendicular to the first two (Fig. 6). This plane is called a "profile plane," and a third view can be projected on it. This view shows the shape of the object when viewed from the side and the distance from bottom to top and front to rear.
Figure the three planes of projection: frontal, horizontal and profile. Each is perpendicular to other two.
The horizontal and profile planes are shown rotated into the same plane as the frontal plane (again thought of as the plane of the drawing paper) in Fig. 7. Thus, related in the same plane, they give correctly the three-dimensional shape of the object.
Figure The horizontal and profile planes rotated into the same plane as the frontal plane. This makes it possible to draw three views of the object.
In orthographic projection the picture planes are called "planes of projection"; and the perpendiculars, "projecting lines" or "projectors."
A point may be situated, in space, in any one of the four quadrants formed by the
Two principal planes of projection or may lie in any one or both. Its
Projections are obtained by extending projectors perpendicular to the planes.
A point is situated in the first quadrant:
The pictorial view [fig. 1 (i)] shows a point A situated above the H.P. And in front of the V.P., i.e. in the first quadrant. a' is its front view and the top view. After rotation of the plane, these projections will be shown in fig. 1 (ii).
The front view a' is above xy and the top view a below it. The line joining a' and a (which also is called a projector), intersects xy at right angles at a point o. It is quite evident from the pictorial view that a'o = Aa, i.e. the distance of the front view from xy = the distance of A from the H.P. Viz. h. Similarly, ao = Aa', i.e. the distance of the top view from xy = the distance of A from the V.P. Viz. d.
Figure 1
A point is situated in the second quadrant:
A point B (fig. 2) is above the H.P. And behind the V.P., i.e. in the second quadrant. b' is the front view and b the top view. When the planes are rotated, both the views are seen above xy. Note that b'o = Bb and bo = Bb'.
Figure 2
A point is situated in Third Quadrant
A point C (fig. 3) is below the H.P. And behind the Y.P., i.e. in the third quadrant. Its front view c' is below xy and the top view c above xy. Also, c'o = Cc and co = Cc'.
Figure 3
A point is situated in Fourth Quadrant
A point f (fig. 4) is below the H.P. And in front of the V.P., i.e. in the fourth quadrant. Both its projections are below xy, and e'o = Ee and eo = Ee'.
Figure 4
Reference/Text Books
1. N. D. Bhatt, Engineering Drawing, Charotar Publishing House, 46th Edition, 2003.
2. K. V. Nataraajan, A text book of Engineering Graphic, Dhanalakshmi Publishers, Chennai, 2006.
3. K. Venugopal and V. Prabhu Raja, Engineering Graphics, New Age International (P) Ltd, 2008.
4. Dhananjay A. Jolhe, Engineering Drawing with an Introduction to Autocad, McGraw Hill Education, 2017
