UNIT 2
Projections of Points and Lines
First angle projection:
We have assumed the object to be situated in front of the V.P. And above the H.P. i.e. in the first quadrant and then projected it on these planes. This method of projection is known as first-angle projection method. The object lies between the observer and the plane of projection. In this method, when the views are drawn in their relative positions, the top view comes below the front view. In other words, the view seen from above is placed on the other side of (i.e. below) the front view. Each projection shows the view of that surface (of the object) which is remote from the plane on which it is projected, and which is nearest to the observer.
Third angle projection:
In this method of projection, the object is assumed to be situated in the third quadrant [fig. 11(a)]. The planes of projection are assumed to be transparent. They lie between the object and the observer. When the observer views the object from the front, the rays of sight intersect the V.P. The figure formed by joining the points of intersection in correct sequence is the front view of the object. The top view is obtained in a similar manner by looking from above. When the two planes are brought in line with each other, the views will be shown in fig.11 (b). The top view in this case comes above the front view.
(a) A line AB (fig. 1) is inclined at θ to the H.P. And is parallel to the V.P.The end A is in the H.P. AB is shown as the hypotenuse of a right-angledtriangle, making the angle θ with the base.
Figure 1
The top view ab is shorter than AB and parallel to xy. The front view a'b'is equal to AB and makes the angle θ with xy.
Keeping the end, A fixed and the angle θ with the H.P. Constant, if theend B is moved to any position, say B1, the line becomes inclined to theV.P. Also.
In the top view, b will move along an arc, drawn with a as centre andab as radius, to a position b1. The new top view ab1 is equal to ab butshorter than AB.
In the front view, b' will move to a point b'1 keeping its distance from xyconstant and equal to b'o; i.e. it will move along the line pq, drawnthrough b' and parallel to xy. This line pq is the locus or path of the end8 in the front view. b'1 will lie on the projector through b1. The new frontview a'b'1 is shorter than a'b' (i.e. AB) and makes an angle a with xy. A is greater than θ.
Thus, as long as the inclination 0 of AB with the H.P.is constant, even when it is inclined to the V.P.
(i) its length in the top view, viz. Ab remains constant; and
(ii) the distance between the paths of its ends in the front view,viz. b'o remains constant.
(b) The same line AB (fig. 2) is inclined at 0 to the V.P. And is parallelto the H.P. Its end A is in the V.P. AB is shown as the hypotenuse of aright-angled triangle making the angle φ with the base.
Figure 2
The front view a'b'2 is shorter than AB and parallel to xy. The top viewab2 is equal to AB and makes an angle 0 with xy.
Keeping the end A fixed and the angle 0 with the V.P. Constant, if B ismoved to any position, say B3, the line will become inclined to the H.P. Also.
In the front view, b'2, will move along the arc, drawn with a' as centreand a'b'2 as radius, to a position b' 3. The new front view a'b'3 is equal toa'b'2 but is shorter than AB.
In the top view, b2 will move to a point b3 along the line rs, drawnthrough b2 and parallel to xy, thus keeping its distance from the path ofa, viz. b2o constant. Rs is the locus or path of the end B in the top view.The point b3 lies on the projector through b'3. The new top view ab3 isshorter than ab2 (i.e. AB) and makes an angle β with xy. β is greater than φ.
Here also we find that, as long as the inclination of AB with the V.P.does not change, even when it becomes inclined to the H.P.
(i) its length in the front view, viz. a'b'2 remains constant; and
(ii) the distance between the paths of its ends in the top view, viz.b2o remains constant.
Hence, when a line is inclined to both the planes, its projections are shorterthan the true length and inclined to xy at angles greater than the true inclinations.These angles viz. α and β are called apparent angles of inclination.
