It is the shortest joining of two end points. In this article, the projections of lines with reference to the different planes are explained. They are when
(A) the line is parallel to one or both the planes.
(B) the line contained by one or both the planes.
(C). The line perpendicular to one plane.
(D) the line inclined to one plane and parallel to another plane and
(E) Line inclined to both the planes.
(A) WHEN THE LINE IS PARALLEL TO ONE OR BOTH THE PLANES.
Q.Draw the projections of a line 60 mm length when it is parallel to both V.P and H.P at a distance of 25 mm and when the line is in the (a) first quadrant (b) third quadrant.
(a) When one line is in the firat quadrant.
Fig. (a) shows the line AB at the distance of 25 mm from each plane of the first quadrant. Fig. (b) is drawn so that a’ – b’ indicates the front view (FV) of the line AB and a – b indicates the top view (T.V) each of which are at the distances of 25 mm from x – y line and parallel to x – y line as this x – y lies on both the V.P and H.P.
NOTE: It is to be noted that the true lengths of lines are visible fully when they are drawn parallel to the concerned planes.
(b) WHEN THE LINE IS IN THIRD QUADRANT.
The views drawn are the same as drawn in the first quadrant from x – y line. But front view (FV) and top view (T.V) are observed opposite to the Fig (b). Th due to the H.P is over the V.P and hence the concerned views.
B) WHEN THE LINE CONTAINED BY ONE or BOTH THE PLANES.
Q. Draw the projection of a line 50 mm in length lying on H.P and parallel to V.Pat a distance of 30 mm when (a) the line is lying in the first quadrant (b) the line is lying in the third quadrant.
SOLUTION:
(a) When the line is lying in the first quadrant :
The line is shown in Fig. (a) such that it is lying at a distance of 30 mm from V.P and also parallel to it. The concerned views are drawn as in Fig. (b).
b) When the line is lying in the third quadrant.
NOTE: As per the SP-46-1998, Bureau of Indian Standards, the projections are considered to be drawn in the first angle method. Hence the projections in the remaining positions are drawn in 1st angle method only.
(C) INCLINED TO ONE PLANE AND PARALLEL TO ANOTHER PLANE
Q.A line AB of length 80 mm is lying on H.P. The end A is 20 mm and end Bis 60 mm from V.P respectively. Draw the front view and to p view of this line.
Solution:
Steps:
(1) Consider any point “a” at a distance of 20 mm from x-y line (ie., from VP)
(ii) Draw a trace line t-t from “b” which is 60 mm from V.P and parallel to it.
(iii) “a” as centre and 80 mm as radius cut the trace line t-t drawn through “b”.
(iv) Now join “a” to “b” which is the T.V and is equal to the true length of 80 mm of the line
(v) Project “a” and “b” on the x-y line to obtain a’ b’ which is known as front view (EV) of the straight line AB as shown in Fig. 6.13 (b).
(D) LINE PERPENDICULAR TO ONE OF THE PLANES
Q.Draw the projections of a line “PQ” of length 70 mm which is perpendicular to H.Pand parallel to V.Pat a distance of 30 mm. The end P is at a distances of 20 mm from H.P.
Solution:
E) LINE INCLINED TO ONE PLANE
Q.Aline All of length 80 mm is parallel to V.Pat a distance of 30 mm. The end A is 25 mm and B is 75 mm above H. Prespectively draw ita front view (elevation) and plan (top view) and find the angle of the line in the H.P.
SOLUTION:
Steps:
(1) Consider any point d’ at a distance of 25 mm from x-y line.
(II) Trace a line t-t through b which is at a distance of 75 mm from x-y line.
(iii) With a radius of 80 mm and a’ as the centre cut the trace t-t at b’.
(iv) Join a’ b’ which indicates FV.
(v) Project the points a’ and b’ into the H.P.
(vi) Draw a parallel line at a distance of 30 mm from x-y on H.P which intersects at a-b and this indicates T.V.
(vill) Measure the angle “0”.
F) LINE INCLINED TO BOTH THE PLANES
Q.Draw the projections of a line AB 75 mm in length and making 30° V.P and 45° to H.P. The end A is 20 mm from V.P and 30 mm from H.P.
SOLUTION
Steps
(1) Assume that the line is parallel to V.P and making 45° to H.P.
(it) Draw the views a’ – b’ and a-b the front view F*V_{1} and top view (T*V_{1}) respectively as shown in Fig. (a).
(i) Draw the locus through b’. t_{1} – t_{1}
(iv) Also assume that the line is parallel to H.P and making an angle of 30° to V.P. Therefore draw the views Le., a_{1} – b_{1} (T, V_{2}) and a_{1}’ bi (F, V_{2}) the top view and front view respectively.
(v) Draw the locus t_{2} – t_{2} through b_{1}
(vi) a b (The top view T*V_{1} of Fig. (a)) as radius and a_{1} (in Fig. (b)) as the centre cut the path of the trace t_{2} – t_{2} at b_{2} Join a_{1} to b₂ to obtain final top views a_{2} – b_{2}
(vii) a_{1}’ – b_{1}’ ( F*V_{2} of Fig (b)) as radius and a_{1} as centre cut the path traced through b’ to obtain final front view a_{2}’ – b_{2}’ (t_{1} – t_{1})
(viii) It is to be noted that the projection line joined from b_{2} to b_{2}’ should be parallel to the other projected lines.
(ix) Otherwise, combined views can also be drawn as shown in Fig. (c) without the Fig. (a) and (b).
