Engineering Drawing & Design Lab

18B15GE111

Experiment No. 04

Orthographic Projection of Straight line

 Contents
Sl. Topic Slide No.
i Introduction 03
ii Line Parallel to one or both the planes. 04
iii Line Contained by one or both the planes 05
iv Line Perpendicular to one of the planes. 06
v Line Inclined to VP and parallel to HP 07
vi Line Inclined to HP and parallel to VP 08
vii Line Inclined to both the planes. 09
viii Line contained by a plane perpendicular to both the reference planes 11
ix Traces of a Line 12
x Assignment Problems 15
xi References 16
 Introduction
A straight line is the shortest distance between two points. Hence, the projections of a straight line may be drawn
by joining the respective projections of its ends which are points.

The position of a straight line may also be described with respect to the two reference planes :
1. Parallel to one or both the planes.
2. Contained by one or both the planes.
3. Perpendicular to one of the planes.
4. Inclined to one plane and parallel to the other.
5. Inclined to both the planes.
6. Line contained by a plane perpendicular to both the reference planes.
 Line Parallel to one or both the planes

Line AB is parallel to the H.P. Points a and b are the top

views of the ends A and B respectively. It can be clearly seen
that the figure ABba is a rectangle. Hence, the top view ab is
equal to AB. a'b' is the front view of AB and is parallel to xy.

Line CD is parallel to the V.P. The line c'd' is the front view
and is equal to CD; the top view cd is parallel to xy.

Line EF is parallel to the H.P. and the V.P. Line ef is the

top view and e'f' is the front view; both are equal to EF and
parallel to xy.
 Line Contained by one or both the planes

Line AB is in the H.P. Its top view ab is equal to AB; its

front view a' b' is in xy.

Line CD is in the V.P. Its front view c'd' is equal to CD;

its top view cd is in xy.

Line EF is in both the planes. Its front view e' f' and the
top view ef coincide with each other in xy.

when a line is contained by a plane, its projection on that

plane is equal to its true length; while its projection on the
other plane is in the reference line.
 Line Perpendicular to one of the planes.

Line AB is perpendicular to the H.P. The top views

of its ends coincide in the point a. Hence, the top view
of the line AB is the point a. Its front view a' b' is
equal to AB and perpendicular to xy.

Line CD is perpendicular to the V.P. The point d' is

its front view and the line cd is the top view. cd is
equal to CD and perpendicular to xy.

when a line is perpendicular to a plane its projection

on that plane is a point; while its projection on the
other plane is a line equal to its true length and
perpendicular to the reference line.
 Line Inclined to VP plane and parallel to HP
Line RS1 is inclined at an angle Ø to the V.P. and
is parallel to the H.P. Assuming the line to be
parallel to both the H.P. and the V.P., its projections
r's' and rs are drawn parallel to xy and equal to its
true length. When the line is turned about its end R
to the position RS1 so that it makes the angle Ø with
the V.P. while remaining parallel to the H.P., in the
top view the point s will move along an arc drawn
with r as center and rs as radius to a point s1 so that
rs1 makes the angle Ø with xy. In the front view, the
point s' will move towards r' along the line r's'1 to a
point s'1on the projector through s1.
Line rs and r's' are the projections of the line
RS.
 Line Inclined to HP and parallel to VP
Line PQ1 is inclined at an angle Ɵ to the H.P. and is
parallel to the V.P. The projections may be drawn by
first assuming the line to be parallel to both the H.P. and
the V.P. Its front view p'q' and the top view pq will both
be parallel to xy and equal to the true length. When the
line is turned about the end P to the position PQ1 so that
it makes the angle Ɵ with the H.P. while remaining
parallel to the V.P., in the front view the point q' will
move along an arc drawn with p' as centre and p'q' as
radius to a point q'1 so that p'q'1 makes the angle Ɵ with
xy. In the top view, q will move towards p along pq to a
point q1 on the projector through q'1.
Line p'q'1 and pq1 are the front view and the top
view respectively of the line PQ.
 Line Inclined to both the planes.
Line AB, its inclinations Ɵ with the H.P. and Ø with the V.P. and the position of one end A.
Steps to be followed:
(1) Draw the projection of line AB assuming it to be parallel to the V.P. and inclined at Ɵ to the H.P. (Fig. i)
(2) Again draw the projection of line AB assuming it to be parallel to the H.P. and inclined at Ø to the V.P. (Fig. ii)
 Line Inclined to both the planes.

(3) Final Projection of line AB

having inclinations Ɵ with the
H.P. and Ø with the V.P.
obtained with both the steps (1)
and (2) combined in one
diagram as shown in Fig. (iii)

Terms to be introduced:
• True length
• True Inclination
• Apparent Length
(iii)
• Apparent Inclination
Line contained by a plane perpendicular to both the reference planes.

Line EF, is inclined at Ɵ to the H.P. and at Ø to the

V.P. The line is thus contained by the profile plane
marked P.P.

The front view e'f' and the top view ef are both
perpendicular to xy and shorter than EF. Therefore,
when a line is inclined to both the reference planes
and contained by a plane perpendicular to them, i.e.
when the sum of its inclinations with the H.P. and the
V.P. is 90°, its projections are perpendicular to xy and
shorter than the true length.
 Traces of a Line
When a line is inclined to a plane, it will meet that plane,
produced if necessary. The point in which the line or
line-produced meets the plane is called its trace.
The point of intersection of the line with the H.P. is called
the horizontal trace, usually denoted as H.T. and that with the
V.P. is called the vertical trace or V.T.

when a line is parallel to reference plane:

i. A line AB is parallel to the H.P. and the V.P. It has no trace.
ii. A line CD is inclined to the H.P. and parallel to the V.P. It
has only the H.T. but no V.T.
iii. A line EF is inclined to the V.P. and parallel to the H.P. It
has only the V.T. but no H.T.
 Traces of a Line

When a line is perpendicular to reference plane:

i. Line PQ is perpendicular to the H.P. Its H.T.
coincides with its top view which is a point. It has no
V.T.

ii. Line RS is perpendicular to the V.P. Its V.T.

coincides with its front view which is a point. It has
no H.T.
 Traces of a Line
When a line has an end in reference plane:
i. Line AB has its end A in the H.P. and the end B in the V.P. Its H.T. coincides with a the top view of A and the
V.T. coincides with b' the front view of B.

ii. Line CD has its end C in both the H.P. and the V.P. Its H.T. and V.T. coincide with c and c' in xy.
 Assignment Problems

Problem 1. A 80 mm long line AB has end A at a distance of 20 mm above the H.P. and 40 mm in front of
the V.P. The line is inclined at 30° to the V.P. and parallel to the H.P. Draw its projections and also
represent its traces.

Problem 2. The length of the top view of a line parallel to the V.P. and inclined at 40⁰ to the H.P. is 50
mm. One end of the line is 25 mm above the H.P. and 35 mm in front of the V.P. Draw its projections,
locate its traces and also determine its true length.

Problem 3. The front view of a 75 mm long line measures 55 mm. The line is parallel to H.P. and one of
its ends is in the V.P. and 35 mm above the H.P. Draw the projections of the line and determine its
inclination with the V.P.

Problem 4. Line AB of 50 mm length and its inclination with VP and HP are 30° and 45° respectively.
End A of the line is 25 mm above HP and 55 mm in front of VP. Draw the orthographic projection of this
line and also find the H.T. and V.T. of the same.
 References

[1] Bhatt N.D., Panchal V.M. & Ingle P.R., Engineering Drawing, Charotar Publishing House, 2014.

[2] Shah, M.B. & Rana B.C., Engineering Drawing and Computer Graphics, Pearson Education, 2008.