Problem 4.4 :

Projection of Straight Lines – The top view and the front view of the line EF, measures 60 mm and 50 mm respectively. The line is inclined to HP and VP by 300 and 450, respectively. The end E is on the HP and 10 mm in front of VP. Other end F is in the 1st quadrant. Draw the projections of the line EF and find its true length.

Procedure:

Step-1 Draw a horizontal line, which is x-y line of some suitable length.

Step-2 Mark a point e’ on the x-y line.

Step-3 From the point e’, draw a vertical line in upward direction, which is perpendicular with the x-y line and at the distance 60 mm from the point e’.

Step-4 Draw a line from the point e’ in upward direction in such a way that it will intersect the previously drawn vertical line, at an angle 30° ( represented by the letter θ) with the x-y line, and give the name of that point of intersection f ’1.

Step-5 Find the length of the line e’-f ’1, which is the true length of the line EF, it is equal to 70 mm.

Step-6 From the point f ’1, draw a horizontal line parallel with the x-y line.

Step-7 Draw a horizontal line which is parallel, below & at the distance 10 mm from the line x-y.

Step-8 From the point e’ draw a vertical line on the previously drawn horizontal line. And give the name of that point e as shown into the figure.

Step-9 From the point e, draw a vertical line in downward direction, which is perpendicular with the x-y line and at the distance 50 mm from the point e.

Step-10 Draw a line from the point e in downward direction in such a way that it will intersect the previously drawn vertical line, at an angle 45° ( represented by the letter Φ) with the x-y line, and give the name of that point of intersection f 2.

Step-11 Find the length of the line e-f 2, which is the true length of the line EF, & it is equal to 70 mm.

Step-12 From the point f 2, draw a horizontal line parallel with the x-y line.

Step-13 From the point f2 draw a vertical line up to the x-y line in upward direction and perpendicular to the line x-y. Now make an arc with the point e’ as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the x-y line, which will cut the horizontal line passing through the point f’1. And give the name of that point f ’.

Step-14 Now draw a line between the points e’ & f ’, which is the elevation of the line EF. Find its inclination with the x-y line, which is represented by the letter α.

Step-15 From the point f ’1 draw a vertical line up to the line passing through the point e, in downward direction and perpendicular to the line x-y. Now make an arc with the point e as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the line passing through the point e, which will cut the horizontal line passing through the point f2. And give the name of that point f.

Step-16 Now draw a line between the points e & f, which is the plan of the line EF. Find its inclination with the x-y line, which is represented by the letter β.

Step-17 Give the dimensions by any one method of dimensions and give the notations as shown into the figure. And make a list of the True Length & Angles made by the line EF as shown into the figure.