Problem 4.9 Projection of Straight Lines

Problem 4.9 Projection of Straight Lines – A line PQ contains a point O on it such that the ratio of the distance of the PO: OQ is 1:2. The end P is 20 mm above H.P. and it is in 1st quadrant. And the other end Q is in V.P. The point O is 35 mm above H.P. The line is inclined with the H.P. at an angle 30°. The elevation length of the line PQ is 70 mm. Draw the projections of the line PQ.

Procedure:

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

Step-2 Mark a point p’ at the distance 20 mm above the x-y line.And draw a horizontal line at the distance 35 mm above the x-y line.Then from the point p’ draw a line at an angle 30° with the x-y line such that it should intersect the previously drawn horizontal line at the distance 35 mm and mark that point as o’1.And measure the distance between p’ – o’1, which is 30 mm.The ratio of the points PO: OQ is 1:2.So  extend the line p’ – o’up to the distance 60 mm, hence the total length of the line p’-q’is 90 mm. This is true length of the line in front view and its inclination with the x-y  line is represented by the letter Ɵ.

Step-3 From the point q’1 draw a horizontal line parallel to x-y line. This is the locus of the point q’1. Now form the point p’ draw a line such that its length should be equal to 70 mm and it should intersect the line passing through the point q’1. Give the name of that point as q’. This is elevation of the line PQ. And its inclination with the x-y line is represented by the letter α.

Step-4 From the point q’, draw a downward projector up to the x-y line. And give that point name as q.

Step-5 Now qs’1 as center and p’ as radius draw an arc such that it should intersect with the horizontal line passing through the point q’1. And give the name of that point as p1’. From p1’ draw a vertical downward projector below the x-y line of some suitable length.

Step-6 From the previously marked point q, draw a line of length equal to 90 mm which should intersect with the vertical downward projector form the point  p1’. And give the name of that point as p2. It is true length of the line in top view. Its inclination with the x-y line is represented by the letter ø. And from the point p2 draw a horizontal line of suitable length. This is locus of the point p2.

Step-7 Now draw a downward projector form the point p’ up to the line which is locus of the point p2. And give the name of that point as q. Then draw a line between the point p & q. This is plan of the line PQ. Its inclination with the x-y line is represented by the letter β.

Step-8 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 PQ as shown into the figure.

Author: Vasim Machhar

An Engineering Drawing Geek. Working at Noble Group of Institutions, Junagadh as Head of Mechanical Engineering Department.