Problem 4.3 :

Projection of Straight Lines – A line CD is 65 mm long, has its end point C 15 mm above HP and 10 mm in front of VP & end point D 45 mm above HP and 50 mm in front of VP. Determine true inclinations of the line CD with HP and VP.

Procedure:

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

Step-2 Draw two horizontal lines at the distance 15 mm & 45 mm respectively above & parallel with the x-y line. And draw another two horizontal lines at the distance 10 mm & 50 mm respectively below & parallel with the x-y line.

Step-3 On the line, which is at the distance 15 mm above & parallel with the x-y line, mark a point c’. With this point c’ as center make an arc with radius equal to 65 mm, which will cut the line at the distance 45 mm above & parallel with the x-y line. And give the name of that point d’1 as shown into the figure.

Step-4 Now draw a line connecting the points c’ & d’1, which is represented by the letter θ. And find its inclination with the x-y line.

Step-5 From the point c’, draw a vertical line in downward direction up to the line which is at the distance 10 mm below & parallel with the x-y line. And give the name of the point c as shown into the figure.

Step-6 With this point c as center make an arc with radius equal to 65 mm, which will cut the line at the distance 50 mm below & parallel with the x-y line. And give the name of that point d2 as shown into the figure.

Step-7 Now draw a line connecting the points c & d2, which is represented by the letter Φ. And find its inclination with the x-y line.

Step-8 From the point d2 draw a vertical line up to the line which is passing through the point c’ & parallel with the line x-y, in upward direction and perpendicular to that line. Now make an arc with the point c’ as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the line which is passing through the point c’, which will cut the horizontal line passing through the point d’1. And give the name of that point d’.

Step-9 Now draw a line between the points c’ & d’, which is the elevation of the line CD. Find its inclination with the x-y line, which is represented by the letter α.

Step-10 From the point d’1 draw a vertical line up to the line which is passing through the point c & parallel with the line x-y, in downward direction and perpendicular to that line. Now make an arc with the point c’ as center and radius equal to the distance of the point of intersection of the previously drawn vertical line with the line which is passing through the point c, which will cut the horizontal line passing through the point d2. And give the name of that point d.

Step-11 Now draw a line between the points c & d, which is the plan of the line CD. Find its inclination with the x-y line, which is represented by the letter β.

Step-12 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 CD as shown into the figure.