Introduction
There are a number of simple geometrical constructions with which a draughtsman or an engineer should be familiar, as these are essential in the preparation of engineering drawing figures. Though these geometrical constructions are generally studied in the lower classes, they are being discussed here because of their importance in engineering drawing.
Bisection of a Straight Line
(i) Draw a straight line AB.
(ii) With centre A and radius greater than half AB, draw arcs on either side of AB.
(iii) With centre B and same radius, draw arcs intersecting the above arcs at C and D.
(iv) Draw a line joining C and D to intersect the given line AB at E. The point E bisects the line AB and the line CD is called the perpendicular bisector of the line AB, as shown in Fig. 5.1.
Dividing a Line into Equal Parts
(a) Dividing a given straight line into a specified number of equal parts, say six:
There are two methods to divide a given line into equal number of parts.
Method I
(i) Draw the given line AB.
(ii) From A, draw another line AC at any acute angle with respect to line AB.
(iii) Open the compass to suitable distance and mark six equal divisions on line AC, as shown in Fig. 5.3, and mark them as 1'–6'.
(iv) Draw a line joining the mark 6’ and B.
(v) With the help of a mini-draughter, draw lines through 1', 2', 3', etc., parallel to 6’ B to meet the line AB at 1, 2, 3….. etc., respectively.
The points 1, 2, 3, etc., divide the line AB into six equal parts.
Method II
(i) Draw the given line AB.
(ii) Draw a line AC that makes an angle θ with the line AB.
(iii) Draw AC and BD parallel to each other. Lines AC and BD make the same angle θ to AB, at A and B, respectively.
(iv) Mark the required number of equal divisions (say six) of any suitable length on AC and BD.
(v) Join 1 1', 2 2', etc., which divides the line AB into six equal parts. See Fig. 5.4.
Review the options below to login to check your access.
Log in with your Cambridge Higher Education account to check access.
If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.