ENGN103 Engineering Drawing Lecture 3

SCALE When the object is bigger than the size of drawing sheet, it is drawn at reduced scale. Therefore, scale is the ration of actual object and the size shown on the drawing. The scales are designated as: SCALE 1: X for reduced scale (X is the ratio) SCALE X:1 for enlarged scale SCALE 1:1 for full size Standard recommended ratios are multiples of 2, 5 and 10 as: Enlargement: 50:1, 20:1, 10:1, 5:1, 2:1 Reduction: 1:2, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000, 1:2000, 1:5000

Geometrical Construction To bisect a line To divide a line into a number of equal parts To divide a line in a given proportion To bisect an angle To find the center of an arc To inscribe a circle in a triangle. To draw the circumscribing circle of a triangle.

To bisect a line Draw the given line AB, with centers A and B and radius R greater than half of AB, draw arcs to intersect a t C and D. Join CD, when E will be the mid point of the line. Also CD will be perpendicular to AB

To divide a line into a number of equal parts From one end of the given line (say A), draw AC at any convenient angle. Using dividers or a scale, mark off from A on AC the required number of equal parts, making them of any suitable length. Join the last point to B on the given line, and through the other points draw parallels to this line to cut the given line. This construction makes use of the properties of similar triangles.

To divide a line in a given proportion Suppose the proportion to be 2 : 3. using the previous construction, proceed as if to divide the line into 5 parts (2 plus 3) but only draw a line through point 2 on AD. Then AB will be divided in the required proportion.

To bisect an angle Draw the given angle ABC and from the apex B draw an arc of radius R to cut AB and CD at D and E. R may be any convenient radius. With D and E as centers and radius R’, draw two arcs to meet F. Again, R’ may be any convenient radius. Join FB to bisect the angle.

To find the center of an arc Select three points, A, B and C on the arc and join AB and BC. Bisect these lines and produce the bisectors to meet at O. O is the center of the arc.

To inscribe a circle in a triangle. Draw the given triangle ABC and bisect an two angles. Produce the bisectors to intersect at O, which is the center of the inscribe circle.

To draw the circumscribing circle of a triangle. Draw the given triangle ABC. Bisect any two of the sides and produce the bisectors to intersect at O. O is the center of the circumscribing circle.