Textbook of Engineering Drawing, Second Edition

4.44 Textbook of Enginnering Drawing------------------

Through Q erect vertical such that ppi ::;:: double ordinate::;:: 90mm ::;:: 2PQ.

2. Construct the rectangle ppi RIR. Divide PR and PIRI into any number of equal parts (say 4)
   as 1,2,3, and Jl2^1 31 starting from P on PR and pi on pi RI respectively. Join Bl, B2, B3,
   BJI, B21 and B3^1.


3. Divide the ordinates PQ and QPI into the same number of equal !larts as II 21 31 and III 211
   311 starting from P on PQ and pi on PIQ respectively.


4. Join OIl to meet Bl at PI' Join 021 and 03) to meet B2 and B3 at P 2 and P 3 respectively,
   Similarly join 01\ 02\ and 03\ to meet B JI B21 B3^1 at P\ pI 2 pI3 respectively.


5. Join P, PI ' P 2 ' P 3 ' B, pI3 ' pI 2 ' P\ and pi by a smooth hyperbola.

Problem: Construct a rectangular hyperbola when a point P on it is at a distance 000 mm and
40 mm resepctively from the two asymptotes.

Solution: (Fig.4.64)

3 2

o ~~==--~f-------l Q

Fig. 4.63

}' ,

1. For a rectangular hyperbola, angle between the asymptotes is 90°. So, draw ORI and O~
   such that the angle RIOR 2 is 90°.


2. Mark A and B along O~ and ORI respectively such that OA ::;:: 40 mm and OB ::;:: 30 mm.
   From A draw AX parallel to ORI and from B draw BY parallel to O~. Both intersect at P.


3. Along BP mark 1, 2, and 3 at approximately equal intervals. Join 01, 02, and 03, and
   extend them to meet AX at 11 ,2 1 and 31 respectively.


4. From II draw a line parallel to O~ and from 1 draw a line parallel to ORI. From 2 and 3
   draw lines parallel to ORI. They intersect at P 2 and P3 respectively.

5. Then along PAmark points 41 and 51 at approximately equal inervals. Join 041 and 051 and

extend them to meet BY at 4 and 5 respectively.