Mechanical Drawing Self-Taught / Comprising instructions in the selection and preparation of drawing instruments, elementary instruction in practical mechanical drawing; together with examples in simple geometry and elementary mechanism, including screw threads, gear wheels, mechanical motions, engines and boilers

by Joshua Rose

Fig. 80.

Fig. 81.

A very near approach to the true form of a true ellipse may be drawn by the construction given in Figure 81, in which A A and B B are centre lines passing through the major and minor axis of the ellipse, of which a is the axis or centre, b c is the major axis, and a e half the minor axis. Draw the rectangle b f g c, and then the diagonal line b e; at a right angle to b e draw line f h, cutting B B at i. With radius a e and from a as a centre draw the dotted arc e j, giving the point j on line B B. From centre k, which is on the line B B and central between b and j, draw the semicircle b m j, cutting A A at l. Draw the radius of the semicircle b m j, cutting it at m, and cutting f g at n. With the radius m n mark on A A at and from a as a centre the point o. With radius h o and from centre h draw the arc p o q. With radius a l and from b and c as centres, draw arcs cutting p o q at the points p q. Draw the lines h p r and h q s and also the lines p i t and q v w. From h as a centre draw that part of the ellipse lying between r and s, with radius p r; from p as a centre draw that part of the ellipse lying between r and t, with radius q s, and from q as a centre draw the ellipse from s to w, with radius i t; and from i as a centre draw the ellipse from t to b and with radius v w, and from v as a centre draw the ellipse from w to c, and one-half of the ellipse will be drawn. It will be seen that the whole construction has been performed to find the centres h, p, q, i and v, and that while v and i may be used to carry the curve around on the other side of the ellipse, new centres must be provided for h p and q, these new centres corresponding in position to h p q. Divesting the drawing of all the lines except those determining its dimensions and the centres from which the ellipse is struck, we have in Figure 82 the same ellipse drawn half as large. The centres v, p, q, h correspond to the same centres in Figure 81, while v', p', q', h' are in corresponding positions to draw in the other half of the ellipse. The length of curve drawn from each centre is denoted by the dotted lines radiating from that centre; thus, from h the part from r to s is drawn; from h' that part from r' to s'. At the ends the respective centres v are used for the parts from w to w' and from t to t' respectively.

Fig. 82.