651
OF ENGINEERING FORM ULÆ.
Curves—continued.
Conchoid Curve.
From the point P on the straight line P A lay off P B = b
— the distance of the generating point from the asymptote C1 >
which is at right angles to P A ; also lay off B A = a = axis
of the conchoid. Draw from P any radiating lines cutting
the asymptote at F F F, and on these lines produced lay off F E,
F E, &c., = a; these distances will give points in a “jti st ”
conchoid (or a conchoid on that side of the asymptote which
is opposite to the generating point P).
I or a second conchoid (or one formed on the same side as
the generating point) the distances F G, F G, &c. = a are laid
off towards P ; if 6 is less than a the curve will have a node
at the centre, if b = a it will have a cusp at the centre. The
left-hand curve is drawn with p as the generating point;
b being less than a.
y — aib- + 2ai bx + a"x$, for a first conchoid.
= — 2 a* b x + afx'i, for a second conchoid.
MODE QF TRACING A CONCHOID CURVE.
PIN OH TRACING LATH f
RAGINS POINT G
rtxeo pin P
For a first conchoid the tracing point must be in th'1 pro-
longation of the latji above the straight-edge.