56
THE THEORY OF SCREWS. £62,
at B C, their centre of gravity must lie on the three lines AX BY CZ
Ihese lines must therefore be concurrent at I, which is the centre of gravity
of the three masses. 5 J
is the centre of gravity
Let BY intersect the circle again at H. Then, since AC is the polar of
7<’ B H bt 1 -8; »«»equenlly lhe four
ie B J BC.
*•thc of
Suppose the axis of pitch to be drawn (it is not shown in the figure) and
let h be the perpendicular let fall from Z on this axis, also let P1 p p be the
pitches of the screws A, B, C. P P P
Then, by a familiar property of the centre of gravity, we must have
A«2 + pJ>* - pp2 = (a2 + b2 - c2) h = 2abh cos C.
We shall take 4, B as the two screws of reference, and if P1 and p„ be the co
ordinates of C W1th respect to A and B - then, from the principles of screw
co-ordinates (§ 30), we have P 1
Pi = pipi2 + p2p22 + 2CT12p1P3)
where „„ is the virtual coefficient of A and B. In the present case we have
a b
Pl=~', P-2 = ~',
c r c
whence
and, finally,
Pi a? + p,b2- p3c2 + 2®-12 «6 = 0;
w13 = — hcosC.