126
THE THEORY OF SCREWS.
[136-
equal and opposite twist velocities on the common instantaneous screw.
The body would then not move, and therefore the two impulsive wrenches
must equilibrate. But this is impossible, if they are on two different
screws.
137 Two Homographic Systems.
From what has been shown it might be expected that the points corre-
sponding to the instantaneous screws and those corresponding to the
impulsive screws should, on the representative circle, form two homographic
systems. That this is so we shall now prove.
Let A, B (fig. 20) be a pair of impulsive screws, and let A', B' be respec-
tively the corresponding pair of instantaneous screws, i.e. an impulsive
wrench on A will make the body commence to twist about A', and similarly
for B and B1. Let an impulsive wrench on A, of unit intensity, generate a
twist velocity, d, about A', and let ß be the similar quantity for B and B’.
Let X be any other screw on which an impulsive wrench is to be applied
to the body supposed quiescent. The body will commence to twist about
some other screw, X', with a certain twist velocity 6>. We can determine
ö> in the following mannerThe unit impulsive wrench on X can be
replaced by two component wrenches on A and B, the intensities of these
being
BX AX
AB' AB’
respectively.
These impulsive wrenches will generate about A', B' twist velocities
respectively equal to
BX A AX
aAB’ 13 AH'