136
THE THEORY OF SCREWS.
[146-
The chord joining any impulsive screw A to the corresponding instantaneous
screw A' envelops a conic, and the point of contact, I, divides the chord into
segments, so that the ratio of AI to A'I is proportional to the square of the
twist velocity acquired about A' by the unit impulsive wrench on A.
147. Constrained Motion.
We can now give another demonstration of the theorem in § 90, which is
thus stated:—
If a body, constrained to twist about the screw a, be acted upon by an
impulsive wrench on the screw r/, then the twist velocity acquired varies as
w«2 ’
The numerator in this expression is the virtual coefficient of the two
screws, and the denominator is the function of § 134, which is proportional
to the kinetic energy of the body when twisting about a with the unit of
twist velocity.
Let a and p be represented by A' and I respectively (Fig. 29), and let A
be the impulsive screw which would correspond to A’ if the body had been
free to twist about any screw whatever on the cylindroid defined by A and
A'. Let K be reciprocal to A’.
The impulsive wrench on I is decomposed into components on K and A.
The former is neutralized by the constraints; the latter has the intensity
KI
KA ’
whence the twist velocity co, acquired by A', is (§ 141) proportional to
KI HO’.
KA ’ HO ’