155
Substituting fl = f111, 21 = hlfSl1, w2 = "212 and
Y2 = h2w232 into Eq. (5.13), the virtual work produced by
the wrench can thus be expressed as
U = flw2 {(h1 + h2)cosal2 al2sinal2} (5.14)
If the pitches hI and h2, the twist angle l12, and mutual
perpendicular distance a12 between the axes S1 and S2 of the
two screws are chosen such that
(h1 + h2)cosal2 al2sinal2 = 0 (5.15)
then the wrench cannot produce motion on the screw $2 no
matter how large is the intensity f1. The screws $1 and 12
are then said to be reciprocal. It is noted that Eq. (5.15)
is symmetrical, and a wrench on the screw $2 cannot produce
motion on the screw $1.
Hunt [49] shows that, when the line of action of a
force passes through an axis of an revolute pair, the force
does not affect the rotation around the revolute pair
because it cannot exert any moment about it. Reciprocity
between a force F and an angular velocity u about an
revolute pair axis means that when a body is attached to a
base through a single revolute pair about which it can turn
at an angular velocity c at any instant, a force F is
reciprocal to when its contribution to the rate of working
is zero. For the prismatic pair, when the line of action of