N) are the direction ratios of the line and (P, Q, R) are
the x, y and z components of the moment of the line about
the origin, then we can express the screw coordinates as
(S ; So) where
S = Li + Mi + Nk (5.11)
So = Pi + OQ + Rk (5.12)
and
L = x2 x
M = YZ Y
N = z2 1
P = ylN zM
Q = -x1N + zlL
R = x1M ylL
Figure 5.3 shows a rigid body which is constrained to
move on a screw 12 = (S2; o2). A wrench (fl; Ci) of
intensity fl is applied to the body on a screw 1, = (Sl;
Sol) and it produces a twist (22; Y2) of amplitude w2 on
the screw $2. Thus the moment of the force fi about the
point A is al2al2 x fl, and the virtual work produced by the
wrench can be expressed as follow:
U = fi Y2 + 91 E2 a12a12 x fl 52
(5.13)