In order to find r$11, which is reciprocal to all other
screws in first subchain but $ll, the following equations
must be satisfied:
L21Prl + M21Qrl + N21Rrl + LrlP21 + MrlQ21 +
L31Prl + M31Qrl + N31Rrl + LrlP31 + MrlQ31 +
L41Prl + M41Qrl + N41Rrl + LrlP41 + MrlQ41 +
L51Prl + M51Qrl + N51Rrl + LrlP51 + MrlQ51 +
L61Prl + M61Qrl + N61Rrl + LrlP61 + MrlQ61 +
NrlR21 = 0
(5.17)
NrlR31 = 0
(5.18)
NrlR41 = 0
(5.19)
NrlR51 = 0
(5.20)
NrlR61 = 0
(5.21)
Therefore, r$11 is obtained by selecting the ratio Rrl/Mrl =
4 and solving Eqs. (5.17) (5.21) simultaneously, which
yields
r$ll = (0, 1, 0; -2.732, 0, 4)
Similarly, ri21 can be obtained by selecting the ratio
Rrl/Mrl = 4 and solving the Eqs. (5.18) -(5.22)
simultaneously, which yields
r' 21 = (4, 1, 6.928; -2.732, -16.784, 4)
where
LllPrl + MlQrl + NllRrl + LrlPll + MrlQll + NrlR11 = 0
(5.22)