101
p = R2(d5 R4z + d3 z + a2 x). (9.15)
Vector it is given by
it = RI-1 t = R2R4R5 z. (9.16)
A reduced system of equations can be obtained from the last two equations by considering the expressions of 1pz, itz, It.1p, and 1p. 1p.
Computinq itz. From Eq. (9.16) and using Eqs. (4.5) and (4.6) as necessary yields
itz = It z = R5z R4-1y.
Since R5z = [S5, -C5, 0]T and R4-1y = [S4, 0, -C41T, the preceding equation becomes
Itz = S4 S5. (9.17)
1 11
Computing 19-. Since pz p z, from Eq. (9.15),
properties (4.5) and (4.6) and R2-1z = y, we.obtain
pz = (d5 R4z + d3 z + a2 x) y which is easily seen to produce
ipz = -d5 C4. (9.18)
Computing It.p. Eqs. (9.15), (9.16) and use of Eqs. (4.5) and (4.6) yield
it.lp = t.p = R5z (d5 z + d3 R4-1z + a2 R4-x).
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