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).

..