o3qx S3 a3qy C3 a4a5 S5 = r3 (7.22)

a3qy S3 + a3qx C3 + a4a5d4 S5 + a4a5 C5 = r4 (7.23)


with


rI = q.u 75d5 d3uz T4T5d4 (7.24)

r2 475 3uz (7.25)

r3 T3(d3 qz) + d4 + '4d5 (7.26)

r4= (q.q + a32 + d32 a42 d42 a52 d52 )/2

 d3qz T4d4d5. (7.27)


Solving this system of equations will yield the values of 83 and 85. The value of e4 can then be computed from the two equations


(a4d5- T4a5S5) S4 + (a4+a5C5) C4 = C3qx + S3qy a3 (7.28)

and

(a4+a5C5) S4 (o4d5-r4a5S5) C4 =

 -T3S3qx + r3C3qy + C3(qz-d3) (7.29) (7.29)


derived from Eqs. (5.23) and (5.24), or from the equations (T4u5C5+"4-5) S4 + c5S5 C4 = C3u + S3uy (7.30)

and

a5S5 S4 (4a5C5+475) C4 =

 -T3S3ux + r3C3uy + C3uz, (7.31)


corresponding to Eqs. (5.25) and (5.26).

..