Step 2. Compute e2 and 83 from the reduced system of equations
a2uy S2 + a2ux C2 + a3o4 S4 o3a4d3 C4 = r1 (6.15)
a2ux S2 a2uy C2 + 0304 C4 = r2 (6.16)
o2qx S2 92qy C2 o3a4 S4 = r3 (6.17)
a2qy S2 + a2qx C2 + a3a4d3 S4 + a3a4 C4 = r4 (6.18)
with
rl = q.u 74d4 d2uz 73T4d3 (6.19)
r2 = TT4 2u (6.20)
r3= T2(d2 qz) + d3 + T3d4 (6.21)
r4 = (q.q+a22+d22-a32-d32-a42-d42)/2
d2qz r3d3d4, (6.22)
derived from Eqs. (5.13)-(5.20) by proper index substitution (the indexes are incremented to fit the 4-DOF problem of Eq. (6.2)). Vectors u and q play the roles of vectors t and p respectively. The last system of equations gives the values of e2 and 84. Equations (5.23) and (5-.24), with the proper index changes,
(o3d4- T3a4S4) S3 + (a3+a4C4) C3
= C2qx +S2qy a2 (6.23)
and
(a3+a4C4) S3 (a3d4-T3a4S4) C3
= -72S2qx + 2C2qy + a2(qz-d2), (6.24)
..