100
Table 9-2. GP66 manipulator
joint d 8
kinematic parameters.
a a
7r/ 2 7r/ 2 R/2
R/2
0
7r/ 2
7r/ 2 0/2 7/2
0
Joint 3 is prismatic.
We will implement an iterative technique to find the zeros of a real valued function of 81. First we show that knowledge of l81 is sufficient to determine a solution set. Assuming a guess of l81, the corresponding x and z components of 1p=R1-ip and it=R1-1t can be computed,
px = Px C1+p y S1 Pz = Px Sl-Py C1 itx = tx C1+ty S1 itz = tx Sl-t y C.
(9.11) (9.12) (9.13)
(9.14)
For this robot 11 = 14 = 16 = 0, R2-112 = a2x, 13 = d3z 15 = d5z and R3 = I. With these values, (4.4) yields
p = R1R2(d5 R4z + d3 z + a2 x) or after multiplication by R1-1
..