Table 5-2. Special structures of 4-DOF manipulators Condition Description
1 al=a2=0 First 3 joint axes (1,2,3) are parallel
2 0l=03=0 First 2 axes (1,2) are parallel and
Last 2 axes (3,4) are parallel
3 al=a3=0 First 2 axes (1,2) are parallel and
last 2 axes (3,4) intersect
4 C2=a3=0 Last three axes (2,3,4) are parallel
5 a2=a3=0 Middle axes (2,3) are parallel and
last 2 axes (3,4) intersect
6 C3=al=0 First 2 axes (1,2) intersect & last 2
axes (3,4) are parallel
7 a3=a2=0 Middle axes (2,3) intersect & last 2
axes (3,4) are parallel
8 al=a3=0 First 2 axes (1,2) intersect & last 2
axes (3,4) intersect
9 al=a2=d2=0 First 3 axes (1,2,3) intersect 10 a2=a3=0 Middle 2 axes (2,3),intersect and last
2 axes (3,4) intersect
be zero for the geometries described in Table 5-2 at any pose. We now examine in detail the inverse kinematics of each of the special 4-DOF robot architectures described in Table 5-2 and illustrated in Figure 5.1.
..