subworkspace. From the inverse kinematics of subchain (R-
L)-R-S solved in section 2.5.1, we know it has up to four
possible solutions for a given position of the S joint.
Once the orientation and position of the hand is given, we
may have up to 64 solutions for the manipulator. Therefore,
the study of root regions in the subworkspace is also
important.
A manipulator with R-L actuators in the subchains whose
axes are arranged in triangle form on the base can be
represented as shown in Fig. 3.19. The notation is as
follows:
OXYZ global fixed coordinate system.
i i-th subchain.
Ai, Bi R-L actuator joint and revolute joint in the
i-th subchain.
oixiYiZi local fixed coordinate systems with the zi
axis along the axis of the cylindric joint
Ai.
AixaiYaizai, BixbiYbizbi moving coordinate systems
embedded in joints Ai and Bi,
respectively.
8ai, 9bi relative rotation angle between successive
links.
di translation along the axis zi of cylindric
joint Ai from the origin of the local fixed
coordinate system oixiYizi.