CHAPTER 3
EXISTING SOLUTIONS
Closed-Form Architectures
The ability to compute the coordinates in joint space of an end-effector pose given in Cartesian space is an important criterion in the design of computer-controlled manipulators. A desirable property for an industrial manipulator is the possibility of computing the joint
variables necessary to position and orient the end-effector as specified in Cartesian space, in closed-form. Pieper
(1968) has shown that a closed-form solution is possible when the manipulator has three adjacent joint axes intersecting at a common point. The inverse kinematic
problem reduces then to a quartic polynomial equation in one
of the joint variables. Manipulators with the last three joint axes intersecting are said to be "wrist-partitioned". Computationally efficient methods for computing the
position, velocity, and acceleration inverse kinematics for this type of manipulators have been presented by
Featherstone (1983), Hollerbach and Sahar (1983), Paul and Zhang (1986), and Low and Dubey (1986). Several industrial six- and five-DOF manipulators such as the PUMA series
robots are of the wrist-partitioned type. If, on top of
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