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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