having a wrist, the manipulator has some added structural feature such as two parallel or intersecting joint axes then closed-form solutions may be obtained in a simpler form than a quartic polynomial equation. This is the case of the PUMA 560 robot whose inverse kinematics are discussed in Example 1 of Chapter 9. An algebraic method for solving the inverse kinematics of the PUMA 560 can be found in Craig (1986) and a geometric approach is described in Fu, Gonzalez, & Lee (1987). Another sufficient condition for closed-form solutions is that three adjacent joint axes be parallel (Duffy 1980, Fu, Gonzalez, & Lee 1987).
Record and Plavback
An industrial robot manipulator is usually equipped with sensors that can measure information such as joint variable values and rates of change of those values. A
method that avoids the computational complexity of the inverse kinematic problem altogether- consists of remotely guiding a robot end-effector trajectory by activating each joint separately while storing joint space coordinates and information -from -the sensors at -selectedpoints alongC the trajectory. The robot can then indefinitely repeat the recorded motion. Should the robot be needed for a different task or should a change in the workcell occur that requires different end-effector -trajectories the motion of the Irobot will have to be recorded again.
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