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An exact kinematic model of the Unimation PUMA 600 robotic manipulator is presented. Discrepancies found between the actual manipulator in laboratory tests and the first model presented are discussed. The link coordinate frames are redefined in order to introduce a new transformation for a tool frame. Modifications are made to previously published solutions of the inverse kinematics and differential kinematics. The actual reference orientation frame of the manipulator is formulated such that the orientation of the end effector can be expressed in terms of the actual coordinate angles.