Design Conditions for the Orientation and Attitude of a Robot Tool Carried by a 3-R Spherical Wrist

The orientational (directional) and attitudinal capabilities for a generally-dimensioned 3-R spherical robot-wrist are presented. The wrist is treated both with joints which can freely rotate and with joints which encounter limits to rotation. A principal method is to consider a hypothetical tool-plane to be associated with the tool and to use the locus of this plane as a measure of tool orientation. Design conditions are developed and presented, among wrist dimensions and limits to rotation at the actuators, which permit a tool to be placed in any direction by the robot. A different range of directions is also established, for each of which the wrist is able to rotate the end-effector a full turn about an axis in that direction. These results contain all the attitudinal possibilities for the end-effector and are presented separately for a wrist (i) which is operated only in one closure, and (ii) which can be operated in both closures to provide a combined range of attitudes. The results are summarized in five tables.