Any industrial robot user knows from experience that the order in which the robot joints are controlled has no effect on the final positioning of the robot tool. This is a direct consequence of what we suggest to call the commutativity of robot joint displacements. We have taken advantage of Hong Genin's paper about the commutativity of finite rotations in robotic design to discuss this question. We emphasize the importance of the so-called Roth's proof for the understanding of this industrial robotics specific commutativity property.
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