An uncontrolled angular displacement compensating device for compensating an uncontrolled angular displacement of a robot hand mounted on a robot hand mounting link of a robot hand shifting linkage of an industrial robot, resulting from the expansion or contraction of the robot hand shifting linkage. The uncontrolled angular displacement compensating device comprises a pair of identical sprockets fixed to a first shaft supported on the free end of the robot hand mounting link and on a second shaft rotatably supported on the basal end of the same link, respectively, a driving bevel gear fixed to the first shaft, a driven bevel gear rotatably mounted on a robot hand mounting member pivotally joined to the free end of the same link and engaging the driving bevel gear, and an endless chain extended between the sprockets. The sprocket mounted on the second shaft is turned either clockwise or counterclockwise when the robot hand mounting link is turned either counterclockwise or clockwise as the robot hand shifting linkage is extended or contracted, so that the driving bevel gear is turned so as to compensate an angular displacement of the robot hand on its own axis caused by the expansion or contraction of the robot hand shifting linkage.