Position reverse solution on 6R manipulator with error tolerance property

while there happened a failure in a joint of an ordinary 6R manipulator it becomes a 5R manipulator or calls it an insufficient DOF manipulator.If the manipulator is holding a bar shaped object,there could be no restrictions added to the posture parameters for the fingers' rotation around the center line of bar,thus makes the rotation be virtualized as an unknown rotational joint,like this the problem of position reverse solution on the insufficient DOF manipulator was transformed into the problem of position reverse solution that includes 6 unknown quantities.On account of variations will occur on its structural parameters and the failure joint is indeterminate,as a result the reverse solution program ought to satisfy the need of uncertainty.Once the kinematics equations of position reverse solution were established,the equations solving course is similar to the algorithm of ordinary 6R manipulator.Through numerical computing example,it was verified that the number of position reverse solutions is 16 for this kind of ordinary 6R manipulator with single joint failure when there is no restriction on the posture of manipulator ends.