On the Determination of Parallel Mechanism Unmanipulable Singularities

Y. Yang and J.F. O'Brien (USA)


Parallel robots, Unmanipulable, Singularities, 3-RRR.


A geometric method is presented to determine the unma nipulable singular configurations of a general class of par allel robots. In unmanipulable singular configurations, the composite Jacobian matrix that maps active joint veloci ties to end-effector velocity loses rank, indicating the loss of a task degree-of-freedom (DOF). Finding unmanipula ble configurations is difficult due to the complexity of the Jacobian matrix. The problem is greatly simplified by a novel decomposition of the matrix presented in this paper. It shows that for stable configurations the unmanipulable singularities are individual arm singularities. The method is used to find singularities in several example parallel ma chines.

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