Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra

Details Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra

2009-10-21

arxiv.org/abs/0910.4012v1

IEEE Transactions on Robotics 25, 5 (2009) 995-1004

Computer Science

Robotics

Scientific paper

10.1109/TRO.2009.2017132

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel manipulators, of which some legs do not have any spherical joint, are such manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.

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