Yi Lu, Shu-Yan Li, and Yan Shi
Parallel manipulator, singularity, Jacobian matrix
An analytic approach based on translational/rotational Jacobian matrices is proposed for determining the singularities of some 3-DOF (degree of freedom) parallel manipulators (PMs) with linear active legs. First, the constraint and displacement of a general 3-DOF PM are analysed. Second, a common 3 × 3 translational Jacobian matrix and a common 3 × 3 rotational Jacobian matrix are derived, and a common formula is derived for solving 3 × 3 general Jacobian matrix of the 3-DOF PMs. Third, the singularities of some 3-DOF PMs with three pure translations, or with three pure rotations, or with combined translation–rotations are determined and analysed, respectively.
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