DETERMINING SINGULARITIES OF SOME 3-DOF PARALLEL MANIPULATORS WITH LINEAR ACTIVE LEGS BY 3×3 TRANSLATIONAL/3×3 ROTATIONAL JACOBIAN MATRICES

摘要

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.