Determination of singularities of some 4-DOF parallel manipulators by translational/rotational Jacobian matrices

A novel analytic approach is proposed for determining the singularities of some four degree of freedom (DOF) parallel manipulators (PMs). First, the constraint and displacement of a general 4-DOF PM are analyzed. Second, a common 3 x 4 translational Jacobian matrix Jv and a common 3 x 4 rotational Jacobian matrix Ja are derived, and a 4 x 4 general Jacobian matrix J of the 4-DOF PMs is derived from Jv and Ja). Since a complicated process to determine singularities from the 4 x 6 Jacobian matrix is transformed into a simple process to determine singularity from J, the singularities of the some 4-DOF PMs with 3 translations and 1 rotation, or with 3 rotations and 1 translation, or with combined translation-rotations are analyzed and determined easily by this approach.