The singularities of the Jacobian matrices of two manipulator with three degrees of freedom are analyzed. One is a planar 3-legged manipulator; the other, a planar double-triangular manipulator. A general classification of parallel-manipulator singularities into three groups is described. The classification scheme relies on the properties of the Jacobian matrices of the manipulator. Finally, the three types of singularity are identified for the two manipulators.