Although singularities of planar parallel manipulators have been treated extensively, this paper wants to draw the attention to a fact that seemingly has been overlooked in almost all the papers. It will be shown, that, even when all solutions of the direct kinematics coincide, the manipulator does not have a self motion. Furthermore it is shown that even this sixfold solution of the direct kinematics corresponds only to rank deficiency one of the Jacobian matrix. Rank deficiency two is in general not possible for this type of manipulator, but if one design condition is fulfilled then the manipulator can have local mobility two.