Singularity is a major problem for parallel manipulators as it causes severe problems: uncontrollable or unstable motions, loss of stiffness, infinite forces/torques in actuated joints, and possibility of a breakdown. Many studies have been devoted to these problems. In particular, various criteria for measuring the closeness to singularities have been proposed. They are based on the limitation of the values of the input force/torque, pressure angle, natural frequency, etc. The present paper expands the previous work by incorporating a new criterion into mentioned problem, which allows the limitation of the reaction in passive joints. For this purpose, a new approach is developed, which shows that for given external force and moment applied on the platform, the reactions in passive joints depend not only on the pressure angle but also the position of the instantaneous centre of rotation of the platform. The developed approach is not only an effective way to reduce computation time but also to give a qualitative and geometrical interpretation of the problem. The suggested procedure for the determination of the reachable manipulator workspace taking into account the admissible reactions in passive joints is illustrated via a planar 3-RRR parallel manipulator.