Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joints, possibly leading to a robot breakdown. In the recent years classification and detection of singularities have made large progress. However, the issue of closeness to a singularity is still open and we propose in this paper an approach that is based on a static analysis. Our measure of closeness to a singularity is based on the very practical issue of having the joint forces/torques lower than a given threshold. We consider a planar parallel robot whose end-effector has a constant orientation and is submitted to a known wrench and we show that it is possible to compute the border of the region that describes all possible end-effector location for which the joint forces are lower than the fixed threshold.