The　dexterous　workspace　is　of　significant　importance　in　design　of　a　planar　manipulator.　To　determine　the　dexterous　workspace　of　a　planar　3-DOF　parallel　manipulator,　the　auxiliary　linkages　are　constructed　with　the　reference　point　of　the　moving　platform　as　the　fixed　hinge.　If　the　reference　point　lies　in　the　dexterous　workspace,　the　moving　platform　should　be　able　to　rotate　around　the　reference　point　by　the　definition　of　the　dexterous　workspace　and　the　platform　becomes　the　crank　in　the　auxiliary　linkage.　Based　on　the　Grashof　criteria　for　the　auxiliary　linkages,　the　conditions　for　the　reference　point　to　lie　in　the　dexterous　workspace　are　derived　and　the　boundary　of　the　dexterous　workspace　can　then　be　drawn　in　a　simple　graphical　method.　Different　examples　are　given　to　verify　the　effectiveness　of　the　method　and　meanwhile　the　possible　separation　of　the　dexterous　workspace　is　analyzed.