The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.