Low energy ion scattering (LEIS) and low energy electron diffraction (LEED) have been employed to investigate the Pd/Cu(001), Pt/Cu(001) and Pd/Pt/Cu(001) systems. A monolayer of Pd deposition on a Cu(001) surface at room temperature (RT) induced a (2 x 2) p4g clock reconstruction. We present evidence that this reconstructed phase corresponds to a model of ~20% pure Pd islands above an ordered c (2 x 2) substrate, which is mixed with c (2 x 2) Cu-Pd regions. The lateral displacement of surface island Pd atoms was measured to be 0.25+/-0.07 a through comparisons with 3D computer simulation. For 1 ML Pt on Cu(001) at RT, however, an ordered c (2 x 2) structure formed only after annealing to 150-200 o C. No reconstruction was evidenced. Two simple rules for governing the occurrence of the clock reconstruction are proposed. In order to learn whether the size difference between Pd and Cu in an ordered (2 x 2) substrate has a strong influence and acts as a template for the reconstruction, we have also studied the Pd/Pt/Cu(001) system. Evidence for the p4g clock reconstruction was found by deposition of 0.5ML Pd above an ordered c (2 x 2) Cu-Pt substrate.