Experimental and theoretical studies of the self-propelled motional dynamics of a new genre of catalytic sphere dimer, which comprises a non-catalytic silica sphere connected to a catalytic platinum sphere, are reported for the first time. Using aqueous hydrogen peroxide as the fuel to effect catalytic propulsion of the sphere dimers, both quasi-linear and quasi-circular trajectories are observed in the solution phase and analyzed for different dimensions of the platinum component. In addition, well-defined rotational motion of these sphere dimers is observed at the solution-substrate interface. The nature of the interaction between the sphere dimer and the substrate in the aqueous hydrogen peroxide phase is discussed. In computer simulations of the sphere dimer in solution and the solution-substrate interface, sphere-dimer dynamics are simulated using molecular-dynamics methods and solvent dynamics are modeled by mesoscopic multiparticle collision methods taking hydrodynamic interactions into account. The rotational and translational dynamics of the sphere dimer are found to be in good accord with the predictions of computer simulations.