In this paper, we investigate the leaderless consensus problem for second-order multi-agent systems (MASs) with unknown inertias and parametric uncertainties. The graph that describes the interaction among the agents is generally directed. We consider both fixed and switching graphs. For a fixed directed topology, the associated graph needs to contain a spanning tree. For dynamically switching topologies, the uniform joint connectivity is required. We proposed consensus algorithms without relative velocity measurements, which are fully distributed in the sense that no common control gains are used and no global gain dependency conditions are required. The cases of agent dynamics with unknown nonidentical control directions and the asymptotic consensus in the presence of external disturbances are further investigated.