In 2005 the HERMES collaboration published first evidence for azimuthal single-spin asymmetries in semi-inclusive production of charged pions on a transversely polarised hydrogen target. The distinctive Fourier components of the measured asymmetries caused by both the Collins and the Sivers mechanisms provide signals for previously unmeasured quantities: the transversity quark distribution in conjunction with the Collins fragmentation function (Collins mechanism) and the Sivers parton distribution (Sivers mechanism). The transversity distribution will provide a detailed insight into the relativistic nature of the quarks inside the nucleon. Recent theoretical work demonstrated a relation between the Sivers function and the contribution of the orbital angular momentum of quarks within the nucleon. The results presented for charged pions have a much higher statistical significance than the published data. In addition the Collins and Sivers asymmetries for neutral pions and charged kaons are provided.