||Sunspot observations in chromospheric spectral lines have revealed the existence of short-lived linear bright transients, commonly referred to as penumbral micro-jets (PMJs). Details on the origin and physical nature of PMJs are to large extend still unkown. We aim to characterize the dynamical nature of PMJs to provide guidance for future modelling efforts. We analyze high spatial (0.1 arcsec) and temporal resolution (1 s) Ca II H filtergram (0.1 nm bandwidth) observations of a sunspot obtained on two consecutive days with the Swedish 1-m Solar Telescope. We find that PMJs appear to be the rapid brightening of an already existing (faint) fibril. The rapid brightening is the fast increase (typically less than 10 s) in intensity over significant length (several 100s of km) of the existing fibril. For most PMJs, we cannot identify a clear root or source from where the brightening appears to originate. After the fast onset, about half of the PMJs have a top that is moving with an apparent velocity between 5 and 14 km/s, most of them upwards. For the other PMJs, there is no significant motion of the top. For about a third of the PMJs we observe a splitting into two parallel and co-evolving linear features during the later phases of the lifetime of the PMJ. We conclude that mass flows can play only limited role in the onset phase of PMJs and that it is more likely that we see the effect of a fast heating front. From different datasets from coordinated SST and IRIS observations, we analyse the response of IRIS diagnostics to PMJs and find that sometimes PMJs get sufficiently heated to produce signal in the Si IV lines.