We have applied the Tremaine-Weinberg method to 10 late-type barred spiral galaxies using data cubes, in Hα emission, from the FaNTOmM and GHAFAS Fabry-Perot spectrometers. We have combined the derived bar (and/or spiral) pattern speeds with angular frequency plots to measure the corotation radii for the bars in these galaxies. We base our results on a combination of this method with a morphological analysis designed to estimate the corotation radius to bar-length ratio using two independent techniques on archival near-infrared images, and although we are aware of the limitation of the application of the Tremaine-Weinberg method using Hα observations, we find consistently excellent agreement between bar and spiral arm parameters derived using different methods. In general, the corotation radius, measured using the Tremaine-Weinberg method, is closely related to the bar length, measured independently from photometry and consistent with previous studies. Our corotation/bar-length ratios and pattern speed values are in good agreement with general results from numerical simulations of bars. In systems with identified secondary bars, we measure higher Hα velocity dispersion in the circumnuclear regions, whereas in all the other galaxies, we detect flat velocity dispersion profiles. In the galaxies where the bar is almost purely stellar, Hα measurements are missing, and the Tremaine-Weinberg method yields the pattern speeds of the spiral arms. The excellent agreement between the Tremaine-Weinberg method results and the morphological analysis and bar parameters in numerical simulations suggests that although the Hα emitting gas does not obey the continuity equation, it can be used to derive the bar pattern speed. In addition, we have analyzed the Hα velocity dispersion maps to investigate signatures of secular evolution of the bars in these galaxies. The increased central velocity dispersion in the galaxies with secondary bars suggests that the formation of inner bars or disks may be a necessary step in the formation of bulges in late-type spiral galaxies.