  We present a calculation of the Mellin moments of the nucleon transverse
quark spin densities extracted from the unpolarized and transversity
generalized form factors. We use three $N_F=2+1+1$ ensembles of twisted mass
fermions with quark masses tuned to their physical values and lattice spacings
$a\sim 0.08$~fm, $a\sim 0.07$~fm and $a\sim 0.06$~fm and extrapolate the form
factors to the continuum limit. Besides isovector densities we also include
results for the tensor charge for each quark flavor using the ensemble with
$a\sim 0.08$~fm for which we include the disconnected contributions.
