  Assuming for Weakly Interacting Massive Particles (WIMPs) a Maxwellian
velocity distribution in the Galaxy we explore in a systematic way the relative
sensitivity of an extensive set of existing and projected Dark Matter (DM)
direct detection experiments to each of the 14 couplings that parameterize the
most general non-relativistic (NR) effective Hamiltonian allowed by Galilean
invariance for a contact interaction driving the elastic scattering off nuclei
of WIMPs of spin 1/2. We perform our analysis in terms of two free parameters:
the WIMP mass $m_{\chi}$ and the ratio between the WIMP-neutron and the
WIMP-proton couplings $c^n/c^p$. We include the modified signal spectral shape
due to non-standard interactions when it is needed in the determination of the
bound, such as in the case of background subtraction or of the application of
the optimal-interval method. For each coupling, in the $m_{\chi}$-$c^n/c^p$
plane we provide contour plots of the most stringent 90 % C.L. bound on the
WIMP-nucleon cross section and show the experiment providing it. We also
introduce NRDD_constraints, a simple interpolating code written in Python that
allows to obtain the numerical value of the bound as a function of the WIMP
mass $m_{\chi}$ and of the coupling ratio $c^n/c^p$ for each NR coupling. We
find that 9 experiments out of the 14 present Dark Matter searches considered
in our analysis provide the most stringent bound on some of the effective
couplings for a given choice of $(m_{\chi},c^n/c^p)$: this is evidence of the
complementarity of different target nuclei and/or different combinations of
count-rates and energy thresholds when the search of DM is extended to a wide
range of possible interactions.
