  We measure the star formation quenching efficiency and timescale in cluster
environments. Our method uses N-body simulations to estimate the probability
distribution of possible orbits for a sample of observed SDSS galaxies in and
around clusters based on their position and velocity offsets from their host
cluster. We study the relationship between their star formation rates and their
likely orbital histories via a simple model in which star formation is quenched
once a delay time after infall has elapsed. Our orbit library method is
designed to isolate the environmental effect on the star formation rate due to
a galaxy's present-day host cluster from `pre-processing' in previous group
hosts. We find that quenching of satellite galaxies of all stellar masses in
our sample ($10^{9}-10^{11.5}\,{\rm M}_\odot$) by massive ($> 10^{13}\,{\rm
M}_\odot$) clusters is essentially $100$ per cent efficient. Our fits show that
all galaxies quench on their first infall, approximately at or within a Gyr of
their first pericentric passage. There is little variation in the onset of
quenching from galaxy-to-galaxy: the spread in this time is at most $\sim 2$
Gyr at fixed $M_*$. Higher mass satellites quench earlier, with very little
dependence on host cluster mass in the range probed by our sample.
