We have measured the sky-projected spin-orbit alignments for three transiting hot Jupiters, WASP-103b, WASP-87b, and WASP-66b, using spectroscopic measurements of the Rossiter-McLaughlin effect, with the CYCLOPS2 optical fiber bundle system feeding the UCLES spectrograph on the Anglo-Australian Telescope. The resulting sky-projected spin-orbit angles of lambda = 3 degrees +/- 33 degrees, lambda- = -8 degrees +/- 11 degrees, and lambda- = -4 degrees +/- 22 degrees for WASP-103b, WASP-87b, and WASP-66b, respectively, suggest that these three planets are likely on nearly aligned orbits with respect to their host star's spin axis. WASP-103 is a particularly interesting system as its orbital distance is only 20% larger than its host star's Roche radius and the planet likely experiences strong tidal effects. WASP-87 and WASP-66 are hot (T-eff = 6450 +/- 120 K and T-eff = 6600 +/- 150 K, respectively) mid-F stars, making them similar to the majority of stars hosting planets on high-obliquity orbits. Moderate spin-orbit misalignments for WASP-103b and WASP-66b are consistent with our data, but polar and retrograde orbits are not favored for these systems