  We have obtained high-resolution spectra of four eclipsing binary systems (FM
Leo, NN Del, V963 Cen and AI Phe) with the view to gaining insight into the
relative orientation of their stellar spin axes and orbital axes. The so called
Rossiter-McLaughlin (RM) effect, i.e. the fact that the broadening and the
amount of blue- or redshift in the spectra during an eclipse depend on the tilt
of the spin axis of the background star, has the potential of reconciling
observations and theoretical models if such a tilt is found. We analyse the RM
effect by disentangling the spectra, removing the front component and measuring
the remaining, distorted lines with a broadening function (BF) obtained from
single value decomposition (SVD), weighting by the intensity centre of the BF
in the eclipse. All but one of our objects show no significant misalignment,
suggesting that aligned systems are dominant. We provide stellar as well as
orbital parameters for our systems. With five measured spin-orbit angles we
significantly increase (from 9 to 14) the number of stars for which it has been
measured. The spin-orbit angle $\beta$ calculated for AI Phe's secondary
component shows a misalignment of 87$\pm$17 degrees. NN Del, with a large
separation of components and a long dynamical timescale for circularisation and
synchronisation, is an example of a close to primordial spin-orbit angle
measurement.
