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Abstract. The paper presents combined spectroscopic and photometric orbital solutions for four close binary systems: SW Lyn, QW Gem, AP Leo and V2150 Cyg. The photometric data are new, while the spectroscopy has been recently obtained within the radial velocity programme at the David Dunlap Observatory. This paper is the first in the planned series of investigations. We give an extensive description of the motivation for the series and of the main assumptions made in our solutions. The four targets of this investigation span a range of typical configurations and thus present different levels of difficulty for the combined spectroscopic and photometric orbital solutions.

This paper presents the results of a combined spectroscopic and photometric study of 20 contact binary systems: HV Aqr, OO Aql, FI Boo, TX Cnc, OT Cnc, EE Cet, RW Com, KR Com, V401 Cyg, V345 Gem, AK Her, V502 Oph, V566 Oph, V2612 Oph, V1363 Ori, V351 Peg, V357 Peg, Y Sex, V1123 Tau, and W UMa, which was conducted in the frame of the W UMa Project. Together with 51 already covered by the project and an additional 67 in the existing literature, these systems bring the total number of contact binaries with known combined spectroscopic and photometric solutions to 138. It was found that mass, radius, and luminosity of the components follow certain relations along the MS and new empirical power relations are extracted. We found that 30 per cent of the systems in the current sample show extreme values in their parameters, expressed in their mass ratio or fill-out factor. This study shows that, among the contact binary systems studied, some have an extremely low mass ratio (q < 0.1) or an ultrashort orbital period (Porb < 0.25 d), which are expected to show evidence of mass transfer progress. The evolutionary status of these components is discussed with the aid of correlation diagrams and their physical and orbital parameters compared to those in the entire sample of known contact binaries. The existence of very short orbital periods confirms the very slow nature of the merging process, which seems to explain why their components still exist as MS stars in contact configurations even after several Gyr of evolution.

Orbital period changes of three close binaries, TW And, TT Her and W UMi, were studied using the Kraków data base of minima of eclipsing binaries, and new photoelectric observations obtained by the authors. The interval of the observations spans roughly a century. The major orbital period change in TW And is explained by the presence of a third body with P3= 49.6 yr and a continuous secular period increase. A third body, with P3= 41.0 yr, was also found in the system TT Her. The (O–C) diagram of W UMi can be interpreted as either an abrupt orbital period decrease which occurred around the end of 1973 or as a secular orbital period decrease combined with cyclic change. In this case, the orbital period of the third body is 62.2 yr and the sum of squares of residuals is lower than for a broken‐line fit, therefore cyclic variations should be preferred. In all three systems, the third body is a low‐mass companion.

A new sample of contact systems, consisting of more than 100 stars, was created for binaries for which the physical parameters have been determined using both photometric light curves and radial velocity measurements of both components. Properties of components are discussed including their evolutionary status.