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tokens: a list of new associations in the Galaxy. Clustering depends on the choice of length-scale and groups begin to merge for larger length-scales. In this scenario, although the presence of different groups and associations is ascertained from the results of their cluster analysis using an independent method, their boundaries are not well defined. This, consequently, affects the membership assignment and identification of parent associations for those stars located at the association boundaries. Here, we investigate the properties of the well-known association Cyg OB3. We primarily focus on the distances, proper motions, and three-dimensional velocity components of the members. We study a particular case of a confirmed black hole X-ray binary Cyg X-1 (otherwise known as HD 226868; Bolton 1972 ; Webster Murdin 1972 ) located at the association boundary (Fig. 1 ). Cyg X-1 is one of the brightest X-ray binaries in the X-ray sky and is composed of a black hole of 14.8 ± 1.0 M ⊙ (Orosz et al. 2011 ) and a companion of 19.2 ± 1.9 M ⊙ (Orosz et al. 2011 ) of spectral type O9.7Iab (Walborn 1973 ). Cyg X-1 has been included in the catalogues of Humphreys ( 1978 ), Garmany Stencel ( 1992 ), Ruprecht et al. ( 1981 ), and Blaha Humphreys ( 1989 ) as a member of Cyg OB3. The cluster analysis algorithm implemented by Mel’Nik Efremov ( 1995 ) divided the association Cyg OB3 into two subgroups for a length-scale of 15 pc viz. Cyg 3A and Cyg 3B; however, Cyg X-1 was not included in either of the subgroups and remained as a field star. Figure 1. Image obtained with DSS2 in the R band shows the Cyg OB3 region. The positions of the O- and B-type stars studied in this work are encircled. Cyg X-1 is encircled in red. There are a total of 41 stars shown in the image and given in Table 1 . Mirabel Rodrigues ( 2003 ) studied the connection between Cyg X-1 and the association Cyg OB3 using the astrometry from the Hipparcos mission. The authors suggested that the parent association of Cyg X-1 is indeed Cyg OB3, and showed that the binary is located at the same distance as the other stars in Cyg OB3 and exhibits a proper motion similar to that of the association. The authors also showed that the peculiar velocity of Cyg X-1 is very small (9 ± 2 km s −1 ) with respect to the association, and is consistent with the expected random velocities of stars in expanding associations. These results indicate that Cyg X-1 is most likely a member of Cyg OB3. This was later confirmed with precise measurement of the trigonometric parallax and the proper motion of Cyg X-1 using VLBI radio observations (Reid et al. 2011 ). In this paper, we revisit the proposed connection between Cyg X-1 and Cyg OB3 using the astrometric data from Gaia DR2, which provides trigonometric parallaxes and proper motions for over 1 billion stars in the Galaxy with the best accuracy and precision available to date (Gaia Collaboration 2018 ). We define the sample of stars and their filtering criteria in the next