We present an analysis of three southern open star clusters NGC 6067 , NGC 2506 and IC 4651 using wide-field photometric and Gaia DR2 astrometric data .
They are poorly studied clusters .
We took advantage of the synergy between Gaia DR2 high precision astrometric measurements and ground based wide-field photometry to isolate cluster members and further study these clusters .
We identify the cluster members using proper motions , parallax and colour-magnitude diagrams .
Mean proper motion of the clusters in \mu _ { \alpha } cos \delta and \mu _ { \delta } is estimated as -1.90 \pm 0.01 and -2.57 \pm 0.01 mas yr ^ { -1 } for NGC 6067 , -2.57 \pm 0.01 and 3.92 \pm 0.01 mas yr ^ { -1 } for NGC 2506 and -2.41 \pm 0.01 and -5.05 \pm 0.02 mas yr ^ { -1 } for IC 4651 .
Distances are estimated as 3.01 \pm 0.87 , 3.88 \pm 0.42 and 1.00 \pm 0.08 kpc for the clusters NGC 6067 , NGC 2506 and IC 4651 respectively using parallaxes taken from Gaia DR2 catalogue .
Galactic orbits are determined for these clusters using Galactic potential models .
We find that these clusters have circular orbits .
Cluster radii are determined as 10 ^ { \prime } for NGC 6067 , 12 ^ { \prime } for NGC 2506 and 11 ^ { \prime } for IC 4651 .
Ages of the clusters estimated by isochrones fitting are 66 \pm 8 Myr , 2.09 \pm 0.14 Gyr and 1.59 \pm 0.14 Gyr for NGC 6067 , NGC 2506 and IC 4651 respectively .
Mass function slope for the entire region of cluster NGC 2506 is found to be comparable with the Salpeter value in the mass range 0.77 - 1.54 M _ { \odot } .
The mass function analysis shows that the slope becomes flat when one goes from halo to core region in all the three clusters .
A comparison of dynamical age with cluster ’ s age indicates that NGC 2506 and IC 4651 are dynamically relaxed clusters .