We study the orbital properties of dumbbell galaxies which harbor twis
ted radio jets. Velocity and velocity dispersion profiles for four dum
bbell pairs (3C66B, 3C75, 3C449, 0326+39) are presented. We analyze op
tical CCD images in search of isophote off-centering and large isophot
e twists. Combining the kinematic and isophotal information, we discus
s whether each system is an interacting pair, and derive constraints o
n the relative orbit. The types of isophotal distortions, combined wit
h the prograde/retrograde nature of the relative orbit, suggest that t
hree of the objects (3C66B, 3C75 and 0326+39) are unlikely to be in ci
rcular orbits. Only 3C449 may be in a close, moderate-ellipticity orbi
t. We find that the distribution of relative velocity with separation
for dumbbells with distorted radio morphology from the catalogue of Pa
rma et al. (1991) also suggests a prevalence of eccentric orbits. We d
iscuss that dumbbells with distorted radio morphology may deviate sign
ificantly from the circular orbit model proposed by Valentijn & Casert
ano (1988). The genesis of radio distortions could be related to such
distinct orbital behaviour. The amplitude and wavelength of jet oscill
ations in these objects correlates with the projected separation of th
e pairs, pointing at a dynamical origin for the jet oscillations. Howe
ver, for three of the four systems studied in detail here, the jet osc
illations cannot be easily traced to orbital displacements of the pare
nt galaxies. Either interactions trigger radio beam precession, or the
intracluster medium plays a role in setting the radio beam oscillatio
ns.