slopppiness in drive train on 1998 Lincoln Town Car

Noticing a vibration (low frequency)felt -a sort of slopppiness in drive train comes and goes as though something were loose-also I had
a rebuilt transmission put in at around110000 miles

Asked by for the 1998 Lincoln Town Car
Maybe your u joints need replacement I see some models came with single cardan joints and some with double cardan joints, its possible that they have worn out and become out of balance.