Ground noise under load

I have a 1993 Jeep Grand Cherokee V8 with 210,000 miles on it. When I press the gas it is a grounding sound coming from underneath the drivers side. It happens during sharp turns also. I have been told that it is the universal joint or maybe the transmission. The sound doesn't happen if I am act a constant speed, only if I slow down and then type to accelerate. Why do you think.