Just had transmission and transfer case rebuilt. I noticed when I picked the truck up that the dealer had forgot to tighten down the rear u-joint where it connects to the rear diff (Ford 9.75 w/ 3.73s). I tightened down the bolts myself after it became obvious after maybe two days of driving.

Anyways now I am noticed a slight shudder/vibration when accelerating from a stop. The truck is nice and smooth with low miles so it is obvious to me when I feel the shudder and its driving me nuts, and I never noticed it before the transmission rebuild.

FWIW, I have a one-piece driveshaft.

So today I topped off the rear diff with 1 quart of Royal Purple oil w/ friction modifier. The rear diff was a little low on oil but topping it off didnt seem to help in the couple of miles I drove since doing that.

Next plan is to find a hydraulic jack and get the rear axle off the ground and wiggle the driveshaft and see if there is any play in there. Also my third thing is to check the slip joint where the driveshaft goes into the transfer case, but I'd imagine since they rebuilt the transfer case that they wouldn't have put the driveshaft back in there without re-greasing the input shaft/slip joint but who knows.

The best way to describe the shudder/ vibration is it feels like there are big mud tires on there and you can feel the tread vibrations when accelerating but then it goes away quickly (I just have street tires)

 

My '07 is a scab and has a 1 piece driveshaft, but my '77 has a two piece drive shaft with a carrier bearing between the trans & rear axle. Your truck is a screw, it more than likely has a carrier bearing too. Point is my '77 was doing something like you describe, even when accelerating around a turn like when I was pulling out from a stop sign onto the highway. I was gonna replace the bearing but found the rubber was shot. Added some shims between the rubber and the mount & strap to snug up the rubber, the issue faded.

Another thing to look at is when they put the driveshaft back in, if they ever seperated it at the slip joint, did they put the two pieces back together in the properly phased position. like ---<------>--- or --->------<--- where the yokes on both ends of the shaft section are "back to back"