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Hi y'all. We just bought a 1976 Stingray to restore a couple of weeks ago.
We were in the process of moving it to the garage where the work will be done, having just bled the brakes (the dealer had put new brakes on it right before we bought it) and driven it around the block a few times. We were backing out of the driveway when suddenly the car screeched to a halt, as if we had hit something. Our mechanically-inclined friend who was driving said that the rear end had "locked up."
There was nothing we could do to get the car to go any further in reverse (even though we had just driven it in reverse successfully on our around-the-block trip a few minutes prior). The car would move fine going forward, but wouldn't budge in reverse. After a few minutes of thinking, he said the only thing we could do is try to rock the car back far enough so that it would break the lock on the rear end. Well, we did, and the car made what I could only call a very nasty (and perhaps costly) sound, but it did roll backward. Every time the tires rotated around again, we could hear a quieter version of that sound. But he was successful in getting it out of the driveway and onto the street so we could move in into the work garage.
My question is, what was that?! It sounds expensive to fix but I couldn't tell you what it is. Our friend said something about the suspension locking up and "32 little teeth" somewhere inside there that were catching, but he didn't elaborate further.
Assuming it's a manual transmission, check all the bolts holding the levers onto the shafts on the side of the trani. Make sure the shifter is in neutral and the 1-2 and 3-4 levers are centered. I believe the reverse lever should be forward but you can tell by the shifter movement as you place it into reverse.
About 7-8 years ago I had an identical problem on my '76. I pulled the rear end and found a hole, about .22 cal., in the rear cover. I took the unit to a local Corvette rear axle expert.
When we opened it up, we found 2 of the bolts that attach the ring gear to the carrier were laying in the bottom of the case. After inspecting the parts, we found all of the other ring gear to carrier bolts were loose. He said they were supposed to lock-tite the bolts, but sometimes this step was overlooked. He said he did see this before.
No internal parts were damaged but I decided to replace the posi clutches, and both yokes. 7 years later - no problems. Also replaced the cover with a HD unit from Muskegon(sp) brakes.