Reverse threading with a screw on chuck.

never had a problem reverse threading or reversing the chuck in general. as tq60 said, I give it a short "slam" onto the shoulder when I thread a chuck on and a sharp tug on the key loosens it up again. As long as you're not doing an interrupted cut or crash the lathe, you should be fine with some common sense.
 
I don't want to discount the wisdom of those who have posted here, but I run my Atlas 10 in reverse for single-pointing threads. The little 1/3-hp motor does not have Holleys or Headers to pump it up, so for a thread cutting tool at DOC .020-.040 things go smoothly. I do not want to roll my good chuck off the back side of my lathe, but I feel pretty good about threading in reverse.
 
My 6" Atlas/Craftsman has never loosened a chuck in almost fifty years in spite of my using it in reverse many times. My chuck is tightened to an excess of 10 lb-ft. of torque. My belt will slip before I would develop that amount of torque.

However, that is a small lathe and the 3" chuck weighs only 4 lbs.; 8 lbs.for the 4" chuck. It might be a totally different experience with a larger lathe.

Along the same lines, if the lathe is equipped with a VFD with electronic braking, a sudden stopping of the spindle while turning in the forward direction could also unthread a chuck.
 
Good or bad, I thread my chucks onto my 12x36 by hand, then place a 4' 2x4 in the chuck jaws and give it a just little oomph with the back and bull gears locked (spindle is mechanically locked). I keep the threads and register on the spindle very clean for a better connection.

There is a real risk of damaging the back gears, but I am pretty gentle with it.

I have very little fear of the chuck unthreading in reverse unless there is a crash with the tool and workpiece.

I also modified the electrical of my lathe to include a FWD/REV enable switch. When the switch is FWD enable, lifting the start lever will not run the lathe in reverse. Same goes when the switch is in REV enable, pulling the start lever down will not run the lathe forward. The main concern is that if you shut off the lathe (with a single phase capacitor start reversible motor) while running forward, but miss the middle position and go into reverse, the centrifugal switch in the motor will have the start winding disconnected and the motor will continue to run forward at full speed. This could be particularly problematic when metric threading where the spindle is constantly started and reversed.
 
Decided to take a break from cutting, splitting and stacking firewood. A day in the shop is always good. So I decided to make a keeper to hold the chuck on if I had to run the lathe in reverse. The keeper came out ok. I had some 1 1/2" mystery steel and some 1/2" rods on hand. I have no idea what kind of steel it was. I got an offal finish. I tried different speeds and feeds. I tried every one of my tool bits. Nothing seemed to help. Yet I was able to get it done. The part that fits inside the chuck bore I welded onto the 1/2" rod. I didn't want to not be able to see if it got loose. So I welded it. I tapered the part that fits inside the spindle bore to keep it centered in the bore. I did this to the piece that goes on the outboard end too. Nothing fancy. Just functional.

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