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Correct Socket Size for '71 383 road runner Harmonic Balancer "Goldilocks" Bolt?!?

I have 10 crank bolts here from both big and small blocks, they are all 1 1/4".
It is funny, this seems like a simple question but I've found that out of several 1 1/4" sockets I've tried, NONE fit the balancer bolt just right. They are all loose. Obviously you don't want to have to hammer it on but it should not slip on and be able to wobble or rotate a couple of degrees. I've used a 1 3/16 and it fit fine.
Having stated that....
I have taken open end wrenches and opened them up a bit for some specific use, taking a cutoff wheel or grinder disc to the ears of the wrench to get a 1 inch to a 1 1/16" or some other number that is not a common size.
We have all modified wrenches like these, right?

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This whole thread is really perplexing to me as I have just always used a 6 point 1 1/4" socket on these bolts. After reading Greg's post this morning, I had to go measure the bolts I have here. I have 11 of them. With a caliper, they measure between 1.22" - 1.48" across the flats. I have 2 with "LE" on the head like the op has. They both measure 1.23". There isn't a single one that I have that my 1 3/16" socket fits on.

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When I get to work today I’ll dig out my machinery handbook and see what the tolerance is on a screw like that.
 
I recently worked on a friend’s 440, and my 1 1/4 socket didn’t fit. It was 1 1/8.
 
I actually just took a 1/2" drive rachet to a couple motors last week to see if they would turn over. A 64 318 Poly and a 74 400. Both took an 1 1/4"
 
I used to be able to just grab the fan belt and turn it over.
Sadly those days are gone... :(

Now I spend my days wandering aimlessly looking for 10mm sockets.
 
Every OEM Mopar balancer bolt I have taken off I used 1 1/4 six-point socket. And that is a bunch of them. If you go to the hardware store and buy a replacement bolt it will have a 1 1/8 head, at least in my experience.

I had a similar experience with a pinion nut the other day, bought a Yucon gear set with installation kit, and the new pinion nut was a weird size. Called Yukon and it was not what it was supposed to be, so I reused the original nut.
 
My Hemi has a 1 1/8" crank bolt. Never really gave it much thought, now I'm wondering. Been in there awhile, way before I have owned it.
 
The harmonic balancer, or vibration damper, to crankshaft mounting bolt, or screw, for a 1971 383 engine is Chrysler part number 1731525, the same as most other big block wedge engines. The proper fitting socket or wrench size for a Chrysler original, undamaged, or heavily worn bolt head is 1.25".



1731525 was used in the 1958 - 1978 big block wedge engines, except some industrial and heavy truck applications, for the harmonic balancer, or vibration damper, to crankshaft mounting bolt, or screw.

1731525 is a 3/4"-16 x 1.25" bolt and is considered a heavy hex head size, per ANSI/ASME B18.2.1, with a 1.25" nominal measurement across the head flats. Variance of 1.215" - 1.245" might be seen in use.

The 3/4" washer used with this bolt and application is Chrysler number 1855561 and is 1.94" wide with a thickness of 0.26".



Some industrial and heavy truck big block wedge engines and the 1966 - 1971 426 Hemi engines use the LA engine harmonic balancer, or vibration damper, to crankshaft mounting bolt, or screw, Chrysler part number 1821414.

The 3/4" washer used with this bolt and application is Chrysler number 2463649 and is 1.94" wide with a thickness of 0.37".



The 1964 - 1991 LA engine, except some early 273 engines, harmonic balancer, or vibration damper, to crankshaft mounting bolt, or screw, is Chrysler part number 1821414.

1821414 is a 3/4"-16 x 2.25" bolt and is also considered a heavy hex head size, per ANSI/ASME B18.2.1, with a 1.25" nominal measurement across the head flats. Variance of 1.215" - 1.245" might be seen in use.

Some early 273 engines used the A engine harmonic balancer, or vibration damper, to crankshaft mounting bolt, or screw, Chrysler part number 182177. 182177 is a 3/4"-16 x 1.62" bolt.

The 3/4" washer used with this bolt and application is Chrysler number 1855561 and is 1.94" wide with a thickness of 0.26".
 
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