1982 Quarter Liberty Looks Like Right On The Egde Where Rim Also Maybe Die

That is damage at UNITED. The design being so close to the rim is from spreading of the master hub. From usage year after year the hub eventually spreads out in diameter, and when the die is turned down on the lathe to the proper diameter for coining the outer design features get closer and closer to the rim. Eventually a new master hub is created moving the details back in away from the rim. A very well known example of this is when they redid the master hub on the cents in 1969. They did the same thing to the nickels in mid 1982. The early 1982 nickels used the hub of 1981 with the lettering right up against the rim, then in mid 82 they changed to new master hubs with the lettering moved back away from the rim. It is possible to find nickels with all four hub combinations (81/81, 81/82, 82/81, and 82/82) from all three mints.

Correct,each time the master hub is pressed into a die blank to create a master die it spreads out a tiny amount (master dies and working hubs do as well. Over the years the diameter of the face of the hub get larger and larger as do the dies, hubs and working dies made from it. But after the hubbing the diameter of the dies and hubs are reduced to the proper diameter to make the coin.

Say you have a cent hub 19 mm in diameter and the lettering is .2 mm from the rim. Then you use it for awhile and it spreads to 19.2 mm. It mades a die with a face 19.1 mm in diameter as well. But that is then turned in a lathe down to 19 mm. The lettering is now only .1 mm from the rim. The more the hub is used the closer and closer the lettering gets untilit reaches the point that hean the turn the die down the the proper diameter they start cutting into the lettering. Take a look at the 1968 cents and you will see the L in LIBERTY merging into the rim.and sometimes the top of IGWT as well.