Very few doubled dies produced by the single-squeeze method show doubling of peripheral design elements. Most single-squeeze doubled dies exhibit doubling of elements near the center of the coin.  Two different scenarios
account for the dominance of the latter pattern.  Sometimes a working hub or a working die is not aligned properly.  When subjected to pressure, the hub or die will spasmodically settle into a more stable position.  That settling accounts for some centrally-located doubled dies.  In other cases, a squeeze is intentionally interrupted and the hub or die is re-positioned.  When hubbing resumes, a doubled die may result.

It’s not entirely clear why a few doubled dies produced by the single-squeeze method show peripheral hub doubling. While one or both scenarios mentioned above could play a role, it seems rather late in the hubbing process for this to be the case.

The images below show peripheral doubling affecting the motto “IN GOD WE TRUST” in a 2006(P) Lincoln cent.

Images are courtesy of Coppercoins.