The following images illustrate rotated Hub doubling with a centered pivot point with 1 Degree to 5 Degree rotation.
It would be a very interesting excercise to repeat this experiment for each of the different types of hub doubling. You show rotated hub doubling (around the center) here. Could you show us other types, and maybe explain the differences?
Just a little test - that has no wrong answer. Which obverse in the following image is square? The one that best depicts the coin's design at the 12 o'clock position?
Don't know if I can illustrate all use 2-D drawings. Following are images illustrating offset hub doubling with the offset equal to 1% of the radius of the black circle.
The problem showing pivoted hub doubling is that the pivot point can be anywhere on the coin, or even off of it. The images show the pivot point on the rim at 3:00, but if it was say at 6:00 the areas of doubling would be quite different. The 1995 DDO cent is an example of pivoted hub doubling with the pivot point located close to the date. On pivoted hub doubling the doubling will be greatest 180 degrees across from the pivot point. If the pivot point is not on the rim there will be doubling on both sides of the pivot, the greatest at 180 degrees and a much lesser behind it. The closer the pivot point get to the center of the coin the greater the doubling will be behind it. Rotated hub doubling is actually just a special case of pivoted hub doubling where the pivot point is at the center of the die.
Anybody who has installed crown molding understands the concept of compound miter joints. Well what about compound hub doubling? In the following illustrations of compound hub doubling the gray image was rotated at the coin's center first and pivoted at the rim 2nd.
Two other forms of hub doubling attributed to heat warping of the die due to annealing of the die between squeezing. There is some debate on Class VI (distended) doubling as many attribute this form to working hub deterioration.
OK, i’m Giving up on trying to figure out which doubling I can see on a cent. If the cent is circulated (which almost all of mine are) I don’t think I could see it with great magnification. I am 71 years old now and would probably be deceased before I could develope the expertise to figure all this stuff out! Maybe I should start collecting dollar sized coins, at least I would have a fighting chance.
It takes a lot of time, practice, patience, and experience to figure out what kind of doubling there is. JAF has only gotten through class VI... there are ten! These images are really good. Keep them coming!
Actually Class V (Pivot) doubling is a specific form of compound doubling of Class I (Rotated) and Class IV (Offset) Hub Doubling. I have added a third obverse in Blue to illustrate this in the following images.
One thing that should be clear from these images, the doubling on just about any doubled die in the US coinage is the result of rotations or offsets of less than 2 degrees, in most cases less than 1 degree.
Thank you for all that information. Just curious to know if there are any 3, 4, or 5 degree Rotated Hub Doubling coins out there? The 1955 doubled die Lincoln cent looks closer to 2 degrees and that's the best I've ever seen. If someone has a 3, 4, or 5, I'd love to see a photo of it.
I'm not sure how to illustrate Class VIII (Tilted Hub) using these type of drawings. Class VII (Modified Hub Doubling) is basically a the same type of Doubling as Class II (Design Hub Doubling). Wexler says there are no known varieties consisting of this type of doubling (so why bother). I guess one could make an argument concerning the "Broken 4" doubled die cents. So that makes 8 forms. I haven't delved into coinage and doubled dies produced using the single squeeze method.