American Machine and Foundry was a company that made a wide variety of things. They were initially known for cigarette vending machines, but they went on to make a wide variety of sporting and non-sporting equipment. They were well-known in the field of bowling alley equipment. They also were amenable to importing equipment, such as bicycles, and co-branding them. In this case, AMF co-branded imported bikes from England made by Raleigh Industries, which were under the "AMF Hercules" co-branding. So the bike was made by a solid, reputable factory in England and the AMF side of the house importation, branding, and sales. The most common AMF Hercules bikes are the basic 3-speed "sports light roadster" style of bike with a Sturmey Archer hub, hand brakes, and 26 x 1-3/8 wheels. The bike could come plain, or could be bought with matching equipment - a bag that would attach to the saddle, and a light set (usually made by Miller and running a bottle on the tire). Better bikes might be upgraded with Sturmey Archer Dynohubs, but this was a less common upgrade.
These bikes are quite common, though it is uncommon to find them in mint shape with all the extras (the bag, complete light set, etc.) still attached. They make excellent, reliable bicycles, even if they are a bit heavy by today's standards. Other AMF Hercules bicycles included a line of juvenile bikes and "muscle bikes". But as I mention, the most common is the basic 3-speed utility bike.