A drawing or rough sketch of what you're trying to make would be helpful ......
Does the circular piece need to be perfectly circular ? If the circular piece does not need to be perfectly circular - then I'd approach the problem by marking our the circular piece, and then cutting close to the line either by using a hacksaw or band saw, or by milling, a series of straight lines making rough segments of the desired curve. Then use a grinder, linisher, or file, to smooth out the segments to produce the desired circular piece.
If the circular piece does need to be a pretty accurate circle, then without a rotary table or a spin indexer, or similar device - you will have to resort to some far less desirable techniques, and basically those techniques are far less than desirable because they can be very dangerous.
This Youtube video by a highly respected Machinist shows one way of doing the job - ON A SMALL PART. This particular approach should be fairly safe provided you follow all of the instructions and safety precautions provided in Dale's video.
A search on Youtube will show many videos demonstrating ways of cutting a circle, or arc, on a mill without a spin indexer or rotary table. Unfortunately, many of the techniques shown in those videos are demonstrated by machinists with minimal experience, and are highly dangerous. One example of a very dangerous approach that I found this morning is shown in . In this video, the piece being machined is pivoted on some sort of pin located at the centre of the part, and the part if turned against the end mill using hand pressure on the part. I hate to think how much blood would be lost if the end mill bites into the part and starts spinning the part wildly. Don't try this approach !
I disagree with blanik (although I haven't watched that video) and I think it can be done with manual feeding, but you need to be set up correctly and take extreme care. A nice fitting pin has to be used for the centre of the arc/circle to pivot on and ideally it needs to have a cap or nut on top to stop the part being able to climb off it. You also need to have hard stops at the limits of the arc/circle so the part cannot free spin if it does get grabbed by the cutter. Finally, only take shallow cuts and only convential milling so that if the cutter does grab it takes the part away from your fingers and don't have a 'death grip' on the part so that if it does grab it will come out of your hand and you can't be dragged into the cutter. I've successfully machined radii on many conrods and similar parts with this method and it's reasonably safe if done correctly and carefully. On the other hand, without hard stops, etc, you are just asking for trouble if/when the cutter grabs on you. Take care!
Depends upon the diameter but a woodworking router will shift aluminium like crazy. I have made 12 inch and greater circles in inch thick aluminium plate using a trammel bar fixed to the router and a centre hole pivot.
Milling a part by holding it placed on a dowel with your hands is very dangerous unless one has lot of machining experience an know what to expect, in that case one had most likely acquired a rotary table negating the need.
Is an operation commonly done, like rounding the head of con rods.
Cogsy pointed out the problems of the mill helix lifting the part or grabbing and spinning.
Use a good set up, patience, shallow cuts, conventional milling and a small end mill.
If the part ca be flipped is possible to conventional mill toward both ends of the arc.
If a part has no "handle" make sure one is provided by attaching or a bar hinged on the dowel restraining the part in some way.
It's important to note that what Cogsy does I've done myself. On relatively small and long parts it works just fine. It's very important that the milling is conventional not climb.
I cannot speak for steel, but aluminum and brass can be machined this way, but care must be taken. Some hardwoods can be very tough/strong/dense (use whatever term you like) and these are cut with routers all the time. (I've cut 1/2" aluminum plate with a circular saw with carbide tipped blades before).