I would like help figuring out what machine I have
 

Hello -

Can anyone tell me what type/age this unit is? Was given to us by my grandmother many years ago. Thanks in advance.

I believe it is a Singer 404. You need to check your hinge pins. It look like only the front one is holding. That's a lot of a machine to have falling in your lap. With a helper, tilt the machine back and look at eh front hinge and see the set screw that holds the hinge arm. you may need to loosen it to get the back one in place. Hope it is there. Lots of love for those early slantnose machines.

mid to late 50s? Welcome aboard.

I don't know how reliable this person's information is, but it is written with authority so I believe it:

https://www.singersewinginfo.co.uk/404a/

Joe, it's usually very reliable, but this is not correct about dropping the feed dogs. They don't drop on any of the 400's, 500's 600's or 700's that I am aware of. The rest may be true.
bkay

Looks like a 404 (doesn't it say at the top the stitch indicator plate?).

I have a 401a and the lever on the right front has 3 settings: Down, Up and Unlock. Allegedly, you can use the UP position for darning, and theoretically, for free motion work. In the manual it says, "for darning, embroidery, and sewing on buttons." (Page 16)

So, you don't drop the feed dogs, but raise the feed dog cover. The result is the same, theoretically. You can also do free motion by loosening the presser foot pressure and setting the stitch length at 0. Haven't tried that yet, because my presser foot screw was missing until I got one recently, and other things have been more important.

Do you mean the hinges in the front flap are holding? But the back hinge pins are not? It looks to me like the back left is ok, but the back right is not. But either way, what Leon says is true: the first order of business must be to get those seated and tightened for safety. These machines weigh 40 or 50 pounds, and will absolutely do damage to whatever they fall on. The medical costs of crushed foot repair will definitely overcome the free cost of the machine!!

I think there is a miscommunication here. The hinge pins are on the back edge of the opening for the machine in the cabinet. The sewing machine is held in place on those pins by little tiny set screws in the sewing machine. If those set screws are missing, the machine will not stay on the pins.

I once bought a 301 in a nice cabinet for $50.00 because it was missing a set screw. I didn't realize the problem until I got the machine home. They had taken wire and tried to wire the machine to the hinge pin.

bkay

Yes that back pin is missing. To be clear, we were not planning on using it. One of the other commenters mentioned that they might be a place on the plate that would say what model it is definitively.... I'll look again but did not see anything including a serial number but I could just be a little clueless. Or a lot.