Can I mount this machine in a sewing cabinet - White Sewing 2037 Mechanical Sewing Machine

Unless the cabinet was made to your machine's specifications, you will most likely need to modify the cabinet to make the machine fit. Sometimes it's easier to find a cabinet that will fit your machine.

Check places like JoAnn's Fabric where you can find a table with a dropped platform where you can set your machine so the sewing surface is level with the table top. I have one of these and it works with several machines.

No make/model provided.

Most machines can be mounted in a cabinet. However, the attachment method and the cut-out would need to fit the machine.

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If it could be attached to a table so the machine will flip down and be hidden, it would need some sort of metal loops (hinge pin attachment) on the bottom at the back of the machine. You also would have to have the hardware (bolts, nuts, etc) to attach it.
How to Install Sewing Machine into Cabinet

or, frequently, you will have a sewing table with a separate insert that can be lowered or raised and your sewing machine just sets on that adjustable insert. Then you just raise or lower the dropped insert until the sewing machine surface is level with the table's top surface.
example: White Sewing Table with Wheels Jo Ann

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Unless your Necchi has fold out prongs undernerath it will have to remain on top of the cabinet, unless you have a very handy husband!

Some models you cannot especially if the body is a two piece machine

If the machine is a two piece body machine you may not be able to

If it can be attached, there will be a set of screws/hinges on the back side of it.

I actually modified a sewing machine cabinet to be able to place my machine inside for storage, on its side. When sewing, I have
the modified board on the hinge and the machine sets on top of that. When not is use, cabinet looks like a "table" cabinet.

More info, contact [email protected].

There are these things called sewing machine hinges. They have a round fitting that slip in to the cabinet and a shaft that fits into the machine itself. I've seen other styles as well. Examine your singer cabinet for 2 circular holes near the back of the spot where the sewing machine hits. You'll need to measure those holes. then find the correstponding holes on the sewing machine casting. You'll likely need some set screws as well.

Here is an etsy listing for a sewing machine hinge that someone has made a steampunk necklace from. LOL Really. At least it's a good photo of what a hinge looks like.
http://www.etsy.com/listing/88963367/necklace-steampunk-key-1937-singer-201?ref=sr_gallery_1&ga_search_query=sewing+machine+mounting+hinges&ga_view_type=gallery&ga_ship_to=US&ga_search_type=all

I don't think you would be able to - some sewing machine models came with a "Duplex" base which is different from the standard flat base with feet.

The duplex base is like a shallow dish with fixing points around it and allows the base portion to be bolted into a cabinet.

From the description of your cabinet I think you'd need some means to attach the bottom of the machine to the plate that swings to the horizontal plane.

I think someone would need to make a mounting up to suit your machine and somehow bolt this to the base/chassis of your machine.

The sewing machine is attached to the cabinate with special hinge that are mounted to the cabinate which in turn are clamped into the machine thru 2 holes on the base in back. The clamping bolts are either standard bolt threads or metric bolts that clamp onto the pin part of the hinge. You should be able to get them at a local sewing machine repair shop. If you don't have one localy I can provide them for you.