Ethel,
The 27 has the bobbin winder mounted low, the 127 has it mounted high.
There might be other small differences too, but that's how I tell the difference between them.
This is a 127 ( my machine ):
[ATTACH=CONFIG]435082[/ATTACH]
Notice the position of the bobbin winder.
The 28 / 128 is the same, but smaller. It's a 3/4 size machine.
Joe