The 401 and 403 accept twin needles. Twin needles require two spools of thread feeding through the tension assembly and thus, into each needle. Hence, an additional disc is required for the added thread. I don't know if the 404 can take a twin needle. If not, Singer just used the same tension assembly as a cost effective measure. (Maybe?)
Start by locating the set screw inside the face plate on the machine. Loosen this. It is not necessary to remove it.
Identify the small set screw in the knob
Take note of the position of the tension spring as you remove it. The first coil should wind around the bottom prong of the stub
Pull the check spring and the discs off of the tension stud. I don't know why there was a washer in there as well. It certainly is not OEM.
Oh, not quite. When you test stitch your machine you may want to set the numbered dial so that your balanced stitch on test fabric (I use light weight cotton that has been starched a little) with white thread is at about 3 or 4. To do so, loosen the set screw on the knob and turn it to the desired setting. Tighten set screw.
June 10, 2014
In the photo below: 1 points to the end of the tension release pin. When the presser foot is raised, the lever pushes on the end of the TRP and releases the tension on the tension discs.