The bobbin winder on this machine is known to be problematic. It can still wind bobbins if the bobbin wider cam (triangular shaped piece) is cracked. Do not super glue it if its cracked. Instead cut a small piece of "thin" lightweight aluminum mesh from pet proof window screen and attach it between the 2 set screws on the bobbin winding cam. This will hold it snug, preventing slippage.
There are 2 positions on the bobbin latch. In order for the bobbin winder to wind bobbins, the latch must be in position 2. To get it working again, you will need to disassemble the bobbin winding cam and pop up mechanism completely, then clean and grease all the metal parts, making sure there is no old grease remaining and no grease on any of the plastic parts. This will allow the bobbin latch to move all the way into the 2nd position and the pop up pin will catch the bottom of the bobbin and hold it in place while the bobbin is winding.
The bobbin cam swings over to make the pop up pin go up high enough for bobbin winding to initiate. If your bobbin won't wind because the pin is not catching at the bottom, you can adjust the height of the bobbin cam so that the pop up mechanism doesn't slip out of place. The pop up mechanism has an L shaped piece at the base that that slips into a hold which keeps the base of the pop up mechanism in place so that the pin is high enough to catch the bobbin. If it is out of adjustment, then the pin won't stay up and slips back down causing the bobbin to not catch in the cross shaped grove in the botton of the bobbin and consequently not wind.
Make sure that when you adjust the height of the bobbin winding pin, you push up the L catch pin before you tighten the adjustment screw. If the L shaped catch pin is too high, the bobbin wont wind. If the L shaped catch pin is too low, the bobbin won't wind. If your repair doesn't work, don't worry... you have options. Option 1 - obtain a donor machine with a good bobbin cam. Option 2 - obtain an external bobbin winder.
The two adjustments should work providing you have a good Singer #181551 bobbin in the machine and if the bobbin cam is in good working order. Be sure to remove all old grease and use Singer #022717 lubricant.