What do you do if you want to check your motor brushes and the plastic cap (the black screw) broke off? Singer did us no great favors by making the screw for access to the brushes out of plastic. They can be replaced but at a price you might not like. There is only one place in the world that makes these screws and they can dictate the price accordingly.
To remove the motor brush cap (screw), I use a pocket knife. I like a pointy blade style of pocket knife that I feel naked when I don't have it in my pocket. Open the blade (it took me years to learn that trick) and point the tip of the blade at the center of what is left of the cap on the motor. You need to try to "drill a hole" in the cap using the tip of the knife blade. The knife is to be turned to the left, counter-clockwise while pressing fairly firm (but not hard) on the knife tip. After about twenty turns you are going to be asking what Dave is talking about. The tip of the knife blade is not the best drill, but it becomes the ideal tool shortly. You've made a dimple in the plastic stuck in the hole by this time and sometime shortly the knife blade will start dragging (scraping) in the hole as it is turned. Then the blade will start jamming (sticking) in the hole you are trying to make. Add a little more pressure, turning to the left, and what's left of the old cap in the hole will unscrew and it can be removed. It takes but a minute in reality.
Use care when installing the new cap as well. It breaks easily. I don't know why the new caps are not made out of a superior plastic. My cure is simple. I use my thumb nail as a screw driver and I never get them too tight. But then I use my car keys to scratch in my ears too. If I use a screw driver I do not hold it by the handle but turn it by holding only the metal shank of the screw driver and I sing a little song about it "ain't got to be tight" as it doesn't hold the machine together. And you can sing the next verse about "Dave don't need no more of my money". I don't work for the Government.
Your questions are welcome. My answers are long-winded. It's the price you pay when the answers are free.