Sunbeam Mixmaster model 9 speed control problem

OK, this may not be a solution, but might help you get there.
The speed control is NOT a potentiometer, it is a mechanical governer, and may be out of adjustment, or one of two components in the speed control mechanism has failed. The following is a test/ adjustment procedure.
During this procedure you will not be fiddling with electrical components (No risk of shock) You will be making adjustments with the motor running.
In the centre of the speed finder dial is a chrome cap. This can be *carefully* pried out. Be gentle, it's easy to chip the phenolic resin plastic.
Behind this cap is a nut around a threaded part with a screwdriver slot. Using a spanner and screwdriver to stop the centre part turning, loosen the nut some.
Turn the speed finder dial to 1. Plug the motor in and switch on. Whilst restraining the outer nut with a spanner, turn the central screw. From memory, it needs to be turned clockwise, that is, screwed inwards. The motor should respond by slowing down. Should you get no speed change, try turning the screw the other way some.
If you get a speed change, continue turning the screw in that direction until the motor stops. Now screw the other way until the motor just starts again.
This is the lowest speed and corresponds to 1 on the dial. Check the speed finder dial is still pointing to the 1 position. Lock the adjustment screw by restraining the central part, and turning the nut clockwise with the spanner until tight. Try turning the dial to see that the speed changes smoothly throughout the range. You may need to tweak the adjustment a little to get things just right.
Once you're happy with the speed control refit the chrome button, and you're done.

If you could get no speed change, one of two components under the speed finder dial has indeed failed.
Now you will need to determine just what the machine is worth to you. A motor specialist should be able to diagnose which part has failed. However, new parts will not physically fit and modifications will be needed. This could prove costly. If you know an inveterate tinkerer, you're costs could be substantially lowered.
Best of Luck.

Try www.davesrepair.com/pdfmanuals
You can download the manual for your specific model there, and most of them that I saw included at least basic maintenance like oiling and greasing locations. Good luck!

If I recall right, there is a switch and resistor(looks like piece of a cigar with one terminal on each end- for lack of a better description) located behind the black bakelite cover that will cause speed regulation and on/off problems. Over the years flour dust gets pulled through mixer and coats all insides. sometimes just a thorough cleaning is sufficient.