Hotpopint motor speed control?

My hotpoint washing machine is running through its cycle, but the drum does not rotate in any of them. So I have got the motor off with a view to replacing the brushes. However I find it has a plastic (or nylon) device which presses on the spindle of the motor and is controlled by a thing like a clutch cable (which of course I wrecked getting it off). What the devil is this thing and what is its function? Can anybody fill me in? Information very much appreciated.