I have about a 5 year old KitchenAid (Whirlpool) top loading, direct drive
(no belt), washing machine that rapidly progressed from vibrating on all
cycles to no tub or agitator motion at all. I got a book from the library
titled "Washing Machine Repair Under $40" which is quite good -- I had used
this series of books before for dryer belt replacement. I've found that the
motor is fine but the three plastic teeth of the coupling between the motor
and transmission are sheared off. The book says this would typically be
caused by transmission lockup but the transmission turns freely in both
directions by hand which the book suggests is indicative of the transmission
being OK. So there's a gap in the guidance given by the book. Is there a
way for me to evaluate transmission function? Would an appliance repair
shop do this for me? Is it possible that I need do nothing more than
replace the coupling because shear force from repeated stops and starts
simply caused it to break?

Roger