I had the same problem. Look under the washer you'll probably find a small pile of shredded black rubber. If so, its the direct drive coupling. New part is about $12 + shipping. Remove the shell, disconnect the water pump and motor. Install new coupling (3 pieces). New improved parts did not fit smoothly. I had to gently tap them with a hammer to fully seat them on the motor and gearshafts.

Our Whirlpool washer motor cycles but the basket stopped moving. I did find two piles of ground rubber under the washer. Your post helped. Thanks for the advice.

My Whirlpool washer stopped spinning and was making a squealing sound. I ordered and installed the new direct drive coupling ($20 including shipping) and the problem is solved. I was able to replace the part in less than an hour.) I replaced the part from the bottom of the washer without removing the shell. I removed the white plastic water pump first by releasing the two clasps and pushing it to the side. There was no need to remove any hoses from the water pump. Next I removed the motor by removing two electrical connections--one multi-pronged and one single prong black wire (very easy). I then removed two small screws from clasps holding the motor. Once the clasps were removed, the motor came right off. Under the motor was a flat plate with two bolts. I'm not sure that I even needed to remove the plate. It may have made it a little easier to get to the direct drive coupling. The direct drive coupling (a black component sandwiched by two white components) was exposed. I quickly noticed that the white piece closest to the gear box was cracked. I installed the new part (better quality now with a metal insert in the white plastic) and reversed the procedures to reassemble. I appreciate applicance parts pros having this forum and for those individuals sending me responses.