John Deer self propelled mower drive problem

Friend's John Deere about 6 years old runs well but when the self propelled bar is pulled the back end of the mower chatters and vibrates. Both drive wheels pull hard and do not seem to be slipping.

I took the wheels off and both drive gears and wheel gears teeth look to be in perfect order.

The vibration stays when the wheels are removed and the mower is lifted on to its front wheels.

The drive cable that the engagement handle is snug and I even pulled it tighter to be sure the transmission was engaging fully.

My friend said it happened all at once on one single drive engagement.

The belt is on both front and rear pulleys.

Any ideas.

 

What does the belt look like? Cracked and worn? Pulleys are smooth and unbent?

 

That's what I was thinking, belt or pulley issue.