The traction belt is the one that delivers engine power to the transmission. Start by removing the deck and raising the tractor up so you can work underneath safely. Deck removal is covered in the operators manual, which you can view for free on John Deere's website in case you don't have one of your own. (The operators manual doesn't cover replacing the traction belt.)
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Step 1: It Isn't As Bad As It Looks.
The belt rides up above the steering mechanism and the crossbars for the brake and deck lift. At first glance it looks like you're going to need to remove all these things, but you don't have to. The only thing you'll need to do to get the belt clear of these components is disconnect the steering tie rods.
Step 2: Remove the Tension Spring.
The tension spring is hooked around a bushing on the idler and a notch on the tension arm. Remove the spring to release tension on the belt. You'll want the brake in the released position for this step. Once the spring is off and the tension is released, you'll be able to pull the belt off the transmission sheave and pull some slack up toward the front of the mower, which you'll need in the next step.
Step 3: Disconnect the Tie Rods and Remove the Belt From the Motor.
I disconnected mine at the front because the cotter pins are easier to get to up there. It would probably be a lot easier to see what you're doing if you disconnect them from the bellcrank on the steering sector. Either way, pull the loop off the motor pulley and drop it below the steering sector.
Step 4: Remove the Idler.
The belt is trapped between this little idler and the frame on the left side of the mower so you'll need to remove it. Use a 13mm socket to loosen the nut and try not to lose the bushing that the spring hooks to. You can get to the head of the bolt to pull it up and out by reaching through the opening where the steering sector gear is located.
Step 5: Remove the Belt From the Tensioner Assembly.
Use your 13mm socket to remove the tensioner idler sheave then remove the guide from the tensioner pulley to free the belt from the tensioner assembly. After you do this, the belt can be removed by threading it out from on top of the brake and lift shafts. There's a pawl lever sticking up on the deck lift shaft that you'll need to work the belt over top of to get the belt all on the same side. You can see a good view of the pawl in the picture of the idler in step 2. Pull the rear loop forward over the two shafts until the entire belt is clear of the mower.
Step 6: Put the New Belt on the Same Way the Old One Came Off.
Thread the new belt over top of the two shafts and work the left side of it over the pawl on the lift shaft. Put the idler back on next to the left side of the frame.
Step 7: Put the Tensioner Back Together.
Thread the belt around the tension pulley and put the guide back on, then thread it around the tension idler and finish reassembling the tensioner assembly. The tension pulley is bolted through a slot in the tension arm, and I think this is so you can fine tune the belt tension by moving the pulley back and forth along the slot. I left mine where it originally was and it worked fine.
Step 8: Put the Tension Spring Back on and Finish Up.
Thread the belt over the engine pulley at the front and the transmission pulley at the back, then put the tension spring back on to tension the belt. Make sure the new belt is routed properly, reattach the steering tie rods, and you're ready to put the deck back on and put the mower back into service.