Since it is a Woods 18186 belt, and the layout sounds the same; I will guess that you have a Woods L59 K17 mower deck. It discharges out the center, towards the rear, right? The manual is available from the Woods website as a .pdf download. The belt does not go on the way logic says it should. One side has a 3/4 twist and the other side has a 1/4 twist when you get it right.
I have an abysmally slow connection, or I would send the manual to you via email.
To put the belt on, I start with the belt under the rear end of the tractor. Put it around the right side of the lower groove on the center sheave, then take it around the left sheave, bring the belt to the center groove of the center sheave, then to the right side sheave, and back around the top groove of the center sheave. now you bring it back to the rear of the tractor, you should have the 3/4 twist on the left side and the 1/4 twist on the right. Then bring it up the back and around the PTO drive pulley.
I have to take the cover off the left mandrel when I put on a new belt, the belt will fit between the cover and sheave on the right side. Adjusting the idlers below the PTO has been a trial and error thing with me. The right one should be lower than the left.
When I got my L175; it came with a new belt, and no manuals. I tried to put the belt on for a couple of days before I found the manual online. The new Woods belt didn't last a mowing season before it was getting stretched out and jumping off every time I used it. I priced a new belt at the local dealer, and almost had a heart attack: $78.00 and change, plus shipping. I found a belt online for $42.00 shipped. It has been working all this year, and hasn't needed adjusting yet.
Oh yeah, the PTO needs to be in the 1000 RPM range, and the tractor at governed speed to run the best. I usually mow in 4th or 5th gear, depending on the grass.
Hope this helps,
Robert