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Toro Titan
If you are looking for more information on what is the best brand of riding lawn mower, the best place to look is on www.ridingmower.com/best-riding-lawn-mowers
transmission or transaxle
The same as any riding mower. The following is a site which explains how the work: http://www.ehow.com/how-does_4689999_rideon-lawn-mower-work.html
Depends on the size of the lawn mostly. A push mower (or better yet a powered drive push mower) would have the best control in rough terrain, but if it is a large lawn a riding mower is better.
MTD
Can I do it myself, set the timing on my riding mower.
You probably have a bad bearing.
The best riding mower for hilly terrain is would be any kind of walk behind mower as you control it's movements, speed, and direction. However, if you have a large yard and want a riding mower newer LG mowers a good bet. An older option would be a Gravely Garden Tractor.
10W-30
price
Check the belt.