Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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The mower deck shaking is most likely caused by a bad spot on the belt that runs the blades. Every time this spot comes around through the pulleys it will cause a shake or vibration. Take a really close look at the mower deck belt too make certain that it is the same thickness all the way around the belt, any narrow spots or chunks missing from the inside of the belt will cause this.
Does the shifting problem seem to happen more often when on an incline? Or flat ground? If and incline, this is common with these machines since you have to get the gears to release inside the transmission it is difficult for this to happen when there is pressure on them from being on an incline.
My experiences in the past when you have a shaking or vibrating mower deck and it is not an unbalanced blade issue, it is normally the mower belt. Inspect is very closely looking especially at the width of the belt I bet you will find a spot that is narrow in it possibly the inside of the belt.
Have you had the blades balanced?