I was thinking about the operating problems here. A couple things to consider:
1. I typically plant the loader bucket (or grapple) firmly on the ground. Sometimes I also set the emergency brake to keep the tractor in place or stand on the brakes to hold the tractor in place as I cut....but I try to keep the tractor motionless as I operate.
2. As stated above: Position the 3 point linkage to eliminate the float in the draft links. Also try to make the swing level for a even cut. (being on unlevel ground sucks.)
3. The position of the cutting wheel to the stump could cause jumping. I generally cut down from the stump at the side of the stump closest to the tractor....taking as much as 1/3 of the stump in one position.....and then work back to the far side of the stump after grinding about 6" of stump. Then repositon to the front of the stump again.....and repeat to below grade. Most often this would require slightly repositioning about 4 to 6 times (hydrostatic tranny really helps out here). Do NOT reposition the tractor while you make the swing of the grinder.
a. My soil is quite sandy. even with the frame of the grinder planted on the ground I will oftentimes reposition my tractor and simply allow the frame to "plow" into the ground as I move. I think some would cringe at this....but that is what I do when repositioning a foot or so. I certainly do not "baby" my grinder.
4. If I encounter any "bucking" usually the feed is too agressive and I need to change the way I am operating.
5. In all "woodworking" or metal working.....the speed and feed is critical to operating efficiently. Having a solid position of the cutting tool is fundemental too....therefore adding weight to the frame to keep the grinder solid with the ground makes sense to me.
Occasionly when I get in a "tyro" grinding mode.....I encounter the bucking and jumping you have stated. That's when I find I need to slow down my operating mode. Just as in sawing.....crowding the cut is hard on the equipment and counter-productive.....and it sure is hard on my nerves.
