Not having electricity in the shop might be an issue! Maybe a cord from the house?
First off, as I see the pictures, this would not have been the brush cutter that I would have picked in order to do a 4.5 acre overgrown lot that I just purchased and wanted to clean up! There are way too many hidden obstacles in newly purchased lots that are unfamiliar to the new owner, and finding some of them with a cutter bar like you are trying to use is probably the reason the gearbox is missing parts. The splined fitting welded to a cross bar that holds the blades has no provision for things like hidden rocks, old engine blocks, well casings, (do I need to continue or do you get the picture?) The flat side tends to hit the hidden object and stop the swinging blades and something in between the engine and the blades has to give. Slip clutches, shear pins are typically the weak link, but old gears can only take so much before they give way.
Since you are replacing the gearbox, I would seriously consider looking for a rusted out deck with a gearbox and stump-jumper still intact, hopefully with blades that will fit your deck. Blade length can be adjusted a little, but usually not enough to go from a six footer to a five footer, etc, so look for rusted out decks in the size range you currently have.
I actually purchased a trailer load of rusted out brush hogs from a guy 90 miles away and hauled them home. The remains of that load are still piled up out back, and if memory serves me, there was even a blue one (as opposed to all rusty colored ones) in that bunch! However, getting it dug out to just look at it, and realizing the cost of shipment to the midwest, doesn't make it feasible, even at the heavily discounted price I purchased all of them at!
Good luck with this project,
David from jax
