Power off the Craftsman machine and allow the engine a few minutes to cool.
Look along the top of the engine block for the flywheel. The flywheel is a distinctive circular piece that conceals the clutch shaft. It is covered itself by the flywheel shroud, which is an iron piece held down via bolts. Remove each bolt using a socket wrench and pull the shroud off the flywheel.
Inspect the fins on the outside of the exposed Craftsman flywheel. Check for burrs on any of these fins. Burrs can cause transmission failure due to the flywheel becoming inoperable, so file down any existing burrs using a hand file.
Reattach the flywheel shroud and test your Craftsman machine after removing any burrs. Remove the shroud once more if the machine's transmission still fails to operate properly.
Position a flywheel pulley over the exposed Craftsman flywheel so that the pulley's arms lower down against the outside of the flywheel. Use your socket wrench to tighten the pulley's center bolt. Continue tightening until the pressure causes the Craftsman flywheel to pop loose from the engine block. This will reveal the top of the clutch shaft.
Find the Craftsman's oil pan at the bottom of the engine block, beneath where the clutch shaft exists and the flywheel formerly was positioned. Remove the bolts holding the pan in place using your socket wrench, then pull off the pan. This will reveal the bottom of the clutch shaft. You will be able to see several bolts located along the shaft.
Remove the bolts along the clutch shaft using your socket wrench.
Use a rubber mallet to strike the center of the top of the clutch shaft. This will pop out the clutch shaft for replacement.
Slide a new clutch shaft for your Craftsman machine into the place vacated by the old shaft, then follow your shaft disassembly procedure in reverse to reassemble the engine block.