This is a classic case of flywheel shear-pin (key-way) breakage. What is a shear-pin? Briggs & Stratton engines have a shear-pin that is a small ½ inch by 1/8 inch aluminum pin that protects the crankshaft from damage. The pin is located in a slot between the flywheel and the crankshaft. This shear-pin might be bent or broken and will need to be replaced.
You need to remove the covering (shroud) and the fuel tank. Next off comes the pull-cord assembly. This reveals the flywheel, held on by a large 15/16th nut. To remove this nut you need to keep the flywheel from turning. To do this you will need to secure the flywheel. Strap a good leather belt round the flywheel, and, allowing the buckle to rest against small block of wood against the ignition coil assembly (it works for me). Using a long breaker-bar with either a ½ or ¾ inch square set to fit the 15/16th socket to the flywheel nut. Have someone help you to hold the mower. Turn the nut and remove the nut. Do not loose the nut!
Next, you have to remove the flywheel itself. Here is the trick. You need to hire, beg, borrow, or, dare I say it, steal a large bearing a puller. Fit the three-legged puller over the flywheel. The flywheel is not going to come off easily without some assistance. Two things you can do here.
1) Now, with pressure on the flywheel, sharply tap the top of the puller.
2) Using a small blowlamp, heat the flywheel to expand the metal, and this helps the puller to remove the flywheel from the crankshaft. Either way works well. Remove the flywheel and you either will see the shear-pin attached to the crankshaft’s groove or stuck to the flywheel.
I am going to assume you have purchased a new (I always have two handy) shear-pin from your local small engine repair store. The will cost in the region of $2.50 and look rather expensive for what they are.
To clear any rust from the flywheel, polish the flywheel inner hole. Using some very fine (preferably used) emery cloth, clean the crankshaft. Using a gas soaked rag, wipe away all traces of emery dust from both the crankshaft and the flywheel. Rub a little grease on the crankshaft and then refit the flywheel, remembering to line up the crankshaft slot with the flywheel slot. Place the new shear-pin into the slot and, using a small punch, or if you don’t have one, a long 4" nail comes in handy, tap the shear-pin down until it seats fully home.
Replace the nut and washer and tighten to 65 foot lbs. Refit all other removed items, and start he mower.
Happy mowing