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There can actually be 2 things in between the battery and alternator.
There will be a fuse, which is the first thing you need to check, and there may be a voltage regulator, depending on which stator your engine uses.
What is the brand an model number of the engine?
What is the actual model number of your mower?
Model of mower is Troy-Bilt 128473 13AP60TP766
KOHLER ENGING COURAGE SERIES SV720
I found the fuse finally and it was good when check with ohm meter
Your voltage regulator is mounted to the underside of the engine backing plate, on the oil filter side.
It is a small aluminum box, with a 3 wire harness plugged into it.
Disconnect this harness.
The 2 outside wires of the plug are the AC output from the stator, and the center wire is the DC output from the regulator.
Set your meter to ACV, and connect one lead to each of the outside wires.
Start the engine, and rev it up to at least 3/4 throttle.
It should read at least 28VAC.
If not, there is a good chance the stator is bad.
Shut the motor off.
If you get good voltage, plug the regulator back in.
Set your meter to VDC.
Connect the black lead to a good ground.
Connect the red lead to the center wire of the regulator.
You should read battery voltage of about 12.6VDC.
Now start the engine and rev it up again.
You should get output of about 13.8-14.7VDC.
If you have good AC input, but no DC output, the regulator is bad.