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I have a 356447-0415-G1 horizontal V twin Briggs&Stratton engine on a Walker S18 mower.
Sometimes the main pulley driving the mower from the engine does not spin. If I stop the mower and manually spin the main drive a little back/forth, and then restart the engine, it will spin. It appears like there is some sort of clutch inside this engine that is disengaged sometimes? Anybody have experience with this engine on what could cause this to happen?

Most you got a sheared key in the stub shaft. As for the engine it is direct drive to the stub shaft.