<!-- from fixya rte -->What are governor parts for model 9s502 - Briggs & Stratton Garden

See if the videos help.

https://www.google.com/search?q=Briggs+and+Stratton+engine+model+252416+0757+01.install+the+spring+260695+for+the+governor+lever

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David, This is what I found in google search for B&S carb. linkage diagram, you can also do a search because there are lots more.
Check the attached links,instruction and guides, Good luck
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https://shop.briggsandstratton.com/us/en/repair-parts

governors on this engine are mechanical they are activated by a linkage that extends out side of crank case to a spring , if your rpm is not maintaining correctly id look at spring , if its malformed or broken heres part number of new one (691019) this is avail from sears parts

First thing I need to know is Year,make and,model...Without me knowing it is impossible to answer...I would go get the part and then look for the governor...I need to know more info

Are you saying that it surges at full throttle and wont idle down or shut off? If so it is likely not a governor problem. Surging is a lean condition. Some models, particularly yard machines, will surge no matter the adjustment unless under a load. If it were a governor issue it would run faster and faster beyond full throttle. IF it wont idle down check the throttle control and throttle linkage and check for a sticking throttle shaft before suspecting governor. Not shutting off could also be in the throttle control. A ground clip is in the control. if the tab is not engaging the clip or the wire is not connected then the motor will not ground. Check those things before messing with the governor, especially if the machine was running good and no one has messed with it yet. Governors don't just come out of adjustment by themselves.

that doesn't make sense , surely it has a governor how else can the carby rpm be governed , sounds to me like the internal governor thrust counter weight has come out of it's locking plates. if governor arm has been adjust wrong way or moved from it's original position this will happen .

see http://forum.doityourself.com/outdoor-power-equipment-small-engines/384248-spring-locations

At the front of the mower there should be a metal plate, usually black which has a hole in it, you should be able to see a screw in the hole which will increase the revs of the motor
hope this helps

The trans in your vehicle is a 3 speed auto,A904 model,also designated the 30RH or32RH.The trans is totally hydraulic,no electronic controls with the exception of tcc apply,aka,lockup.The vehicle shifts from throttle pressure and a governor.The governor is inside the tailhousing of the trans and is responsible for the road speed signal in this trans.If the valves in the governor start sticking,the vehicle will take off in 2nd gear.The valves can be cleaned,and sometimes jarred loose,but the more pressing concern is why are the valves sticking?The valves will start sticking when other parts of the trans starts making metal.So the governor sticking can sometimes be the symptom of a larger problem.Pull the trans pan and look for metal,and if so, how bad?One way to clear the governor of debris is to find an abandoned road or parking lot.At a complete stop,engage Reverse gear,and back up as fast as you dare.I have backed cars up at 20-30 mph before,but wouldn't recommend you to.This can blow debris out of the governor hydraulic circuits,and free the governor valves as highest line pressure inside the trans is obtained in Reverse gear.Good luck.