First of all, that is not a starter cup. Apparently you don't read the posts. It is a pulley to drive the front wheel of the mower. I have looked at that briggs and stratton diagram, and yes, it does show two motors. Don't you think it's within the realm of possibility that Swisher decided to alter the motor for their particular lawnmower?Lavatan, I’ve worked on more small engine equipment in one month than you have in your entire life. Who ever installed a starter clutch inside a starter cup should never be allowed to use tools. If you feel that everything was installed properly, then ignore my post. If you look at and understand the picture Hammer posted, you will see two different starting systems were used on that engine. Some idiot combined the two setups. I doubt you will find that that setup has never been seen or used by any of the experienced techs on this site. If it were, someone could provide you with the tool to remove it. Haven’t see that yet, but there is a 1% chance I’m wrong. Believe what you want, it’s your unit.
For further clarification, the belt runs around two pulleys under the hood. There is a tensioner connected to the pedal which, in turn, tensions the belt which then turns a gearbox that turns a chain that goes down the front wheel. It has a 360* turning radius so no reverse. You turn the wheel 180* to go backwards.