If the mower has a transmission in a black composite casing, it is most likely a General Transmissions unit, the RS800. If you're having an issue with it shifting hard or sticking it could be a build up of debris, I'm attaching a link to their site and a video for reference. It shows a guy riding one and it's hard shifting between fwd/rev and a good cleaning takes care of it. They also have a good troubleshooting section and service manual PDFs Hope this helps.
https://www.youtube.com/watch?v=FKH-habvBFg
http://services.generaltransmissions.com/en/tutorial.html