If you just want to design a linkage and se that it behaves properly, I guess any CAD software should do the trick. In both PTC Creo and Catia you can design motion skeletons and analyse these for packaging and envelope interference, for example. I assume that NX has the same functionality, as well as SolidWorks (though I have little to no experience in either).
If you want to simulate dynamic behavior, on the other hand, I think a multi-body simulation tool like Adams would work much better than any functionalities included in CAD software. There are some free tools, but I don’t really know how powerful they are. I think the http://www.fsae.com forum would be a place to look, I know some people are discussing analysis tools there. Sure, they are talking about race cars but if the software can mimic a car suspension it should have no issue with a motorcycle set up.
Edit: I’m a mechanical engineer, it’s early in the morning here, I’m typing on the phone and English is my second language. Excuse the lack of acknowledgeable syntax.