I'm not sure if there is a specific name for this type of activity or not, but anyways:

When a user ssh's into machine1, is there someway to force them to automatically ssh to machine2?

For example, if user Bob ssh's into server1, can you set something up on server1 so that when Bob successfully logs in, he automatically ssh's to server2, so that he only has access to server2 and isn't really able to do anything on server1? Also, when he exits, it would disconnect him from server2 but also server1.

Does that make sense? Is that possible?