This video shows how three interlocking gears in 2-D cannot turn each other, but three interlocking gears in 3-D can. Some of the commentators wondered if interlocking gears could work in 4-D? I did a quick google search and could not find anything on the concept of gears in 4-D. It would be interesting to know if the question has been explored mathematically.
https://www.youtube.com/watch?v=5Mf0JpTI_gg Harry
