The term "hand-turned wheel" can have a few synonyms depending on the context. One possible synonym is "manual wheel," which refers to a wheel that is operated by hand rather than by a machine or motor. Another synonym could be "hand-powered wheel," which similarly conveys the idea that the wheel is turned by human effort. "Crank-operated wheel" is another possible synonym, which emphasizes the use of a mechanical crank to turn the wheel. Finally, "hand-cranked wheel" is a more specific synonym that suggests the use of a handle or crank to turn the wheel.